├── .gitignore ├── .travis.yml ├── LICENSE ├── README.Rmd ├── README.md ├── build.R ├── experiments ├── Tcomp-checks.R ├── experiments.R ├── explore-trends.R ├── maxlags-experiment.R ├── seasonal-adjustment-experiments.R ├── validation.R └── xreg-experiments.R ├── figure ├── unnamed-chunk-10-1.png ├── unnamed-chunk-16-1.png ├── unnamed-chunk-17-1.png ├── unnamed-chunk-2-1.png ├── unnamed-chunk-3-1.png ├── unnamed-chunk-3-2.png ├── unnamed-chunk-4-1.png ├── unnamed-chunk-5-1.png ├── unnamed-chunk-6-1.png ├── unnamed-chunk-7-1.png ├── unnamed-chunk-8-1.png ├── unnamed-chunk-8-2.png ├── unnamed-chunk-8-3.png ├── unnamed-chunk-9-1.png └── unnamed-chunk-9-2.png ├── forecastxg-r-package.Rproj ├── pkg ├── .Rbuildignore ├── DESCRIPTION ├── NAMESPACE ├── R │ ├── extras.R │ ├── forecast.xgbar.R │ ├── forecastxgb.R │ ├── misc-doc.R │ ├── utils.R │ ├── validate_xgbar.R │ └── xgbar.R ├── data │ ├── Mcomp_results.rda │ ├── Tcomp_results.rda │ └── seaice_ts.rda ├── inst │ └── doc │ │ ├── xgbar.R │ │ ├── xgbar.Rmd │ │ └── xgbar.html ├── man │ ├── Mcomp_results.Rd │ ├── Tcomp_results.Rd │ ├── forecast.xgbar.Rd │ ├── forecastxgb-package.Rd │ ├── plot.xgbar.Rd │ ├── seaice_ts.Rd │ ├── summary.xgbar.Rd │ ├── xgbar.Rd │ └── xgbar_importance.Rd ├── pkg.Rproj ├── tests │ ├── testthat.R │ └── testthat │ │ ├── test-correct-classes.R │ │ ├── test-irregular-seasons.R │ │ ├── test-modulus-transform.R │ │ ├── test-ok-noninteger-frequency.R │ │ ├── test-seasonal-methods.R │ │ ├── test-shorter-monthly-data.R │ │ ├── test-utils.R │ │ ├── test-works-range-data.R │ │ └── tests-different-maxlags.R └── vignettes │ └── xgbar.Rmd └── prep └── get-seaice-data.R /.gitignore: -------------------------------------------------------------------------------- 1 | # History files 2 | .Rhistory 3 | .Rapp.history 4 | 5 | # Session Data files 6 | .RData 7 | 8 | # Example code in package build process 9 | *-Ex.R 10 | 11 | # Output files from R CMD build 12 | /*.tar.gz 13 | 14 | # Output files from R CMD check 15 | /*.Rcheck/ 16 | 17 | # RStudio files 18 | .Rproj.user/ 19 | 20 | # produced vignettes 21 | vignettes/*.html 22 | vignettes/*.pdf 23 | 24 | # OAuth2 token, see https://github.com/hadley/httr/releases/tag/v0.3 25 | .httr-oauth 26 | 27 | # knitr and R markdown default cache directories 28 | /*_cache/ 29 | /cache/ 30 | 31 | # Temporary files created by R markdown 32 | *.utf8.md 33 | *.knit.md 34 | .Rproj.user 35 | 36 | # temporary files made by xgboost 37 | xgboost.model 38 | -------------------------------------------------------------------------------- /.travis.yml: -------------------------------------------------------------------------------- 1 | # thanks to https://github.com/travis-ci/travis-ci/issues/5775 2 | sudo: false 3 | 4 | language: r 5 | r: 6 | - oldrel 7 | - release 8 | - devel 9 | 10 | cache: packages 11 | 12 | install: 13 | - Rscript -e 'install.packages(c("devtools","roxygen2","testthat", "knitr", "rmarkdown", "xgboost", "forecast", "fpp", "ggplot2", "scales", "Tcomp", "foreach", "doParallel", "dplyr", "tseries"));devtools::install_deps("pkg")' 14 | script: 15 | - Rscript -e 'devtools::check("pkg")' 16 | 17 | notifications: 18 | email: 19 | on_success: change 20 | on_failure: change -------------------------------------------------------------------------------- /LICENSE: -------------------------------------------------------------------------------- 1 | GNU GENERAL PUBLIC LICENSE 2 | Version 3, 29 June 2007 3 | 4 | Copyright (C) 2007 Free Software Foundation, Inc. 5 | Everyone is permitted to copy and distribute verbatim copies 6 | of this license document, but changing it is not allowed. 7 | 8 | Preamble 9 | 10 | The GNU General Public License is a free, copyleft license for 11 | software and other kinds of works. 12 | 13 | The licenses for most software and other practical works are designed 14 | to take away your freedom to share and change the works. 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But first, please read 674 | . 675 | -------------------------------------------------------------------------------- /README.Rmd: -------------------------------------------------------------------------------- 1 | # forecastxgb-r-package 2 | The `forecastxgb` package provides time series modelling and forecasting functions that combine the machine learning approach of Chen, He and Benesty's [`xgboost`](https://CRAN.R-project.org/package=xgboost) with the convenient handling of time series and familiar API of Rob Hyndman's [`forecast`](http://github.com/robjhyndman/forecast). It applies to time series the Extreme Gradient Boosting proposed in [*Greedy Function Approximation: A Gradient Boosting Machine*, by Jermoe Friedman in 2001](http://www.jstor.org/stable/2699986). xgboost has become an important machine learning algorithm; nicely explained in [this accessible documentation](http://xgboost.readthedocs.io/en/latest/model.html). 3 | 4 | [![Travis-CI Build Status](https://travis-ci.org/ellisp/forecastxgb-r-package.svg?branch=master)](https://travis-ci.org/ellisp/forecastxgb-r-package) 5 | [![CRAN version](http://www.r-pkg.org/badges/version/forecastxgb)](http://www.r-pkg.org/pkg/forecastxgb) 6 | [![CRAN RStudio mirror downloads](http://cranlogs.r-pkg.org/badges/forecastxgb)](http://www.r-pkg.org/pkg/forecastxgb) 7 | 8 | **Warning: this package is under active development and is some way off a CRAN release (realistically, no some time in 2017). Currently the forecasting results with the default settings are, frankly, pretty rubbish, but there is hope I can get better settings. The API and default values of arguments should be expected to continue to change.** 9 | 10 | ## Installation 11 | Only on GitHub, but plan for a CRAN release in November 2016. Comments and suggestions welcomed. 12 | 13 | This implementation uses as explanatory features: 14 | 15 | * lagged values of the response variable 16 | * dummy variables for seasons. 17 | * current and lagged values of any external regressors supplied as `xreg` 18 | 19 | ```{r echo = FALSE} 20 | set.seed(123) 21 | library(knitr) 22 | knit_hooks$set(mypar = function(before, options, envir) { 23 | if (before) par(bty = "l", family = "serif") 24 | }) 25 | opts_chunk$set(comment=NA, fig.width=7, fig.height=5, cache = FALSE, mypar = TRUE) 26 | ``` 27 | 28 | 29 | ```{r eval = FALSE} 30 | devtools::install_github("ellisp/forecastxgb-r-package/pkg") 31 | ``` 32 | 33 | ## Usage 34 | 35 | 36 | ## Basic usage 37 | 38 | The workhorse function is `xgbar`. This fits a model to a time series. Under the hood, it creates a matrix of explanatory variables based on lagged versions of the response time series, and (optionally) dummy variables of some sort for seasons. That matrix is then fed as the feature set for `xgboost` to do its stuff. 39 | 40 | ### Univariate 41 | 42 | Usage with default values is straightforward. Here it is fit to Australian monthly gas production 1956-1995, an example dataset provided in `forecast`: 43 | ```{r message = FALSE} 44 | library(forecastxgb) 45 | model <- xgbar(gas) 46 | ``` 47 | (Note: the "Stopping. Best iteration..." to the screen is produced by `xgboost::xgb.cv`, which uses `cat()` rather than `message()` to print information on its processing.) 48 | 49 | By default, `xgbar` uses row-wise cross-validation to determine the best number of rounds of iterations for the boosting algorithm without overfitting. A final model is then fit on the full available dataset. The relative importance of the various features in the model can be inspected by `importance_xgb()` or, more conveniently, the `summary` method for objects of class `xgbar`. 50 | 51 | 52 | ```{r} 53 | summary(model) 54 | ``` 55 | We see in the case of the gas data that the most important feature in explaining gas production is the production 12 months previously; and then other features decrease in importance from there but still have an impact. 56 | 57 | Forecasting is the main purpose of this package, and a `forecast` method is supplied. The resulting objects are of class `forecast` and familiar generic functions work with them. 58 | 59 | ```{r} 60 | fc <- forecast(model, h = 12) 61 | plot(fc) 62 | ``` 63 | 64 | Note that prediction intervals are not currently available. 65 | 66 | See the vignette for more extended examples. 67 | 68 | ### With external regressors 69 | External regressors can be added by using the `xreg` argument familiar from other forecast functions like `auto.arima` and `nnetar`. `xreg` can be a vector or `ts` object but is easiest to integrate into the analysis if it is a matrix (even a matrix with one column) with well-chosen column names; that way feature names persist meaningfully. 70 | 71 | The example below, with data taken from the `fpp` package supporting Athanasopoulos and Hyndman's [Forecasting Principles and Practice](https://www.otexts.org/fpp) book, shows income being used to explain consumption. In the same way that the response variable `y` is expanded into lagged versions of itself, each column in `xreg` is expanded into lagged versions, which are then treated as individual features for `xgboost`. 72 | 73 | ```{r message = FALSE} 74 | library(fpp) 75 | consumption <- usconsumption[ ,1] 76 | income <- matrix(usconsumption[ ,2], dimnames = list(NULL, "Income")) 77 | consumption_model <- xgbar(y = consumption, xreg = income) 78 | summary(consumption_model) 79 | ``` 80 | We see that the two most important features explaining consumption are the two previous quarters' values of consumption; followed by the income in this quarter; and so on. 81 | 82 | 83 | The challenge of using external regressors in a forecasting environment is that to forecast, you need values of the future external regressors. One way this is sometimes done is by first forecasting the individual regressors. In the example below we do this, making sure the data structure is the same as the original `xreg`. When the new value of `xreg` is given to `forecast`, it forecasts forward the number of rows of the new `xreg`. 84 | ```{r} 85 | income_future <- matrix(forecast(xgbar(usconsumption[,2]), h = 10)$mean, 86 | dimnames = list(NULL, "Income")) 87 | plot(forecast(consumption_model, xreg = income_future)) 88 | ``` 89 | 90 | ## Options 91 | 92 | ### Seasonality 93 | 94 | Currently there are three methods of treating seasonality. 95 | 96 | - The current default method is to throw dummy variables for each season into the mix of features for `xgboost` to work with. 97 | - An alternative is to perform classic multiplicative seasonal adjustment on the series before feeding it to `xgboost`. This seems to work better. 98 | - A third option is to create a set of pairs of Fourier transform variables and use them as x regressors 99 | 100 | ```{r echo = FALSE} 101 | model1 <- xgbar(co2, seas_method = "dummies") 102 | model2 <- xgbar(co2, seas_method = "decompose") 103 | model3 <- xgbar(co2, seas_method = "fourier") 104 | plot(forecast(model1), main = "Dummy variables for seasonality") 105 | plot(forecast(model2), main = "Decomposition seasonal adjustment for seasonality") 106 | plot(forecast(model3), main = "Fourier transform pairs as x regressors") 107 | ``` 108 | 109 | All methods perform quite poorly at the moment, suffering from the difficulty the default settings have in dealing with non-stationary data (see below). 110 | 111 | ### Transformations 112 | 113 | The data can be transformed by a modulus power transformation (as per John and Draper, 1980) before feeding to `xgboost`. This transformation is similar to a Box-Cox transformation, but works with negative data. Leaving the `lambda` parameter as 1 will effectively switch off this transformation. 114 | ```{r echo = FALSE} 115 | model1 <- xgbar(co2, seas_method = "decompose", lambda = 1) 116 | model2 <- xgbar(co2, seas_method = "decompose", lambda = BoxCox.lambda(co2)) 117 | plot(forecast(model1), main = "No transformation") 118 | plot(forecast(model2), main = "With transformation") 119 | ``` 120 | 121 | Version 0.0.9 of `forecastxgb` gave `lambda` the default value of `BoxCox.lambda(abs(y))`. This returned spectacularly bad forecasting results. Forcing this to be between 0 and 1 helped a little, but still gave very bad results. So far there isn't evidence (but neither is there enough investigation) that a Box Cox transformation helps xgbar do its model fitting at all. 122 | 123 | ### Non-stationarity 124 | From experiments so far, it seems the basic idea of `xgboost` struggles in this context with extrapolation into a new range of variables not in the training set. This suggests better results might be obtained by transforming the series into a stationary one before modelling - a similar approach to that taken by `forecast::auto.arima`. This option is available by `trend_method = "differencing"` and seems to perform well - certainly better than without - and it will probably be made a default setting once more experience is available. 125 | 126 | ```{r} 127 | model <- xgbar(AirPassengers, trend_method = "differencing", seas_method = "fourier") 128 | plot(forecast(model, 24)) 129 | ``` 130 | 131 | 132 | ## Future developments 133 | Future work might include: 134 | 135 | * additional automated time-dependent features (eg dummy variables for trading days, Easter, etc) 136 | * ability to include xreg values that don't get lagged 137 | * some kind of automated multiple variable forecasting, similar to a vector-autoregression. 138 | * better choices of defaults for values such as `lambda` (for power transformations), `K` (for Fourier transforms) and, most likely to be effective, `maxlag`. -------------------------------------------------------------------------------- /README.md: -------------------------------------------------------------------------------- 1 | # forecastxgb-r-package 2 | The `forecastxgb` package provides time series modelling and forecasting functions that combine the machine learning approach of Chen, He and Benesty's [`xgboost`](https://CRAN.R-project.org/package=xgboost) with the convenient handling of time series and familiar API of Rob Hyndman's [`forecast`](http://github.com/robjhyndman/forecast). It applies to time series the Extreme Gradient Boosting proposed in [*Greedy Function Approximation: A Gradient Boosting Machine*, by Jermoe Friedman in 2001](http://www.jstor.org/stable/2699986). xgboost has become an important machine learning algorithm; nicely explained in [this accessible documentation](http://xgboost.readthedocs.io/en/latest/model.html). 3 | 4 | [![Travis-CI Build Status](https://travis-ci.org/ellisp/forecastxgb-r-package.svg?branch=master)](https://travis-ci.org/ellisp/forecastxgb-r-package) 5 | [![CRAN version](http://www.r-pkg.org/badges/version/forecastxgb)](http://www.r-pkg.org/pkg/forecastxgb) 6 | [![CRAN RStudio mirror downloads](http://cranlogs.r-pkg.org/badges/forecastxgb)](http://www.r-pkg.org/pkg/forecastxgb) 7 | 8 | **Warning: this package is under active development and is some way off a CRAN release (realistically, no some time in 2017). Currently the forecasting results with the default settings are, frankly, pretty rubbish, but there is hope I can get better settings. The API and default values of arguments should be expected to continue to change.** 9 | 10 | ## Installation 11 | Only on GitHub, but plan for a CRAN release in November 2016. Comments and suggestions welcomed. 12 | 13 | This implementation uses as explanatory features: 14 | 15 | * lagged values of the response variable 16 | * dummy variables for seasons. 17 | * current and lagged values of any external regressors supplied as `xreg` 18 | 19 | 20 | 21 | 22 | 23 | ```r 24 | devtools::install_github("ellisp/forecastxgb-r-package/pkg") 25 | ``` 26 | 27 | ## Usage 28 | 29 | 30 | ## Basic usage 31 | 32 | The workhorse function is `xgbar`. This fits a model to a time series. Under the hood, it creates a matrix of explanatory variables based on lagged versions of the response time series, and (optionally) dummy variables of some sort for seasons. That matrix is then fed as the feature set for `xgboost` to do its stuff. 33 | 34 | ### Univariate 35 | 36 | Usage with default values is straightforward. Here it is fit to Australian monthly gas production 1956-1995, an example dataset provided in `forecast`: 37 | 38 | ```r 39 | library(forecastxgb) 40 | model <- xgbar(gas) 41 | ``` 42 | (Note: the "Stopping. Best iteration..." to the screen is produced by `xgboost::xgb.cv`, which uses `cat()` rather than `message()` to print information on its processing.) 43 | 44 | By default, `xgbar` uses row-wise cross-validation to determine the best number of rounds of iterations for the boosting algorithm without overfitting. A final model is then fit on the full available dataset. The relative importance of the various features in the model can be inspected by `importance_xgb()` or, more conveniently, the `summary` method for objects of class `xgbar`. 45 | 46 | 47 | 48 | ```r 49 | summary(model) 50 | ``` 51 | 52 | ``` 53 | 54 | Importance of features in the xgboost model: 55 | Feature Gain Cover Frequency 56 | 1: lag12 5.097936e-01 0.1480752533 0.078475336 57 | 2: lag11 2.796867e-01 0.0731403763 0.042600897 58 | 3: lag13 1.043604e-01 0.0355137482 0.031390135 59 | 4: lag24 7.807860e-02 0.1320115774 0.069506726 60 | 5: lag1 1.579312e-02 0.1885383502 0.181614350 61 | 6: lag23 5.616290e-03 0.0471490593 0.042600897 62 | 7: lag9 2.510372e-03 0.0459623734 0.040358744 63 | 8: lag2 6.759874e-04 0.0436179450 0.053811659 64 | 9: lag14 5.874155e-04 0.0311432706 0.026905830 65 | 10: lag10 5.467606e-04 0.0530535456 0.053811659 66 | 11: lag6 3.820611e-04 0.0152243126 0.033632287 67 | 12: lag4 2.188107e-04 0.0098697540 0.035874439 68 | 13: lag22 2.162973e-04 0.0103617945 0.017937220 69 | 14: lag16 2.042320e-04 0.0098118669 0.013452915 70 | 15: lag21 1.962725e-04 0.0149638205 0.026905830 71 | 16: lag18 1.810734e-04 0.0243994211 0.029147982 72 | 17: lag3 1.709305e-04 0.0132850941 0.035874439 73 | 18: lag5 1.439827e-04 0.0231837916 0.033632287 74 | 19: lag15 1.313859e-04 0.0143560058 0.031390135 75 | 20: lag17 1.239889e-04 0.0109696093 0.017937220 76 | 21: season7 1.049934e-04 0.0081041968 0.015695067 77 | 22: lag8 9.773024e-05 0.0123299566 0.026905830 78 | 23: lag19 7.733822e-05 0.0112879884 0.015695067 79 | 24: lag20 5.425515e-05 0.0072648336 0.011210762 80 | 25: lag7 3.772907e-05 0.0105354559 0.020179372 81 | 26: season4 4.067607e-06 0.0010709117 0.002242152 82 | 27: season5 2.863805e-06 0.0022286541 0.006726457 83 | 28: season6 2.628821e-06 0.0021707670 0.002242152 84 | 29: season9 9.226827e-08 0.0003762663 0.002242152 85 | Feature Gain Cover Frequency 86 | 87 | 35 features considered. 88 | 476 original observations. 89 | 452 effective observations after creating lagged features. 90 | ``` 91 | We see in the case of the gas data that the most important feature in explaining gas production is the production 12 months previously; and then other features decrease in importance from there but still have an impact. 92 | 93 | Forecasting is the main purpose of this package, and a `forecast` method is supplied. The resulting objects are of class `forecast` and familiar generic functions work with them. 94 | 95 | 96 | ```r 97 | fc <- forecast(model, h = 12) 98 | plot(fc) 99 | ``` 100 | 101 | ![plot of chunk unnamed-chunk-5](figure/unnamed-chunk-5-1.png) 102 | 103 | Note that prediction intervals are not currently available. 104 | 105 | See the vignette for more extended examples. 106 | 107 | ### With external regressors 108 | External regressors can be added by using the `xreg` argument familiar from other forecast functions like `auto.arima` and `nnetar`. `xreg` can be a vector or `ts` object but is easiest to integrate into the analysis if it is a matrix (even a matrix with one column) with well-chosen column names; that way feature names persist meaningfully. 109 | 110 | The example below, with data taken from the `fpp` package supporting Athanasopoulos and Hyndman's [Forecasting Principles and Practice](https://www.otexts.org/fpp) book, shows income being used to explain consumption. In the same way that the response variable `y` is expanded into lagged versions of itself, each column in `xreg` is expanded into lagged versions, which are then treated as individual features for `xgboost`. 111 | 112 | 113 | ```r 114 | library(fpp) 115 | consumption <- usconsumption[ ,1] 116 | income <- matrix(usconsumption[ ,2], dimnames = list(NULL, "Income")) 117 | consumption_model <- xgbar(y = consumption, xreg = income) 118 | summary(consumption_model) 119 | ``` 120 | 121 | ``` 122 | 123 | Importance of features in the xgboost model: 124 | Feature Gain Cover Frequency 125 | 1: lag2 0.253763903 0.082908446 0.124513619 126 | 2: lag1 0.219332682 0.114608734 0.171206226 127 | 3: Income_lag0 0.115604367 0.183107958 0.085603113 128 | 4: lag3 0.064652150 0.093105742 0.089494163 129 | 5: lag8 0.055645114 0.099756152 0.066147860 130 | 6: Income_lag8 0.050460959 0.049434715 0.050583658 131 | 7: Income_lag1 0.047187235 0.088561295 0.050583658 132 | 8: Income_lag6 0.040512834 0.029150964 0.050583658 133 | 9: lag6 0.031876878 0.044225227 0.054474708 134 | 10: Income_lag2 0.020355402 0.015739304 0.031128405 135 | 11: Income_lag5 0.018011250 0.036577256 0.035019455 136 | 12: lag5 0.017930780 0.032143649 0.035019455 137 | 13: lag7 0.016674036 0.034249612 0.027237354 138 | 14: Income_lag4 0.015952784 0.025714919 0.038910506 139 | 15: Income_lag7 0.009850701 0.021724673 0.019455253 140 | 16: lag4 0.008819146 0.028929284 0.038910506 141 | 17: Income_lag3 0.008720737 0.013855021 0.019455253 142 | 18: season4 0.003152234 0.001551762 0.003891051 143 | 19: season3 0.001496807 0.004655287 0.007782101 144 | 145 | 20 features considered. 146 | 164 original observations. 147 | 156 effective observations after creating lagged features. 148 | ``` 149 | We see that the two most important features explaining consumption are the two previous quarters' values of consumption; followed by the income in this quarter; and so on. 150 | 151 | 152 | The challenge of using external regressors in a forecasting environment is that to forecast, you need values of the future external regressors. One way this is sometimes done is by first forecasting the individual regressors. In the example below we do this, making sure the data structure is the same as the original `xreg`. When the new value of `xreg` is given to `forecast`, it forecasts forward the number of rows of the new `xreg`. 153 | 154 | ```r 155 | income_future <- matrix(forecast(xgbar(usconsumption[,2]), h = 10)$mean, 156 | dimnames = list(NULL, "Income")) 157 | plot(forecast(consumption_model, xreg = income_future)) 158 | ``` 159 | 160 | ![plot of chunk unnamed-chunk-7](figure/unnamed-chunk-7-1.png) 161 | 162 | ## Options 163 | 164 | ### Seasonality 165 | 166 | Currently there are three methods of treating seasonality. 167 | 168 | - The current default method is to throw dummy variables for each season into the mix of features for `xgboost` to work with. 169 | - An alternative is to perform classic multiplicative seasonal adjustment on the series before feeding it to `xgboost`. This seems to work better. 170 | - A third option is to create a set of pairs of Fourier transform variables and use them as x regressors 171 | 172 | 173 | ``` 174 | No h provided so forecasting forward 24 periods. 175 | ``` 176 | 177 | ![plot of chunk unnamed-chunk-8](figure/unnamed-chunk-8-1.png) 178 | 179 | ``` 180 | No h provided so forecasting forward 24 periods. 181 | ``` 182 | 183 | ![plot of chunk unnamed-chunk-8](figure/unnamed-chunk-8-2.png) 184 | 185 | ``` 186 | No h provided so forecasting forward 24 periods. 187 | ``` 188 | 189 | ![plot of chunk unnamed-chunk-8](figure/unnamed-chunk-8-3.png) 190 | 191 | All methods perform quite poorly at the moment, suffering from the difficulty the default settings have in dealing with non-stationary data (see below). 192 | 193 | ### Transformations 194 | 195 | The data can be transformed by a modulus power transformation (as per John and Draper, 1980) before feeding to `xgboost`. This transformation is similar to a Box-Cox transformation, but works with negative data. Leaving the `lambda` parameter as 1 will effectively switch off this transformation. 196 | 197 | ``` 198 | No h provided so forecasting forward 24 periods. 199 | ``` 200 | 201 | ![plot of chunk unnamed-chunk-9](figure/unnamed-chunk-9-1.png) 202 | 203 | ``` 204 | No h provided so forecasting forward 24 periods. 205 | ``` 206 | 207 | ![plot of chunk unnamed-chunk-9](figure/unnamed-chunk-9-2.png) 208 | 209 | Version 0.0.9 of `forecastxgb` gave `lambda` the default value of `BoxCox.lambda(abs(y))`. This returned spectacularly bad forecasting results. Forcing this to be between 0 and 1 helped a little, but still gave very bad results. So far there isn't evidence (but neither is there enough investigation) that a Box Cox transformation helps xgbar do its model fitting at all. 210 | 211 | ### Non-stationarity 212 | From experiments so far, it seems the basic idea of `xgboost` struggles in this context with extrapolation into a new range of variables not in the training set. This suggests better results might be obtained by transforming the series into a stationary one before modelling - a similar approach to that taken by `forecast::auto.arima`. This option is available by `trend_method = "differencing"` and seems to perform well - certainly better than without - and it will probably be made a default setting once more experience is available. 213 | 214 | 215 | ```r 216 | model <- xgbar(AirPassengers, trend_method = "differencing", seas_method = "fourier") 217 | plot(forecast(model, 24)) 218 | ``` 219 | 220 | ![plot of chunk unnamed-chunk-10](figure/unnamed-chunk-10-1.png) 221 | 222 | 223 | ## Future developments 224 | Future work might include: 225 | 226 | * additional automated time-dependent features (eg dummy variables for trading days, Easter, etc) 227 | * ability to include xreg values that don't get lagged 228 | * some kind of automated multiple variable forecasting, similar to a vector-autoregression. 229 | * better choices of defaults for values such as `lambda` (for power transformations), `K` (for Fourier transforms) and, most likely to be effective, `maxlag`. 230 | -------------------------------------------------------------------------------- /build.R: -------------------------------------------------------------------------------- 1 | library(devtools) 2 | library(knitr) 3 | 4 | 5 | # compile Readme 6 | knit("README.Rmd", "README.md") 7 | test("pkg") 8 | 9 | 10 | document("pkg") 11 | build_vignettes("pkg") 12 | check("pkg") 13 | build("pkg") 14 | 15 | -------------------------------------------------------------------------------- /experiments/Tcomp-checks.R: -------------------------------------------------------------------------------- 1 | 2 | #=============prep====================== 3 | library(Tcomp) 4 | library(foreach) 5 | library(doParallel) 6 | library(forecastxgb) 7 | library(dplyr) 8 | library(ggplot2) 9 | library(scales) 10 | library(Mcomp) 11 | #============set up cluster for parallel computing=========== 12 | cluster <- makeCluster(7) # only any good if you have at least 7 processors :) 13 | registerDoParallel(cluster) 14 | 15 | clusterEvalQ(cluster, { 16 | library(Tcomp) 17 | library(forecastxgb) 18 | library(Mcomp) 19 | }) 20 | 21 | 22 | #===============the actual analytical function============== 23 | competition <- function(collection, maxfors = length(collection)){ 24 | if(class(collection) != "Mcomp"){ 25 | stop("This function only works on objects of class Mcomp, eg from the Mcomp or Tcomp packages.") 26 | } 27 | nseries <- length(collection) 28 | mases <- foreach(i = 1:maxfors, .combine = "rbind") %dopar% { 29 | thedata <- collection[[i]] 30 | seas_method <- ifelse(frequency(thedata$x) < 6, "dummies", "fourier") 31 | mod1 <- xgbar(thedata$x, trend_method = "differencing", seas_method = seas_method, lambda = 1, K = 2) 32 | fc1 <- forecast(mod1, h = thedata$h) 33 | fc2 <- thetaf(thedata$x, h = thedata$h) 34 | fc3 <- forecast(auto.arima(thedata$x), h = thedata$h) 35 | fc4 <- forecast(nnetar(thedata$x), h = thedata$h) 36 | # copy the skeleton of fc1 over for ensembles: 37 | fc12 <- fc13 <- fc14 <- fc23 <- fc24 <- fc34 <- fc123 <- fc124 <- fc134 <- fc234 <- fc1234 <- fc1 38 | # replace the point forecasts with averages of member forecasts: 39 | fc12$mean <- (fc1$mean + fc2$mean) / 2 40 | fc13$mean <- (fc1$mean + fc3$mean) / 2 41 | fc14$mean <- (fc1$mean + fc4$mean) / 2 42 | fc23$mean <- (fc2$mean + fc3$mean) / 2 43 | fc24$mean <- (fc2$mean + fc4$mean) / 2 44 | fc34$mean <- (fc3$mean + fc4$mean) / 2 45 | fc123$mean <- (fc1$mean + fc2$mean + fc3$mean) / 3 46 | fc124$mean <- (fc1$mean + fc2$mean + fc4$mean) / 3 47 | fc134$mean <- (fc1$mean + fc3$mean + fc4$mean) / 3 48 | fc234$mean <- (fc2$mean + fc3$mean + fc4$mean) / 3 49 | fc1234$mean <- (fc1$mean + fc2$mean + fc3$mean + fc4$mean) / 4 50 | mase <- c(accuracy(fc1, thedata$xx)[2, 6], 51 | accuracy(fc2, thedata$xx)[2, 6], 52 | accuracy(fc3, thedata$xx)[2, 6], 53 | accuracy(fc4, thedata$xx)[2, 6], 54 | accuracy(fc12, thedata$xx)[2, 6], 55 | accuracy(fc13, thedata$xx)[2, 6], 56 | accuracy(fc14, thedata$xx)[2, 6], 57 | accuracy(fc23, thedata$xx)[2, 6], 58 | accuracy(fc24, thedata$xx)[2, 6], 59 | accuracy(fc34, thedata$xx)[2, 6], 60 | accuracy(fc123, thedata$xx)[2, 6], 61 | accuracy(fc124, thedata$xx)[2, 6], 62 | accuracy(fc134, thedata$xx)[2, 6], 63 | accuracy(fc234, thedata$xx)[2, 6], 64 | accuracy(fc1234, thedata$xx)[2, 6]) 65 | mase 66 | } 67 | message("Finished fitting models") 68 | colnames(mases) <- c("x", "f", "a", "n", "xf", "xa", "xn", "fa", "fn", "an", 69 | "xfa", "xfn", "xan", "fan", "xfan") 70 | return(mases) 71 | } 72 | 73 | 74 | 75 | ## Test on a small set of data, useful during dev 76 | small_collection <- list(tourism[[100]], tourism[[200]], tourism[[300]], tourism[[400]], tourism[[500]], tourism[[600]]) 77 | class(small_collection) <- "Mcomp" 78 | test1 <- competition(small_collection) 79 | round(test1, 1) 80 | 81 | #========Fit models============== 82 | system.time(t1 <- competition(subset(tourism, "yearly"))) 83 | system.time(t4 <- competition(subset(tourism, "quarterly"))) 84 | system.time(t12 <- competition(subset(tourism, "monthly"))) 85 | 86 | 87 | system.time(m1 <- competition(subset(M3, "yearly"))) 88 | system.time(m4 <- competition(subset(M3, "quarterly"))) 89 | system.time(m12 <- competition(subset(M3, "monthly"))) 90 | system.time(mo <- competition(subset(M3, "other"))) 91 | 92 | # shut down cluster to avoid any mess: 93 | stopCluster(cluster) 94 | 95 | 96 | #==============present tourism results================ 97 | results <- c(apply(t1, 2, mean), 98 | apply(t4, 2, mean), 99 | apply(t12, 2, mean)) 100 | 101 | results_df <- data.frame(MASE = results) 102 | results_df$model <- as.character(names(results)) 103 | periods <- c("Annual", "Quarterly", "Monthly") 104 | results_df$Frequency <- rep.int(periods, times = c(15, 15, 15)) 105 | 106 | best <- results_df %>% 107 | group_by(model) %>% 108 | summarise(MASE = mean(MASE)) %>% 109 | arrange(MASE) %>% 110 | mutate(Frequency = "Average") 111 | 112 | Tcomp_results <- results_df %>% 113 | rbind(best) %>% 114 | mutate(model = factor(model, levels = best$model)) %>% 115 | mutate(Frequency = factor(Frequency, levels = c("Annual", "Average", "Quarterly", "Monthly"))) 116 | 117 | save(Tcomp_results, file = "pkg/data/Tcomp_results.rda") 118 | 119 | leg <- "f: Theta; forecast::thetaf\na: ARIMA; forecast::auto.arima 120 | n: Neural network; forecast::nnetar\nx: Extreme gradient boosting; forecastxgb::xgbar" 121 | 122 | Tcomp_results %>% 123 | ggplot(aes(x = model, y = MASE, colour = Frequency, label = model)) + 124 | geom_text(size = 6) + 125 | geom_line(aes(x = as.numeric(model)), alpha = 0.25) + 126 | scale_y_continuous("Mean scaled absolute error\n(smaller numbers are better)") + 127 | annotate("text", x = 2, y = 3.5, label = leg, hjust = 0) + 128 | ggtitle("Average error of four different timeseries forecasting methods\n2010 Tourism Forecasting Competition data") + 129 | labs(x = "Model, or ensemble of models\n(further to the left means better overall performance)") 130 | 131 | 132 | 133 | # the results for Theta and ARIMA match those at 134 | # https://cran.r-project.org/web/packages/Tcomp/vignettes/tourism-comp.html 135 | 136 | 137 | #======================Present M3 results======================== 138 | results <- c(apply(m1, 2, mean), 139 | apply(m4, 2, mean), 140 | apply(m12, 2, mean), 141 | apply(mo, 2, mean)) 142 | 143 | results_df <- data.frame(MASE = results) 144 | results_df$model <- as.character(names(results)) 145 | periods <- c("Annual", "Quarterly", "Monthly", "Other") 146 | results_df$Frequency <- rep.int(periods, times = c(15, 15, 15, 15)) 147 | 148 | best <- results_df %>% 149 | group_by(model) %>% 150 | summarise(MASE = mean(MASE)) %>% 151 | arrange(MASE) %>% 152 | mutate(Frequency = "Average") 153 | 154 | Mcomp_results <- results_df %>% 155 | rbind(best) %>% 156 | mutate(model = factor(model, levels = best$model)) %>% 157 | mutate(Frequency = factor(Frequency, levels = c("Annual", "Average", "Quarterly", "Monthly", "Other"))) 158 | 159 | save(Mcomp_results, file = "pkg/data/Mcomp_results.rda") 160 | 161 | leg <- "f: Theta; forecast::thetaf\na: ARIMA; forecast::auto.arima 162 | n: Neural network; forecast::nnetar\nx: Extreme gradient boosting; forecastxgb::xgbar" 163 | 164 | Mcomp_results %>% 165 | ggplot(aes(x = model, y = MASE, colour = Frequency, label = model)) + 166 | geom_text(size = 6) + 167 | geom_line(aes(x = as.numeric(model)), alpha = 0.25) + 168 | scale_y_continuous("Mean scaled absolute error\n(smaller numbers are better)") + 169 | annotate("text", x = 2, y = 3.5, label = leg, hjust = 0) + 170 | ggtitle("Average error of four different timeseries forecasting methods\nM3 Forecasting Competition data") + 171 | labs(x = "Model, or ensemble of models\n(further to the left means better overall performance)") 172 | 173 | -------------------------------------------------------------------------------- /experiments/experiments.R: -------------------------------------------------------------------------------- 1 | library(forecastxgb) 2 | 3 | fc1 <- forecast(auto.arima(AirPassengers), level = FALSE, h = 36) 4 | accuracy(fc1) 5 | object <- xgbar(AirPassengers, maxlag = 12) 6 | plot(object) 7 | 8 | fc2 <- forecast(object, h = 36) 9 | plot(fc1) 10 | plot(fc2) 11 | accuracy(fc2) # looks like rather extreme overfitting! 12 | 13 | xgb.importance(colnames(object$x), model = object$model) 14 | 15 | fc1$mean 16 | fc2$mean 17 | fc2$x 18 | fc1$x 19 | 20 | names(fc1) 21 | 22 | class(fc1$x) 23 | class(fc2$x) 24 | class(fc1$mean) 25 | class(fc2$mean) 26 | frequency(fc1$mean) 27 | frequency(fc2$mean) 28 | fc1$fitted 29 | fc2$fitted 30 | fc1$model 31 | fc2$model 32 | fc1$x 33 | fc2$x 34 | fc1$method 35 | fc2$method 36 | plot(fc1) 37 | plot(fc2) 38 | 39 | modnile <- xgbar(Nile, maxlag = 4) 40 | plot(modnile) 41 | -------------------------------------------------------------------------------- /experiments/explore-trends.R: -------------------------------------------------------------------------------- 1 | library(forecastxgb) 2 | library(dplyr) 3 | library(ggplot2) 4 | library(gridExtra) 5 | # rubbish at picking trends. Why? 6 | 7 | #--------simulated data-------------- 8 | y <- ts(1:100 * rnorm(100, 1, 0.01), frequency = 1) 9 | plot(y) 10 | 11 | 12 | mod1 <- auto.arima(y) 13 | mod2 <- naive(y,h = 20) 14 | mod3 <- ets(y) 15 | mod4 <- nnetar(y) 16 | p1 <- autoplot(forecast(mod1, h = 20)) 17 | p2 <- autoplot(forecast(mod2, h = 20)) 18 | p3 <- autoplot(forecast(mod3, h = 20)) 19 | p4 <- autoplot(forecast(mod4, h = 20)) 20 | 21 | grid.arrange(p1, p2, p3, p4) 22 | 23 | 24 | mod5 <- xgbar(y, maxlag = 8) 25 | fc5 <- forecast(mod5, h = 20) 26 | p5 <- autoplot(fc5) 27 | p5 28 | fc5$newx 29 | names(fc5) 30 | 31 | 32 | grid.arrange(p1, p3, p4, p5) 33 | 34 | #----------------real data-------------- 35 | mod1 <- xgbar(AirPassengers, seas_method = "fourier", trend_method = "differencing") 36 | mod2 <- xgbar(AirPassengers, seas_method = "dummies", trend_method = "differencing") 37 | mod3 <- xgbar(AirPassengers, seas_method = "decompose", trend_method = "differencing") 38 | mod4 <- xgbar(AirPassengers, seas_method = "fourier", trend_method = "none") 39 | mod5 <- xgbar(AirPassengers, seas_method = "dummies", trend_method = "none") 40 | mod6 <- xgbar(AirPassengers, seas_method = "decompose", trend_method = "none") 41 | mod7 <- xgbar(AirPassengers, seas_method = "fourier", trend_method = "differencing", lambda = 1) 42 | mod8 <- xgbar(AirPassengers, seas_method = "dummies", trend_method = "differencing", lambda = 1) 43 | mod9 <- xgbar(AirPassengers, seas_method = "decompose", trend_method = "differencing", lambda = 1) 44 | 45 | 46 | 47 | fc1 <- forecast(mod1, h = 24) 48 | fc2 <- forecast(mod2, h = 24) 49 | fc3 <- forecast(mod3, h = 24) 50 | fc4 <- forecast(mod4, h = 24) 51 | fc5 <- forecast(mod5, h = 24) 52 | fc6 <- forecast(mod6, h = 24) 53 | fc7 <- forecast(mod7, h = 24) 54 | fc8 <- forecast(mod8, h = 24) 55 | fc9 <- forecast(mod9, h = 24) 56 | 57 | 58 | plot(fc1) 59 | plot(fc2) 60 | plot(fc3) 61 | plot(fc4) 62 | plot(fc5) 63 | plot(fc6) 64 | plot(fc7) 65 | plot(fc8) 66 | plot(fc9) 67 | 68 | 69 | 70 | mod9 <- xgbar(AirPassengers, seas_method = "decompose", trend_method = "differencing") 71 | fc9 <- forecast(mod9, h = 24) 72 | plot(fc9) 73 | -------------------------------------------------------------------------------- /experiments/maxlags-experiment.R: -------------------------------------------------------------------------------- 1 | library(forecastxgb) 2 | library(Mcomp) 3 | library(foreach) 4 | library(doParallel) 5 | 6 | 7 | cluster <- makeCluster(4) 8 | registerDoParallel(cluster) 9 | 10 | clusterEvalQ(cluster, { 11 | library(Tcomp) 12 | library(forecastxgb) 13 | library(Mcomp) 14 | }) 15 | 16 | collection <- subset(M1, "quarterly") 17 | 18 | 19 | #================identify best maxlags for a collection===================== 20 | allmases <- list(length(collection)) 21 | 22 | for(i in 1:length(collection)){ 23 | cat(paste("Dataset", i, "\n")) 24 | thedata <- collection[[i]] 25 | 26 | n <- length(thedata$x) 27 | f <- frequency(thedata$x) 28 | maxP <- trunc(n / f / 2) 29 | thedata_mases <- numeric(maxP) 30 | 31 | for(p in 1:maxP){ 32 | mod <- xgbar(thedata$x, maxlag = p * f, nrounds_method = "cv") 33 | fc <- forecast(mod, h = thedata$h) 34 | thisacc <- accuracy(fc, thedata$xx)[2, 6] 35 | print(thisacc) 36 | thedata_mases[p] <- thisacc 37 | } 38 | thedata_mases_rounded <- round(thedata_mases, 1) 39 | bl <- min(which(thedata_mases_rounded == min(thedata_mases_rounded, na.rm = TRUE))) * f 40 | 41 | allmases[[i]] <- list(mases = thedata_mases, bl = bl, n = n, f = f) 42 | 43 | } 44 | 45 | # issue - crashes with the 7th quarterly dataset. n = 13, f = 4. Too short even for v validation. -------------------------------------------------------------------------------- /experiments/seasonal-adjustment-experiments.R: -------------------------------------------------------------------------------- 1 | 2 | 3 | 4 | model1 <- xgbar(AirPassengers, maxlag = 24, trend_method = "none", seas_method = "dummies") 5 | model2 <- xgbar(AirPassengers, maxlag = 24, trend_method = "none", seas_method = "decompose") 6 | model3 <- xgbar(AirPassengers, maxlag = 24, trend_method = "none", seas_method = "fourier") 7 | model4 <- xgbar(AirPassengers, maxlag = 24, trend_method = "none", seas_method = "none") 8 | 9 | model5 <- xgbar(AirPassengers, maxlag = 24, trend_method = "differencing", seas_method = "dummies") 10 | model6 <- xgbar(AirPassengers, maxlag = 24, trend_method = "differencing", seas_method = "decompose") 11 | model7 <- xgbar(AirPassengers, maxlag = 24, trend_method = "differencing", seas_method = "fourier") 12 | model8 <- xgbar(AirPassengers, maxlag = 24, trend_method = "differencing", seas_method = "none") 13 | 14 | fc1 <- forecast(model1, h = 24) 15 | fc2 <- forecast(model2, h = 24) 16 | fc3 <- forecast(model3, h = 24) 17 | fc4 <- forecast(model4, h = 24) 18 | 19 | fc5 <- forecast(model5, h = 24) 20 | fc6 <- forecast(model6, h = 24) 21 | fc7 <- forecast(model7, h = 24) 22 | fc8 <- forecast(model8, h = 24) 23 | 24 | 25 | par(mfrow = c(2, 2), bty = "l") 26 | plot(fc1, main = "dummies"); grid() 27 | plot(fc2, main = "decompose"); grid() 28 | plot(fc3, main = "fourier"); grid() 29 | plot(fc4, main = "none"); grid() 30 | 31 | 32 | par(mfrow = c(2, 2), bty = "l") 33 | plot(fc5, main = "dummies"); grid() 34 | plot(fc6, main = "decompose"); grid() 35 | plot(fc7, main = "fourier"); grid() 36 | plot(fc8, main = "none"); grid() 37 | 38 | 39 | summary(model3) 40 | -------------------------------------------------------------------------------- /experiments/validation.R: -------------------------------------------------------------------------------- 1 | 2 | 3 | validate_xgbar(Nile) 4 | tmp <- xgbar(Nile) 5 | 6 | validate_xgbar(AirPassengers) 7 | tmp <- xgbar(AirPassengers) 8 | 9 | validate_xgbar(WWWusage) 10 | tmp <- xgbar(WWWusage) 11 | 12 | validate_xgbar(USAccDeaths) 13 | tmp <- xgbar(USAccDeaths) -------------------------------------------------------------------------------- /experiments/xreg-experiments.R: -------------------------------------------------------------------------------- 1 | library(fpp) 2 | fit1 <- Arima(usconsumption[,1], xreg=usconsumption[,2], 3 | order=c(2,0,0)) 4 | tsdisplay(arima.errors(fit1), main="ARIMA errors") 5 | summary(fit1) 6 | fc1 <- forecast(fit1, xreg = income_future) 7 | names(fc1) 8 | fc$method 9 | 10 | fit2 <- xgbar(y = usconsumption[,1], xreg = matrix(usconsumption[,2], dimnames = list(NULL, "Income"))) 11 | fit3 <- xgbar(y = usconsumption[,1]) 12 | forecast(fit3) 13 | summary(fit2) 14 | fit2$origxreg 15 | 16 | 17 | income_future <- matrix(forecast(xgbar(usconsumption[,2]), h = 10)$mean, dimnames = list(NULL, "Income")) 18 | 19 | fc2 <- forecast(object = fit2, xreg = income_future) 20 | plot(fc2) 21 | 22 | fc3 <- forecast(fit3) 23 | plot(fit2) 24 | plot(fc3) 25 | names(fc2) 26 | fc2$method 27 | fc1$method 28 | fc2$model 29 | class(fc1$model) 30 | 31 | class(xreg) 32 | plot(xreg) 33 | is.numeric(xreg) 34 | as.matrix(xreg) 35 | dim(xreg) 36 | ncol(xreg) 37 | -------------------------------------------------------------------------------- /figure/unnamed-chunk-10-1.png: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/ellisp/forecastxgb-r-package/fe2894aa43a1805b94c881a32f7a5291e53654d6/figure/unnamed-chunk-10-1.png -------------------------------------------------------------------------------- /figure/unnamed-chunk-16-1.png: -------------------------------------------------------------------------------- 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PackageInstallArgs: --no-multiarch --with-keep.source 19 | PackageRoxygenize: rd,collate,namespace 20 | -------------------------------------------------------------------------------- /pkg/.Rbuildignore: -------------------------------------------------------------------------------- 1 | ^.*\.Rproj$ 2 | ^\.Rproj\.user$ 3 | -------------------------------------------------------------------------------- /pkg/DESCRIPTION: -------------------------------------------------------------------------------- 1 | Package: forecastxgb 2 | Title: Time Series Models and Forecasts using "xgboost" 3 | Version: 0.1.2.9000 4 | Authors@R: person("Peter", "Ellis", email = "peter.ellis2013nz@gmail.com", role = c("aut", "cre")) 5 | Description: What the package does (one paragraph). 6 | Depends: 7 | R (>= 3.1.2), 8 | forecast, 9 | xgboost (>= 0.6-4) 10 | License: GPL-3 11 | Encoding: UTF-8 12 | LazyData: true 13 | RoxygenNote: 6.0.1 14 | Imports: 15 | tseries 16 | Suggests: 17 | testthat, 18 | knitr, 19 | rmarkdown, 20 | Tcomp, 21 | foreach, 22 | doParallel, 23 | dplyr, 24 | ggplot2, 25 | scales, 26 | fpp 27 | VignetteBuilder: knitr 28 | -------------------------------------------------------------------------------- /pkg/NAMESPACE: -------------------------------------------------------------------------------- 1 | # Generated by roxygen2: do not edit by hand 2 | 3 | S3method(forecast,xgbar) 4 | S3method(plot,xgbar) 5 | S3method(print,summary.xgbar) 6 | S3method(summary,xgbar) 7 | export(xgbar) 8 | export(xgbar_importance) 9 | import(forecast) 10 | import(graphics) 11 | import(stats) 12 | import(xgboost) 13 | importFrom(tseries,kpss.test) 14 | importFrom(utils,tail) 15 | -------------------------------------------------------------------------------- /pkg/R/extras.R: -------------------------------------------------------------------------------- 1 | #' Show importance of features in a xgbar model 2 | #' 3 | #' This is a light wrapper for \code{xgboost::xbg.importance} to make it easier to use with objects of class \code{xgbar} 4 | #' @export 5 | #' @param object An object of class \code{xgbar}, usually created with \code{xgbar()} 6 | #' @param ... Extra parameters passed through to \code{xgb.importance} 7 | #' @return A \code{data.table} of the features used in the model with their average gain 8 | #' (and their weight for boosted tree model) in the model. 9 | #' @seealso \code{\link[xgboost]{xgb.importance}}, \code{\link{summary.xgbar}}, \code{\link{xgbar}}. 10 | #' @author Peter Ellis 11 | xgbar_importance <- function(object, ...){ 12 | if(class(object) != "xgbar"){ 13 | stop("'object' should be an object of class xgbar.") 14 | } 15 | xgb.importance(colnames(object$x), model = object$model, ...) 16 | } 17 | 18 | #' Summary of an xgbar object 19 | #' 20 | #' summary method for an object created by xgbar 21 | #' @aliases print.summary.xgbar 22 | #' @export 23 | #' @param object An object created by \code{\link{xgbar}} 24 | #' @param ... Ignored. 25 | #' @author Peter Ellis 26 | #' @seealso \code{\link{xgbar}} 27 | #' @examples 28 | #' \dontrun{ 29 | #' # Half-hourly electricity demand in England and Wales, takes a few minutes 30 | #' electricity_model <- xgbar(taylor) 31 | #' summary(electricity_model) 32 | #' electricity_fc <- forecast(electricity_model, h = 500) 33 | #' plot(electricity_fc) 34 | #' } 35 | summary.xgbar <- function(object, ...){ 36 | ans <- object 37 | ans$importance <- xgbar_importance(object) 38 | ans$n <- length(object$y) 39 | ans$effectn <- length(object$y2) 40 | ans$ncolx <- ncol(object$x) 41 | class(ans) <- "summary.xgbar" 42 | return(ans) 43 | } 44 | 45 | #' @export 46 | #' @method print summary.xgbar 47 | print.summary.xgbar <- function(x, ...){ 48 | 49 | cat("\nImportance of features in the xgboost model:\n") 50 | print(x$importance) 51 | 52 | cat(paste("\n", x$ncolx, "features considered.\n")) 53 | cat(paste0(x$n, " original observations.\n", 54 | x$effectn, " effective observations after creating lagged features.\n")) 55 | } 56 | 57 | 58 | #' Plot xgbar object 59 | #' 60 | #' plot method for an object created by xgbar 61 | #' @export 62 | #' @import graphics 63 | #' @method plot xgbar 64 | #' @param x An object created by \code{xgbar} 65 | #' @param ... Additional arguments passed through to \code{plot()} 66 | #' @author Peter Ellis 67 | #' @seealso \code{\link{xgbar}} 68 | #' @examples 69 | #' model <- xgbar(AirPassengers) 70 | #' plot(model) 71 | plot.xgbar <- function(x, ...){ 72 | ts.plot(x$y, col = "brown", ...) 73 | lines(x$fitted, col = "blue") 74 | 75 | } 76 | 77 | 78 | #' Tourism forecasting results 79 | #' 80 | #' Summary data from four models, and 11 combinations of models, against the data from the 2010 tourism forecasting competition. 81 | #' 82 | #' Full details of how this was generated are in the Vignette. This shows the average mean absolute scaled error 83 | #' (MASE) from using \code{xgbar} (x), \code{auto.arima} (a), \code{nnetar} (n) and \code{thetaf} (f) to generate forecasts of 1,311 tourism data series. 84 | #' 85 | #' 86 | #' \itemize{ 87 | #' \item MASE A mean mean absolute squared error 88 | #' \item model model, or ensemble of models, to which the MASE applies 89 | #' \item Frequency The frequency of the subset of data from which the mean MASE was calculated. 90 | #' } 91 | #' @format A data frame with 60 rows and three columns. 92 | #' @author Peter Ellis 93 | #' @examples 94 | #' if(require(ggplot2)){ 95 | #' leg <- "f: Theta; forecast::thetaf\na: ARIMA; forecast::auto.arima 96 | #' n: Neural network; forecast::nnetar\nx: Extreme gradient boosting; forecastxgb::xgbar" 97 | #' 98 | #' ggplot(Tcomp_results, aes(x = model, y = MASE, colour = Frequency, label = model)) + 99 | #' geom_text(size = 4) + 100 | #' geom_line(aes(x = as.numeric(model)), alpha = 0.25) + 101 | #' annotate("text", x = 2, y = 3.5, label = leg, hjust = 0) + 102 | #' ggtitle("Average error of four different timeseries forecasting methods 103 | #'2010 Tourism Forecasting Competition data") + 104 | #' labs(x = "Model, or ensemble of models 105 | #'(further to the left means better overall performance)", 106 | #' y = "Mean scaled absolute error\n(smaller numbers are better)") + 107 | #' theme_grey(9) 108 | #' } 109 | "Tcomp_results" 110 | 111 | 112 | 113 | #' M3 forecasting results 114 | #' 115 | #' Summary data from four models, and 11 combinations of models, against the data from the M3 forecasting competition. 116 | #' 117 | #' Full details are in the vignette of how a similar series with tourism competition data was generated. 118 | #' The data shows the average mean absolute scaled error 119 | #' (MASE) from using \code{xgbar} (x), \code{auto.arima} (a), \code{nnetar} (n) and \code{thetaf} (f) to 120 | #' generate forecasts of 3,003 data series from a range of sectors, in the M3 forecasting competition. 121 | #' 122 | #' 123 | #' \itemize{ 124 | #' \item MASE A mean mean absolute squared error 125 | #' \item model model, or ensemble of models, to which the MASE applies 126 | #' \item Frequency The frequency of the subset of data from which the mean MASE was calculated. 127 | #' } 128 | #' @format A data frame with 75 rows and three columns. 129 | #' @author Peter Ellis 130 | #' @examples 131 | #' if(require(ggplot2)){ 132 | #' leg <- "f: Theta; forecast::thetaf\na: ARIMA; forecast::auto.arima 133 | #' n: Neural network; forecast::nnetar\nx: Extreme gradient boosting; forecastxgb::xgbar" 134 | #' 135 | #' ggplot(Mcomp_results, aes(x = model, y = MASE, colour = Frequency, label = model)) + 136 | #' geom_text(size = 4) + 137 | #' geom_line(aes(x = as.numeric(model)), alpha = 0.25) + 138 | #' annotate("text", x = 2, y = 3.5, label = leg, hjust = 0) + 139 | #' ggtitle("Average error of four different timeseries forecasting methods 140 | #'M3 Forecasting Competition data") + 141 | #' labs(x = "Model, or ensemble of models 142 | #'(further to the left means better overall performance)", 143 | #' y = "Mean scaled absolute error\n(smaller numbers are better)") + 144 | #' theme_grey(9) 145 | #' } 146 | "Mcomp_results" 147 | 148 | 149 | -------------------------------------------------------------------------------- /pkg/R/forecast.xgbar.R: -------------------------------------------------------------------------------- 1 | #' Forecasting using xgboost models 2 | #' 3 | #' Returns forecasts and other information for xgboost timeseries modesl fit with \code{xbgts} 4 | #' 5 | #' @export 6 | #' @import forecast 7 | #' @import xgboost 8 | #' @importFrom utils tail 9 | #' @method forecast xgbar 10 | #' @param object An object of class "\code{xgbar}". Usually the result of a call to \code{\link{xgbar}}. 11 | #' @param h Number of periods for forecasting. If \code{xreg} is provided, the number of rows of \code{xreg} will be 12 | #' used and \code{h} is ignored with a warning. If both \code{h} and \code{xreg} are \code{NULL} then 13 | #' \code{h = ifelse(frequency(object$y) > 1, 2 * frequency(object$y), 10)} 14 | #' @param xreg Future values of regression variables. 15 | #' @param ... Ignored. 16 | #' @return An object of class \code{forecast} 17 | #' @author Peter Ellis 18 | #' @seealso \code{\link{xgbar}}, \code{\link[forecast]{forecast}} 19 | #' @examples 20 | #' # Australian monthly gas production 21 | #' gas_model <- xgbar(gas) 22 | #' summary(gas_model) 23 | #' gas_fc <- forecast(gas_model, h = 12) 24 | #' plot(gas_fc) 25 | forecast.xgbar <- function(object, 26 | h = NULL, 27 | xreg = NULL, ...){ 28 | # validity checks on xreg 29 | if(!is.null(xreg)){ 30 | if(is.null(object$ncolxreg)){ 31 | stop("You supplied an xreg, but there is none in the original xgbar object.") 32 | } 33 | 34 | if(class(xreg) == "ts" | "data.frame" %in% class(xreg)){ 35 | message("Converting xreg into a matrix") 36 | # TODO - not sure this works when it's two dimensional 37 | xreg <- as.matrix(xreg) 38 | } 39 | 40 | if(!is.numeric(xreg) | !is.matrix(xreg)){ 41 | stop("xreg should be a numeric and able to be coerced to a matrix") 42 | } 43 | 44 | if(ncol(xreg) != object$ncolxreg){ 45 | stop("Number of columns in xreg doesn't match the original xgbar object.") 46 | } 47 | 48 | if(!is.null(h)){ 49 | warning(paste("Ignoring h and forecasting", nrow(xreg), "periods from xreg.")) 50 | } 51 | 52 | # add the lagged versions of xreg. Some of the lags need to come from the original data 53 | h <- nrow(xreg) 54 | xreg2 <- lagvm(rbind(xreg, object$origxreg), maxlag = object$maxlag) 55 | # we just want the last h rows of that big matrix: 56 | nn <- nrow(xreg2) 57 | xreg3 <- xreg2[(nn - h + 1):nn, ] 58 | } 59 | 60 | if(is.null(h)){ 61 | h <- ifelse(frequency(object$y) > 1, 2 * frequency(object$y), 10) 62 | message(paste("No h provided so forecasting forward", h, "periods.")) 63 | } 64 | 65 | # clear up space to avoid using an old xreg3 if it exists 66 | if(is.null(xreg)){ 67 | xreg3 <- NULL 68 | } 69 | 70 | f <- frequency(object$y) 71 | lambda <- object$lambda 72 | seas_method <- object$seas_method 73 | 74 | # forecast time x variable 75 | htime <- time(ts(rep(0, h), frequency = f, start = max(time(object$y)) + 1 / f)) 76 | 77 | # forecast fourier pairs 78 | if(f > 1 & seas_method == "fourier"){ 79 | fxh <- fourier(object$y2, K = object$K, h = h) 80 | } 81 | 82 | forward1 <- function(x, y, model, xregpred, i){ 83 | newrow <- c( 84 | # latest lagged value: 85 | y[length(y)], 86 | # previous lagged values: 87 | x[nrow(x), 1:(object$maxlag - 1)]) 88 | if(object$maxlag == 1){ 89 | newrow = newrow[-1] 90 | } 91 | 92 | # seasonal dummies if 'dummies': 93 | if(f > 1 & seas_method == "dummies"){ 94 | # for dummy variables it's ok to just take the set of dummies from f time periods before: 95 | newrow <- c(newrow, x[(nrow(x) + 1 - f), (object$maxlag + 1):(object$maxlag + f - 1)]) 96 | } 97 | # seasonal dummies if 'fourier': 98 | if(f > 1 & seas_method == 'fourier'){ 99 | # for fourier variables, 100 | newrow <- c(newrow, fxh[i, ]) 101 | } 102 | 103 | if(!is.null(xregpred)){ 104 | newrow <- c(newrow, xregpred) 105 | } 106 | 107 | newrow <- matrix(newrow, nrow = 1) 108 | colnames(newrow) <- colnames(x) 109 | 110 | pred <- predict(model, newdata = newrow) 111 | 112 | return(list( 113 | x = rbind(x, newrow), 114 | y = c(y, pred) 115 | )) 116 | } 117 | 118 | x <- object$x 119 | y <- object$y2 120 | 121 | 122 | for(i in 1:h){ 123 | tmp <- forward1(x, y, model = object$model, xregpred = xreg3[i, ], i = i) 124 | x <- tmp$x 125 | y <- tmp$y 126 | } 127 | 128 | 129 | # fitted and forecast object, on possibly untransformed, undifferenced and seasonally adjusted scale 130 | y <- ts(y[-(1:length(object$y2))], 131 | frequency = f, 132 | start = max(time(object$y)) + 1 / f) 133 | 134 | # back transform the differencing 135 | if(object$diffs > 0){ 136 | for(i in 1:object$diffs){ 137 | y <- ts(cumsum(y) , start = start(y), frequency = f) 138 | } 139 | y <- y + JDMod(object$y[length(object$y)], lambda = lambda) 140 | } 141 | 142 | # back transform the seasonal adjustment: 143 | if(seas_method == "decompose"){ 144 | multipliers <- utils::tail(object$decomp$seasonal, f) 145 | if(h < f){ 146 | multipliers <- multipliers[1:h] 147 | } 148 | y <- y * as.vector(multipliers) 149 | } 150 | 151 | # back transform the modulus power transform: 152 | y <- InvJDMod(y, lambda = lambda) 153 | 154 | output <- list( 155 | x = object$y, 156 | mean = y, 157 | fitted = object$fitted, 158 | newx = x, 159 | method = object$method 160 | ) 161 | class(output) <- "forecast" 162 | return(output) 163 | 164 | } 165 | -------------------------------------------------------------------------------- /pkg/R/forecastxgb.R: -------------------------------------------------------------------------------- 1 | #' Extreme gradient boosting time series forecasting 2 | #' 3 | #' The \code{forecastxgb} package provides time series modelling and forecasting functions that combine 4 | #' the machine learning approach of Chen, He and Benesty's \code{xgboost} 5 | #' with the convenient handling of time series and familiar API of Rob Hyndman's \code{forecast}. 6 | #' 7 | #' It applies to time series the Extreme Gradient Boosting proposed in \emph{Greedy Function Approximation: A 8 | #' Gradient Boosting Machine, by Jermoe Friedman in 2001} (http://www.jstor.org/stable/2699986). 9 | #' 10 | "_PACKAGE" -------------------------------------------------------------------------------- /pkg/R/misc-doc.R: -------------------------------------------------------------------------------- 1 | 2 | 3 | 4 | 5 | #' Arctic sea ice 6 | #' 7 | #' Extent in millions of square kilometres of sea ice in the Arctic from 21 August 1987 to 24 November 2016. 8 | #' 9 | #' @source National Snow and Ice Data Center, \url{https://nsidc.org/data/docs/noaa/g02135_seaice_index/#daily_data_files"} 10 | #' @examples 11 | #' plot(seaice_ts) 12 | "seaice_ts" -------------------------------------------------------------------------------- /pkg/R/utils.R: -------------------------------------------------------------------------------- 1 | 2 | # not exported 3 | # function to take a vector and create a matrix of itself and lagged values 4 | lagv <- function(x, maxlag, keeporig = TRUE){ 5 | if(!is.vector(x) & !is.ts(x)){ 6 | stop("x must be a vector or time series") 7 | } 8 | x <- as.vector(x) 9 | n <- length(x) 10 | z <- matrix(0, nrow = (n - maxlag), ncol = maxlag + 1) 11 | for(i in 1:ncol(z)){ 12 | z[ , i] <- x[(maxlag + 2 - i):(n + 1 - i)] 13 | } 14 | varname <- "x" 15 | colnames(z) <- c(varname, paste0(varname, "_lag", 1:maxlag)) 16 | if(!keeporig){ 17 | z <- z[ ,-1] 18 | } 19 | return(z) 20 | } 21 | 22 | # not exported 23 | # function to take a matrix and make a wider matrix with many lagged versions 24 | lagvm <- function(x, maxlag){ 25 | if(!is.matrix(x)){ 26 | stop("X needs to be a matrix") 27 | } 28 | 29 | if(is.null(colnames(x))){ 30 | colnames(x) <- paste0("Var", 1:ncol(x)) 31 | } 32 | n <- nrow(x) 33 | M <- matrix(0, nrow = (n - maxlag), ncol = (maxlag + 1) * ncol(x)) 34 | for(i in 1:ncol(x)){ 35 | M[ , 1:(maxlag + 1) + (i - 1) * (maxlag + 1)] <- lagv(x[ ,i], maxlag = maxlag) 36 | } 37 | thenames <- character() 38 | for(i in 1:ncol(x)){ 39 | thenames <- c(thenames, paste0(colnames(x)[i], "_lag", 0:maxlag)) 40 | } 41 | colnames(M) <- thenames 42 | 43 | return(M) 44 | } 45 | 46 | 47 | # not exported 48 | # function to perform transformation as per John and Draper's "An Alternative Family of Transformations" 49 | # John and Draper's modulus transformation 50 | JDMod <- function(y, lambda){ 51 | if(lambda != 0){ 52 | yt <- sign(y) * (((abs(y) + 1) ^ lambda - 1) / lambda) 53 | } else { 54 | yt = sign(y) * (log(abs(y) + 1)) 55 | } 56 | return(yt) 57 | } 58 | 59 | InvJDMod <- function(yt, lambda){ 60 | if(lambda != 0){ 61 | y <- ((abs(yt) * lambda + 1) ^ (1 / lambda) - 1) * sign(yt) 62 | } else { 63 | y <- (exp(abs(yt)) - 1) * sign(yt) 64 | 65 | } 66 | return(y) 67 | } 68 | 69 | -------------------------------------------------------------------------------- /pkg/R/validate_xgbar.R: -------------------------------------------------------------------------------- 1 | validate_xgbar <- function(y, xreg = NULL, nrounds = 50, ...){ 2 | n <- length(y) 3 | spl <- round(0.8 * n) 4 | 5 | trainy <- ts(y[1:spl], start = start(y), frequency = frequency(y)) 6 | testy <- y[(spl + 1):n] 7 | h <- length(testy) 8 | 9 | if(!is.null(xreg)){ 10 | trainxreg <- xreg[1:spl, ] 11 | testxreg <- xreg[(spl + 1):n, ] 12 | } 13 | 14 | grunt <- function(nrounds){ 15 | if(!is.null(xreg)){ 16 | trainmod <- xgbar(trainy, xreg = xreg, nrounds_method = "manual", nrounds = nrounds) 17 | } else { 18 | trainmod <- xgbar(trainy, nrounds_method = "manual", nrounds = nrounds) 19 | } 20 | fc <- forecast(trainmod, h = h) 21 | result <- accuracy(fc, testy)[2,6] 22 | return(result) 23 | } 24 | 25 | mases <- sapply(as.list(1:nrounds), grunt) 26 | 27 | best_nrounds <- min(which(mases == min(mases))) 28 | output <- list( 29 | best_nrounds = best_nrounds, 30 | best_mase = min(mases) 31 | ) 32 | return(output) 33 | } 34 | 35 | 36 | -------------------------------------------------------------------------------- /pkg/R/xgbar.R: -------------------------------------------------------------------------------- 1 | 2 | #' xgboost time series modelling 3 | #' 4 | #' Fit a model to a time series using xgboost 5 | #' 6 | #' @export 7 | #' @aliases xgbts 8 | #' @import xgboost 9 | #' @import forecast 10 | #' @import stats 11 | #' @importFrom tseries kpss.test 12 | #' @param y A univariate time series. 13 | #' @param xreg Optionally, a vector or matrix of external regressors, which must have the same number of rows as y. 14 | #' @param nrounds Maximum number of iterations \code{xgboost} will perform. If \code{nrounds_method = 'cv'}, 15 | #' the value of \code{nrounds} passed to \code{xgboost} is chosen by cross-validation; if it is \code{'v'} 16 | #' then the value of \code{nrounds} passed to \code{xgboost} is chosen by splitting the data into a training 17 | #' set (first 80 per cent) and test set (20 per cent) and choosing the number of iterations with the best value. 18 | #' If \code{nrounds_method = 'manual'} then \code{nrounds} iterations will be performed - unless you have chosen 19 | #' it carefully this is likely to lead to overfitting and poor forecasts. 20 | #' @param nfold Number of equal size subsamples during cross validation, used if \code{nrounds_method = 'cv'}. 21 | #' @param maxlag The maximum number of lags of \code{y} and \code{xreg} (if included) to be considered as features. 22 | #' @param verbose Passed on to \code{xgboost} and \code{xgb.cv}. 23 | #' @param nrounds_method Method used to determine the value of nrounds actually given for \code{xgboost} for 24 | #' the final model. Options are \code{"cv"} for row-wise cross-validation, \code{"v"} for validation on a testing 25 | #' set of the most recent 20 per cent of data, \code{"manual"} in which case \code{nrounds} is passed through directly. 26 | #' @param lambda Value of lambda to be used for modulus power transformation of \code{y} (which is similar to Box-Cox transformation 27 | #' but works with negative values too), performed before using xgboost (and inverse transformed to the original scale afterwards). 28 | #' Set \code{lambda = 1} if no transformation is desired. 29 | #' The transformation is only applied to \code{y}, not \code{xreg}. 30 | #' @param seas_method Method for dealing with seasonality. 31 | #' @param K if \code{seas_method == 'fourier'}, the value of \code{K} passed through to \code{fourier} for order of Fourier series to be generated as seasonal regressor variables. 32 | #' @param trend_method How should the \code{xgboost} try to deal with trends? Currently the only options to \code{none} is 33 | #' \code{auto.arima}-style \code{differencing}, which is based on successive KPSS tests until there is no significant evidence the 34 | #' remaining series is non-stationary. 35 | #' @param ... Additional arguments passed to \code{xgboost}. Only works if nrounds_method is "cv" or "manual". 36 | #' @details This is the workhorse function for the \code{forecastxgb} package. 37 | #' It fits a model to a time series. Under the hood, it creates a matrix of explanatory variables 38 | #' based on lagged versions of the response time series, and (optionally) dummy variables (simple hot one encoding, or Fourier transforms) for seasons. That 39 | #' matrix is then fed as the feature set for \code{xgboost} to do its stuff. 40 | #' @return An object of class \code{xgbar}. These have a \code{forecast} method and are generally 41 | #' expected to be used in a way such as \code{forecast(my_xgbar_model, h = 24)}. But the \code{xgbar} 42 | #' object itself can be of use in model checking and diagnosis. It is list with the following elements: 43 | #' \describe{ 44 | #' \item{\code{y}}{The original value of \code{y} fed to \code{xgbar}} 45 | #' \item{\code{y2}}{\code{y} except for its first \code{maxlag} values. } 46 | #' \item{\code{x}}{The features used by \code{xgboost} to model \code{y2}. \code{x} is basically 47 | #' a matrix of numbers created by the automated feature generation of \code{xgbar}, in particular 48 | #' the differencing (if asked for), seasonal adjustment (if asked for), and creation of lagged 49 | #' values. If \code{y} is univariate, 50 | #' \code{x} will be just the lagged values of \code{y} and will have \code{length(y) - maxlag} rows 51 | #' and \code{maxlag} columns. If \code{xreg} was supplied, \code{x} will have \code{maxlag * (ncol(xreg) + 1)} 52 | #' columns - a set of columns for the lagged values of y, and a set of columns for each lagged value 53 | #' of the xreg matrix.} 54 | #' \item{\code{model}}{Object of class \code{xgb.Booster} returned by \code{xgboost}. The actual 55 | #' xgboost model that regressed \code{y2} on \code{x}.} 56 | #' \item{\code{fitted}}{Fitted values of \code{y}. The first \code{maxlag} values will be \code{NA}. 57 | #' The remainder are the predicted values of the xgboost regression of \code{y2} on \code{x}.} 58 | #' \item{\code{maxlag}}{The original user-supplied value of \code{maxlag}, stored for future use by 59 | #' \code{forecast.xgbar}.} 60 | #' \item{\code{seas_method}}{The original user-supplied value of \code{seas_method}, stored for future use by 61 | #' \code{forecast.xgbar}.} 62 | #' \item{\code{diffs}}{The number of rounds of differencing applied to y to make it stationary, if 63 | #' \code{trend_method = "differencing"} was used.} 64 | #' \item{\code{lambda}}{The original user-supplied value of \code{lambda} for modulus transformation, 65 | #' stored for future use by \code{forecast.xgbar}.} 66 | #' \item{\code{method}}{A character string summarising the key arguments to xgbar, of the structure 67 | #' \code{xgbar(maxlag, diffs, seas_method)}.} 68 | #' \item{\code{origxreg}}{The original user-supplied value of \code{origxreg}, 69 | #' stored for future use by \code{forecast.xgbar} (needed to create future values of lagged \code{xreg} 70 | #' for the forecast period) .} 71 | #' \item{code{ncolxreg}}{The number of columns in the original \code{xreg} matrix.} 72 | #' \item{\code{decomp}}{If \code{seas_method = "decompose"} was used, this will be a list of the output 73 | #' from \code{decompose}, which decomposes y (called \code{x} by \code{decompose}) into seasonal, trend 74 | #' and random components.} 75 | #' } 76 | #' @seealso \code{\link{summary.xgbar}}, \code{\link{plot.xgbar}}, \code{\link{forecast.xgbar}}, \code{\link{xgbar_importance}}, 77 | #' \code{\link[xgboost]{xgboost}}. 78 | #' @author Peter Ellis 79 | #' @references J. A. John and N. R. Draper (1980), "An Alternative Family of Transformations", \emph{Journal of the Royal Statistical 80 | #' Society}. 81 | #' @examples 82 | #' # Univariate example - quarterly production of woolen yarn in Australia 83 | #' woolmod <- xgbar(woolyrnq) 84 | #' summary(woolmod) 85 | #' plot(woolmod) 86 | #' fc <- forecast(woolmod, h = 8) 87 | #' plot(fc) 88 | #' 89 | #' # Bivariate example - quarterly income and consumption in the US 90 | #' if(require(fpp)){ 91 | #' consumption <- usconsumption[ ,1] 92 | #' income <- matrix(usconsumption[ ,2], dimnames = list(NULL, "Income")) 93 | #' consumption_model <- xgbar(y = consumption, xreg = income) 94 | #' summary(consumption_model) 95 | #' } 96 | xgbar <- function(y, xreg = NULL, maxlag = max(8, 2 * frequency(y)), nrounds = 100, 97 | nrounds_method = c("cv", "v", "manual"), 98 | nfold = ifelse(length(y) > 30, 10, 5), 99 | lambda = 1, 100 | verbose = FALSE, 101 | seas_method = c("dummies", "decompose", "fourier", "none"), 102 | K = max(1, min(round(f / 4 - 1), 10)), 103 | trend_method = c("none", "differencing"), ...){ 104 | # y <- AirPassengers; nrounds_method = "cv"; nrounds = 100; seas_method = "fourier"; trend_method = "differencing"; verbose = TRUE; xreg = NULL; maxlag = 8; lambda = 1; K = 1 105 | 106 | nrounds_method = match.arg(nrounds_method) 107 | seas_method = match.arg(seas_method) 108 | trend_method = match.arg(trend_method) 109 | 110 | # check y is a univariate time series 111 | if(!"ts" %in% class(y)){ 112 | stop("y must be a univariate time series") 113 | } 114 | 115 | # check xreg, if it exists, is a numeric matrix 116 | if(!is.null(xreg)){ 117 | if(class(xreg) == "ts" | "data.frame" %in% class(xreg)){ 118 | message("Converting xreg into a matrix") 119 | xreg <- as.matrix(xreg) 120 | } 121 | 122 | if(!is.numeric(xreg) | !is.matrix(xreg)){ 123 | stop("xreg should be a numeric and able to be coerced to a matrix") 124 | } 125 | } 126 | f <- stats::frequency(y) 127 | untransformedy <- y 128 | origy <- JDMod(y, lambda = lambda) 129 | 130 | # seasonal adjustment if asked for 131 | if(seas_method == "decompose"){ 132 | decomp <- decompose(origy, type = "multiplicative") 133 | origy <- seasadj(decomp) 134 | } 135 | 136 | # de-trend the y if option was asked for 137 | # `diffs` is the number of differencing operations done, and is defined even if 138 | # trend_method != "differencing" 139 | diffs <- 0 140 | if(trend_method == "differencing"){ 141 | alpha = 0.05 142 | dodiff <- TRUE 143 | while(dodiff){ 144 | suppressWarnings(dodiff <- tseries::kpss.test(origy)$p.value < alpha) 145 | if(dodiff){ 146 | diffs <- diffs + 1 147 | origy <- ts(c(0, diff(origy)), start = start(origy), frequency = f) 148 | } 149 | } 150 | } 151 | 152 | if(maxlag < f & seas_method == "dummies"){ 153 | stop("At least one full period of lags needed when seas_method = dummies.") 154 | } 155 | 156 | orign <- length(y) 157 | 158 | if(orign < 4){ 159 | stop("Too short. I need at least four observations.") 160 | } 161 | 162 | if(maxlag > (orign - f - round(f / 4))){ 163 | warning(paste("y is too short for", maxlag, "to be the value of maxlag. Reducing maxlags to", 164 | orign - f - round(f / 4), 165 | "instead.")) 166 | maxlag <- orign - f - round(f / 4) 167 | } 168 | 169 | if (maxlag != round(maxlag)){ 170 | maxlag <- ceiling(maxlag) 171 | if(verbose){message(paste("Rounding maxlag up to", maxlag))} 172 | } 173 | 174 | 175 | origxreg <- xreg 176 | n <- orign - maxlag 177 | y2 <- ts(origy[-(1:(maxlag))], start = time(origy)[maxlag + 1], frequency = f) 178 | 179 | if(nrounds_method == "cv" & n < 15){ 180 | warning("y is too short for cross-validation. Will validate on the most recent 20 per cent instead.") 181 | nrounds_method <- "v" 182 | } 183 | 184 | 185 | 186 | #----------------------------creating x-------------------- 187 | # set up the matrix "x" of lagged versions of y, time series trend, and seasonal treatment: 188 | if(seas_method == "dummies" & f > 1){ncolx <- maxlag + f - 1} 189 | if(seas_method == "decompose"){ncolx <- maxlag } 190 | if(seas_method == "fourier" & f > 1){ncolx <- maxlag + K * 2} 191 | if(seas_method == "none" | f == 1){ncolx <- maxlag} 192 | x <- matrix(0, nrow = n, ncol = ncolx) 193 | 194 | # All models get the lagged values of y as regressors: 195 | x[ , 1:maxlag] <- lagv(origy, maxlag, keeporig = FALSE) 196 | 197 | # Some models get one hot encoding of seasons 198 | if(f > 1 & seas_method == "dummies"){ 199 | tmp <- data.frame(y = 1, x = as.character(rep_len(1:f, n))) 200 | seasons <- model.matrix(y ~ x, data = tmp)[ ,-1] 201 | x[ , maxlag + 1:(f - 1)] <- seasons 202 | 203 | colnames(x) <- c(paste0("lag", 1:maxlag), paste0("season", 2:f)) 204 | } 205 | 206 | # Fourier models get fourier cycles: 207 | if(f > 1 & seas_method == "fourier"){ 208 | fx <- fourier(y2, K = K) 209 | x[ , (maxlag + 1):ncolx] <- fx 210 | colnames(x) <- c(paste0("lag", 1:maxlag), colnames(fx)) 211 | } 212 | 213 | # Some models get no seasonal treatment at all: 214 | if(f == 1 || seas_method == "decompose" || seas_method == "none"){ 215 | colnames(x) <- c(paste0("lag", 1:maxlag)) 216 | } 217 | 218 | # add xreg, if present 219 | if(!is.null(xreg)){ 220 | xreg <- lagvm(xreg, maxlag = maxlag) 221 | x <- cbind(x, xreg[ , , drop = FALSE]) 222 | } 223 | 224 | 225 | #---------------model fitting-------------------- 226 | if(nrounds_method == "cv"){ 227 | if(verbose){message("Starting cross-validation")} 228 | cv <- xgb.cv(data = x, label = y2, nrounds = nrounds, nfold = nfold, 229 | early_stopping_rounds = 5, maximize = FALSE, verbose = verbose, ...) # should finish with , ... 230 | # TODO - xgb.cv uses cat() to give messages, very poor practice. Sink them somewhere if verbose = FALSE? 231 | 232 | nrounds_use <- cv$best_iteration 233 | } else {if(nrounds_method == "v"){ 234 | nrounds_use <- validate_xgbar(y, xreg = xreg, ...) $best_nrounds 235 | } else { 236 | nrounds_use <- nrounds 237 | } 238 | } 239 | 240 | if(verbose){message("Fitting xgboost model")} 241 | model <- xgboost(data = x, label = y2, nrounds = nrounds_use, verbose = verbose) 242 | 243 | fitted <- ts(c(rep(NA, maxlag), 244 | predict(model, newdata = x)), 245 | frequency = f, start = min(time(origy))) 246 | 247 | # back transform the differencing 248 | if(trend_method == "differencing"){ 249 | for(i in 1:diffs){ 250 | fitted[!is.na(fitted)] <- ts(cumsum(fitted[!is.na(fitted)]), start = start(origy), frequency = f) 251 | } 252 | fitted <- fitted + JDMod(untransformedy[maxlag + 1], lambda = lambda) 253 | } 254 | 255 | # back transform the seasonal adjustment: 256 | if(seas_method == "decompose"){ 257 | fitted <- fitted * decomp$seasonal 258 | } 259 | 260 | 261 | # back transform the modulus power transform: 262 | fitted <- InvJDMod(fitted, lambda = lambda) 263 | 264 | 265 | method <- paste0("xgbar(", maxlag, ", ", diffs, ", ") 266 | 267 | if(f == 1 | seas_method == "none"){ 268 | method <- paste0(method, "'non-seasonal')") 269 | } else { 270 | method <- paste0(method, "'", seas_method, "')") 271 | } 272 | 273 | output <- list( 274 | y = untransformedy, # original scale 275 | y2 = y2, # possibly all three of transformed, differenced and seasonally adjusted 276 | x = x, 277 | model = model, 278 | fitted = fitted, # original scale 279 | maxlag = maxlag, 280 | seas_method = seas_method, 281 | diffs = diffs, 282 | lambda = lambda, 283 | method = method 284 | ) 285 | if(seas_method == "decompose"){ 286 | output$decomp <- decomp 287 | } 288 | 289 | if(seas_method == "fourier" & f != 1){ 290 | output$fx <- fx 291 | output$K <- K 292 | } 293 | 294 | if(!is.null(xreg)){ 295 | output$ origxreg = origxreg 296 | output$ncolxreg <- ncol(origxreg) 297 | } 298 | class(output) <- "xgbar" 299 | return(output) 300 | 301 | } 302 | 303 | #`` @export 304 | xgbts <- function(...){ 305 | warning("xgbts is deprecated terminology and will soon be removed. 306 | Please use xgbar instead.") 307 | xgbar(...) 308 | } 309 | 310 | -------------------------------------------------------------------------------- /pkg/data/Mcomp_results.rda: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/ellisp/forecastxgb-r-package/fe2894aa43a1805b94c881a32f7a5291e53654d6/pkg/data/Mcomp_results.rda -------------------------------------------------------------------------------- /pkg/data/Tcomp_results.rda: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/ellisp/forecastxgb-r-package/fe2894aa43a1805b94c881a32f7a5291e53654d6/pkg/data/Tcomp_results.rda -------------------------------------------------------------------------------- /pkg/data/seaice_ts.rda: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/ellisp/forecastxgb-r-package/fe2894aa43a1805b94c881a32f7a5291e53654d6/pkg/data/seaice_ts.rda -------------------------------------------------------------------------------- /pkg/inst/doc/xgbar.R: -------------------------------------------------------------------------------- 1 | ## ----echo = FALSE, cache = FALSE----------------------------------------- 2 | set.seed(123) 3 | library(knitr) 4 | knit_hooks$set(mypar = function(before, options, envir) { 5 | if (before) par(bty = "l", family = "serif") 6 | }) 7 | opts_chunk$set(comment=NA, fig.width=7, fig.height=5, cache = FALSE, mypar = TRUE) 8 | 9 | ## ----message = FALSE----------------------------------------------------- 10 | library(forecastxgb) 11 | model <- xgbar(gas) 12 | 13 | ## ------------------------------------------------------------------------ 14 | summary(model) 15 | 16 | ## ------------------------------------------------------------------------ 17 | fc <- forecast(model, h = 12) 18 | plot(fc) 19 | 20 | ## ----message = FALSE----------------------------------------------------- 21 | library(fpp) 22 | consumption <- usconsumption[ ,1] 23 | income <- matrix(usconsumption[ ,2], dimnames = list(NULL, "Income")) 24 | consumption_model <- xgbar(y = consumption, xreg = income) 25 | summary(consumption_model) 26 | 27 | ## ------------------------------------------------------------------------ 28 | income_future <- matrix(forecast(xgbar(usconsumption[,2]), h = 10)$mean, 29 | dimnames = list(NULL, "Income")) 30 | plot(forecast(consumption_model, xreg = income_future)) 31 | 32 | ## ----echo = FALSE-------------------------------------------------------- 33 | model1 <- xgbar(co2, seas_method = "dummies") 34 | model2 <- xgbar(co2, seas_method = "decompose") 35 | model3 <- xgbar(co2, seas_method = "fourier") 36 | plot(forecast(model1), main = "Dummy variables for seasonality") 37 | # plot(forecast(model2), main = "Decomposition seasonal adjustment for seasonality") 38 | plot(forecast(model3), main = "Fourier transform pairs as x regressors") 39 | 40 | ## ----echo = FALSE-------------------------------------------------------- 41 | model1 <- xgbar(co2, seas_method = "decompose", lambda = 1) 42 | model2 <- xgbar(co2, seas_method = "decompose", lambda = BoxCox.lambda(co2)) 43 | plot(forecast(model1), main = "No transformation") 44 | plot(forecast(model2), main = "With transformation") 45 | 46 | ## ------------------------------------------------------------------------ 47 | model <- xgbar(AirPassengers, trend_method = "differencing", seas_method = "fourier") 48 | plot(forecast(model, 24)) 49 | 50 | ## ----message = FALSE----------------------------------------------------- 51 | #=============prep====================== 52 | library(Tcomp) 53 | library(foreach) 54 | library(doParallel) 55 | library(forecastxgb) 56 | library(dplyr) 57 | library(ggplot2) 58 | library(scales) 59 | 60 | ## ----eval = FALSE-------------------------------------------------------- 61 | # #============set up cluster for parallel computing=========== 62 | # cluster <- makeCluster(7) # only any good if you have at least 7 processors :) 63 | # registerDoParallel(cluster) 64 | # 65 | # clusterEvalQ(cluster, { 66 | # library(Tcomp) 67 | # library(forecastxgb) 68 | # }) 69 | # 70 | # 71 | # #===============the actual analytical function============== 72 | # competition <- function(collection, maxfors = length(collection)){ 73 | # if(class(collection) != "Mcomp"){ 74 | # stop("This function only works on objects of class Mcomp, eg from the Mcomp or Tcomp packages.") 75 | # } 76 | # nseries <- length(collection) 77 | # mases <- foreach(i = 1:maxfors, .combine = "rbind") %dopar% { 78 | # thedata <- collection[[i]] 79 | # seas_method <- ifelse(frequency(thedata$x) < 6, "dummies", "fourier") 80 | # mod1 <- xgbar(thedata$x, trend_method = "differencing", seas_method = seas_method, lambda = 1, K = 2) 81 | # fc1 <- forecast(mod1, h = thedata$h) 82 | # fc2 <- thetaf(thedata$x, h = thedata$h) 83 | # fc3 <- forecast(auto.arima(thedata$x), h = thedata$h) 84 | # fc4 <- forecast(nnetar(thedata$x), h = thedata$h) 85 | # # copy the skeleton of fc1 over for ensembles: 86 | # fc12 <- fc13 <- fc14 <- fc23 <- fc24 <- fc34 <- fc123 <- fc124 <- fc134 <- fc234 <- fc1234 <- fc1 87 | # # replace the point forecasts with averages of member forecasts: 88 | # fc12$mean <- (fc1$mean + fc2$mean) / 2 89 | # fc13$mean <- (fc1$mean + fc3$mean) / 2 90 | # fc14$mean <- (fc1$mean + fc4$mean) / 2 91 | # fc23$mean <- (fc2$mean + fc3$mean) / 2 92 | # fc24$mean <- (fc2$mean + fc4$mean) / 2 93 | # fc34$mean <- (fc3$mean + fc4$mean) / 2 94 | # fc123$mean <- (fc1$mean + fc2$mean + fc3$mean) / 3 95 | # fc124$mean <- (fc1$mean + fc2$mean + fc4$mean) / 3 96 | # fc134$mean <- (fc1$mean + fc3$mean + fc4$mean) / 3 97 | # fc234$mean <- (fc2$mean + fc3$mean + fc4$mean) / 3 98 | # fc1234$mean <- (fc1$mean + fc2$mean + fc3$mean + fc4$mean) / 4 99 | # mase <- c(accuracy(fc1, thedata$xx)[2, 6], 100 | # accuracy(fc2, thedata$xx)[2, 6], 101 | # accuracy(fc3, thedata$xx)[2, 6], 102 | # accuracy(fc4, thedata$xx)[2, 6], 103 | # accuracy(fc12, thedata$xx)[2, 6], 104 | # accuracy(fc13, thedata$xx)[2, 6], 105 | # accuracy(fc14, thedata$xx)[2, 6], 106 | # accuracy(fc23, thedata$xx)[2, 6], 107 | # accuracy(fc24, thedata$xx)[2, 6], 108 | # accuracy(fc34, thedata$xx)[2, 6], 109 | # accuracy(fc123, thedata$xx)[2, 6], 110 | # accuracy(fc124, thedata$xx)[2, 6], 111 | # accuracy(fc134, thedata$xx)[2, 6], 112 | # accuracy(fc234, thedata$xx)[2, 6], 113 | # accuracy(fc1234, thedata$xx)[2, 6]) 114 | # mase 115 | # } 116 | # message("Finished fitting models") 117 | # colnames(mases) <- c("x", "f", "a", "n", "xf", "xa", "xn", "fa", "fn", "an", 118 | # "xfa", "xfn", "xan", "fan", "xfan") 119 | # return(mases) 120 | # } 121 | 122 | ## ----eval = FALSE-------------------------------------------------------- 123 | # #========Fit models============== 124 | # system.time(t1 <- competition(subset(tourism, "yearly"))) 125 | # system.time(t4 <- competition(subset(tourism, "quarterly"))) 126 | # system.time(t12 <- competition(subset(tourism, "monthly"))) 127 | # 128 | # # shut down cluster to avoid any mess: 129 | # stopCluster(cluster) 130 | 131 | ## ----eval = FALSE-------------------------------------------------------- 132 | # #==============present results================ 133 | # results <- c(apply(t1, 2, mean), 134 | # apply(t4, 2, mean), 135 | # apply(t12, 2, mean)) 136 | # 137 | # results_df <- data.frame(MASE = results) 138 | # results_df$model <- as.character(names(results)) 139 | # periods <- c("Annual", "Quarterly", "Monthly") 140 | # results_df$Frequency <- rep.int(periods, times = c(15, 15, 15)) 141 | # 142 | # best <- results_df %>% 143 | # group_by(model) %>% 144 | # summarise(MASE = mean(MASE)) %>% 145 | # arrange(MASE) %>% 146 | # mutate(Frequency = "Average") 147 | # 148 | # Tcomp_results <- results_df %>% 149 | # rbind(best) %>% 150 | # mutate(model = factor(model, levels = best$model)) %>% 151 | # mutate(Frequency = factor(Frequency, levels = c("Annual", "Average", "Quarterly", "Monthly"))) 152 | 153 | ## ---- fig.width = 8, fig.height = 6-------------------------------------- 154 | leg <- "f: Theta; forecast::thetaf\na: ARIMA; forecast::auto.arima 155 | n: Neural network; forecast::nnetar\nx: Extreme gradient boosting; forecastxgb::xgbar" 156 | 157 | Tcomp_results %>% 158 | ggplot(aes(x = model, y = MASE, colour = Frequency, label = model)) + 159 | geom_text(size = 4) + 160 | geom_line(aes(x = as.numeric(model)), alpha = 0.25) + 161 | scale_y_continuous("Mean scaled absolute error\n(smaller numbers are better)") + 162 | annotate("text", x = 2, y = 3.5, label = leg, hjust = 0) + 163 | ggtitle("Average error of four different timeseries forecasting methods\n2010 Tourism Forecasting Competition data") + 164 | labs(x = "Model, or ensemble of models\n(further to the left means better overall performance)") + 165 | theme_grey(9) 166 | 167 | -------------------------------------------------------------------------------- /pkg/inst/doc/xgbar.Rmd: -------------------------------------------------------------------------------- 1 | --- 2 | title: "Extreme gradient boosting time series forecasting" 3 | author: "Peter Ellis" 4 | date: "26 November 2016" 5 | output: rmarkdown::html_vignette 6 | vignette: > 7 | %\VignetteIndexEntry{Extreme gradient boosting time series forecasting} 8 | %\VignetteEngine{knitr::rmarkdown} 9 | %\VignetteEncoding{UTF-8} 10 | --- 11 | 12 | The `forecastxgb` package provides time series modelling and forecasting functions that combine the machine learning approach of Chen, He and Benesty's [`xgboost`](https://CRAN.R-project.org/package=xgboost) with the convenient handling of time series and familiar API of Rob Hyndman's [`forecast`](http://github.com/robjhyndman/forecast). It applies to time series the Extreme Gradient Boosting proposed in [*Greedy Function Approximation: A Gradient Boosting Machine*, by Jerome Friedman in 2001](http://www.jstor.org/stable/2699986). xgboost has become an important machine learning algorithm; nicely explained in [this accessible documentation](http://xgboost.readthedocs.io/en/latest/model.html). 13 | 14 | **Warning: this package is under active development. The API and default settings should be expected to continue to change.** 15 | 16 | ## Basic usage 17 | 18 | The workhorse function is `xgbar`. This fits a model to a time series. Under the hood, it creates a matrix of explanatory variables based on lagged versions of the response time series, and (optionally) dummy variables of some sort for seasons. That matrix is then fed as the feature set for `xgboost` to do its stuff. 19 | 20 | ```{r echo = FALSE, cache = FALSE} 21 | set.seed(123) 22 | library(knitr) 23 | knit_hooks$set(mypar = function(before, options, envir) { 24 | if (before) par(bty = "l", family = "serif") 25 | }) 26 | opts_chunk$set(comment=NA, fig.width=7, fig.height=5, cache = FALSE, mypar = TRUE) 27 | ``` 28 | 29 | ### Univariate 30 | 31 | Usage with default values is straightforward. Here it is fit to Australian monthly gas production 1956-1995, an example dataset provided in `forecast`: 32 | ```{r message = FALSE} 33 | library(forecastxgb) 34 | model <- xgbar(gas) 35 | ``` 36 | (Note: the "Stopping. Best iteration..." to the screen is produced by `xgboost::xgb.cv`, which uses `cat()` rather than `message()` to print information on its processing.) 37 | 38 | By default, `xgbar` uses row-wise cross-validation to determine the best number of rounds of iterations for the boosting algorithm without overfitting. A final model is then fit on the full available dataset. The relative importance of the various features in the model can be inspected by `importance_xgb()` or, more conveniently, the `summary` method for objects of class `xgbar`. 39 | 40 | 41 | ```{r} 42 | summary(model) 43 | ``` 44 | We see in the case of the gas data that the most important feature in explaining gas production is the production 12 months previously; and then other features decrease in importance from there but still have an impact. 45 | 46 | Forecasting is the main purpose of this package, and a `forecast` method is supplied. The resulting objects are of class `forecast` and familiar generic functions work with them. 47 | 48 | ```{r} 49 | fc <- forecast(model, h = 12) 50 | plot(fc) 51 | ``` 52 | Note that prediction intervals are not currently available. 53 | 54 | ### With external regressors 55 | External regressors can be added by using the `xreg` argument familiar from other forecast functions like `auto.arima` and `nnetar`. `xreg` can be a vector or `ts` object but is easiest to integrate into the analysis if it is a matrix (even a matrix with one column) with well-chosen column names; that way feature names persist meaningfully. 56 | 57 | The example below, with data taken from the `fpp` package supporting Athanasopoulos and Hyndman's [Forecasting Principles and Practice](https://www.otexts.org/fpp) book, shows income being used to explain consumption. In the same way that the response variable `y` is expanded into lagged versions of itself, each column in `xreg` is expanded into lagged versions, which are then treated as individual features for `xgboost`. 58 | 59 | ```{r message = FALSE} 60 | library(fpp) 61 | consumption <- usconsumption[ ,1] 62 | income <- matrix(usconsumption[ ,2], dimnames = list(NULL, "Income")) 63 | consumption_model <- xgbar(y = consumption, xreg = income) 64 | summary(consumption_model) 65 | ``` 66 | We see that the two most important features explaining consumption are the two previous quarters' values of consumption; followed by the income in this quarter; and so on. 67 | 68 | 69 | The challenge of using external regressors in a forecasting environment is that to forecast, you need values of the future external regressors. One way this is sometimes done is by first forecasting the individual regressors. In the example below we do this, making sure the data structure is the same as the original `xreg`. When the new value of `xreg` is given to `forecast`, it forecasts forward the number of rows of the new `xreg`. 70 | ```{r} 71 | income_future <- matrix(forecast(xgbar(usconsumption[,2]), h = 10)$mean, 72 | dimnames = list(NULL, "Income")) 73 | plot(forecast(consumption_model, xreg = income_future)) 74 | ``` 75 | 76 | 77 | ## Advanced usage 78 | The default settings for `xgbar` give reasonable results. The key things that can be changed by the user include: 79 | 80 | - the maximum number of lags to include as explanatory variables. There is a trade-off here, as each number higher this gets, the less rows of data you have. Generally at least two full seasonal cycles are desired, and the default is `max(8, 2 * frequency(y))`. When the data gets very short this value is sometimes forced lower, with a warning. 81 | - the method for choosing the maximum number of boosting iterations. The default is row-wise cross validation, after the matrix of lagged explanatory variables has been created. This is not a traditional approach for cross validation of time series, because the resampling does not preserve the original ordering. However, the presence of the lagged values means this is less of an issue. The main alternative (`nrounds_method = "v"`) is to set aside the final 20% of data and use that for validation of the various numbers of rounds of iterations of the first 80% of training data. Experiments so far suggest that both methods give similar results; if anything the cross-validation method generally recommends a slightly lower number of iterations than does the alternative. 82 | 83 | ## Options 84 | 85 | ### Seasonality 86 | 87 | Currently there are three methods of treating seasonality. 88 | 89 | - The current default method is to throw dummy variables for each season into the mix of features for `xgboost` to work with. 90 | - An alternative is to perform classic multiplicative seasonal adjustment on the series before feeding it to `xgboost`. This seems to work better. 91 | - A third option is to create a set of pairs of Fourier transform variables and use them as x regressors 92 | 93 | ```{r echo = FALSE} 94 | model1 <- xgbar(co2, seas_method = "dummies") 95 | model2 <- xgbar(co2, seas_method = "decompose") 96 | model3 <- xgbar(co2, seas_method = "fourier") 97 | plot(forecast(model1), main = "Dummy variables for seasonality") 98 | # plot(forecast(model2), main = "Decomposition seasonal adjustment for seasonality") 99 | plot(forecast(model3), main = "Fourier transform pairs as x regressors") 100 | ``` 101 | 102 | All methods perform quite poorly at the moment, suffering from the difficulty the default settings have in dealing with non-stationary data (see below). 103 | 104 | ### Transformations 105 | 106 | The data can be transformed by a modulus power transformation (as per John and Draper, 1980) before feeding to `xgboost`. This transformation is similar to a Box-Cox transformation, but works with negative data. Leaving the `lambda` parameter as 1 will effectively switch off this transformation. 107 | ```{r echo = FALSE} 108 | model1 <- xgbar(co2, seas_method = "decompose", lambda = 1) 109 | model2 <- xgbar(co2, seas_method = "decompose", lambda = BoxCox.lambda(co2)) 110 | plot(forecast(model1), main = "No transformation") 111 | plot(forecast(model2), main = "With transformation") 112 | ``` 113 | 114 | Version 0.0.9 of `forecastxgb` gave `lambda` the default value of `BoxCox.lambda(abs(y))`. This returned spectacularly bad forecasting results. Forcing this to be between 0 and 1 helped a little, but still gave very bad results. So far there isn't evidence (but neither is there enough investigation) that a Box Cox transformation helps xgbar do its model fitting at all. 115 | 116 | ### Non-stationarity 117 | From experiments so far, it seems the basic idea of `xgboost` struggles in this context with extrapolation into a new range of variables not in the training set. This suggests better results might be obtained by transforming the series into a stationary one before modelling - a similar approach to that taken by `forecast::auto.arima`. This option is available by `trend_method = "differencing"` and seems to perform well - certainly better than without - and it will probably be made a default setting once more experience is available. 118 | 119 | ```{r} 120 | model <- xgbar(AirPassengers, trend_method = "differencing", seas_method = "fourier") 121 | plot(forecast(model, 24)) 122 | ``` 123 | 124 | 125 | ## Future developments 126 | Future work might include: 127 | 128 | * additional automated time-dependent features (eg dummy variables for trading days, Easter, etc) 129 | * ability to include xreg values that don't get lagged 130 | * some kind of automated multiple variable forecasting, similar to a vector-autoregression. 131 | * better choices of defaults for values such as `lambda` (for power transformations), `K` (for Fourier transforms) and, most likely to be effective, `maxlag`. 132 | 133 | ## Tourism forecasting competition 134 | Here is a more substantive example. I use the 1,311 datasets from the 2010 Tourism Forecasting Competition described in 135 | in [Athanasopoulos et al (2011)](http://robjhyndman.com/papers/forecompijf.pdf), originally in the International Journal of Forecasting (2011) 27(3), 822-844. The data are available in the CRAN package [Tcomp](https://cran.r-project.org/package=Tcomp). Each data object is a list, with elements inlcuding `x` (the original training data), `h` (the forecasting period) and `xx` (the test data of length `h`). Only univariate time series are included. 136 | 137 | To give the `xgbar` model a good test, I am going to compare its performance in forecasting the 1,311 `xx` time series from the matching `x` series with three other modelling approaches: 138 | 139 | - Auto-regressive integrated moving average (ARIMA) 140 | - Theta 141 | - Neural networks 142 | 143 | Those three are all from Rob Hyndman's `forecast` package. I am also going to look at the performance of ensembles of the four model types. With all combinations this means 15 models in total. 144 | 145 | Because all four models use the `forecast` paradigm it is relatively straightforward to structure the analysis. The code below is a little repetitive but should be fairly transparent. Because of the scale and the embarrassingly parallel nature of the work (ie no particular reason to do it in any particular order, so easy to split into tasks for different processes to do in parallel), I use `foreach` and `doParallel` to make the best use of my 8 logical processors. The code below sets up a cluster for the parallel computing and a function `competition` which will work on any object of class `Mcomp`, which `Tcomp` inherits from the `Mcomp` package providing the first three "M" forecasting competition data collections. 146 | 147 | ```{r message = FALSE} 148 | #=============prep====================== 149 | library(Tcomp) 150 | library(foreach) 151 | library(doParallel) 152 | library(forecastxgb) 153 | library(dplyr) 154 | library(ggplot2) 155 | library(scales) 156 | ``` 157 | ```{r eval = FALSE} 158 | #============set up cluster for parallel computing=========== 159 | cluster <- makeCluster(7) # only any good if you have at least 7 processors :) 160 | registerDoParallel(cluster) 161 | 162 | clusterEvalQ(cluster, { 163 | library(Tcomp) 164 | library(forecastxgb) 165 | }) 166 | 167 | 168 | #===============the actual analytical function============== 169 | competition <- function(collection, maxfors = length(collection)){ 170 | if(class(collection) != "Mcomp"){ 171 | stop("This function only works on objects of class Mcomp, eg from the Mcomp or Tcomp packages.") 172 | } 173 | nseries <- length(collection) 174 | mases <- foreach(i = 1:maxfors, .combine = "rbind") %dopar% { 175 | thedata <- collection[[i]] 176 | seas_method <- ifelse(frequency(thedata$x) < 6, "dummies", "fourier") 177 | mod1 <- xgbar(thedata$x, trend_method = "differencing", seas_method = seas_method, lambda = 1, K = 2) 178 | fc1 <- forecast(mod1, h = thedata$h) 179 | fc2 <- thetaf(thedata$x, h = thedata$h) 180 | fc3 <- forecast(auto.arima(thedata$x), h = thedata$h) 181 | fc4 <- forecast(nnetar(thedata$x), h = thedata$h) 182 | # copy the skeleton of fc1 over for ensembles: 183 | fc12 <- fc13 <- fc14 <- fc23 <- fc24 <- fc34 <- fc123 <- fc124 <- fc134 <- fc234 <- fc1234 <- fc1 184 | # replace the point forecasts with averages of member forecasts: 185 | fc12$mean <- (fc1$mean + fc2$mean) / 2 186 | fc13$mean <- (fc1$mean + fc3$mean) / 2 187 | fc14$mean <- (fc1$mean + fc4$mean) / 2 188 | fc23$mean <- (fc2$mean + fc3$mean) / 2 189 | fc24$mean <- (fc2$mean + fc4$mean) / 2 190 | fc34$mean <- (fc3$mean + fc4$mean) / 2 191 | fc123$mean <- (fc1$mean + fc2$mean + fc3$mean) / 3 192 | fc124$mean <- (fc1$mean + fc2$mean + fc4$mean) / 3 193 | fc134$mean <- (fc1$mean + fc3$mean + fc4$mean) / 3 194 | fc234$mean <- (fc2$mean + fc3$mean + fc4$mean) / 3 195 | fc1234$mean <- (fc1$mean + fc2$mean + fc3$mean + fc4$mean) / 4 196 | mase <- c(accuracy(fc1, thedata$xx)[2, 6], 197 | accuracy(fc2, thedata$xx)[2, 6], 198 | accuracy(fc3, thedata$xx)[2, 6], 199 | accuracy(fc4, thedata$xx)[2, 6], 200 | accuracy(fc12, thedata$xx)[2, 6], 201 | accuracy(fc13, thedata$xx)[2, 6], 202 | accuracy(fc14, thedata$xx)[2, 6], 203 | accuracy(fc23, thedata$xx)[2, 6], 204 | accuracy(fc24, thedata$xx)[2, 6], 205 | accuracy(fc34, thedata$xx)[2, 6], 206 | accuracy(fc123, thedata$xx)[2, 6], 207 | accuracy(fc124, thedata$xx)[2, 6], 208 | accuracy(fc134, thedata$xx)[2, 6], 209 | accuracy(fc234, thedata$xx)[2, 6], 210 | accuracy(fc1234, thedata$xx)[2, 6]) 211 | mase 212 | } 213 | message("Finished fitting models") 214 | colnames(mases) <- c("x", "f", "a", "n", "xf", "xa", "xn", "fa", "fn", "an", 215 | "xfa", "xfn", "xan", "fan", "xfan") 216 | return(mases) 217 | } 218 | ``` 219 | 220 | Applying this function to the three different subsets of tourism data (by different frequency) is straightforward but takes a few minutes to run: 221 | 222 | ```{r eval = FALSE} 223 | #========Fit models============== 224 | system.time(t1 <- competition(subset(tourism, "yearly"))) 225 | system.time(t4 <- competition(subset(tourism, "quarterly"))) 226 | system.time(t12 <- competition(subset(tourism, "monthly"))) 227 | 228 | # shut down cluster to avoid any mess: 229 | stopCluster(cluster) 230 | ``` 231 | 232 | The `competition` function returns the mean absolute scaled error (MASE) of every model combination for every dataset. The following code creates a summary object from the objects `t1`, `t4` and `t12` that hold those individual results: 233 | 234 | ```{r eval = FALSE} 235 | #==============present results================ 236 | results <- c(apply(t1, 2, mean), 237 | apply(t4, 2, mean), 238 | apply(t12, 2, mean)) 239 | 240 | results_df <- data.frame(MASE = results) 241 | results_df$model <- as.character(names(results)) 242 | periods <- c("Annual", "Quarterly", "Monthly") 243 | results_df$Frequency <- rep.int(periods, times = c(15, 15, 15)) 244 | 245 | best <- results_df %>% 246 | group_by(model) %>% 247 | summarise(MASE = mean(MASE)) %>% 248 | arrange(MASE) %>% 249 | mutate(Frequency = "Average") 250 | 251 | Tcomp_results <- results_df %>% 252 | rbind(best) %>% 253 | mutate(model = factor(model, levels = best$model)) %>% 254 | mutate(Frequency = factor(Frequency, levels = c("Annual", "Average", "Quarterly", "Monthly"))) 255 | ``` 256 | 257 | The resulting object, `Tcomp_results`, is provided with the `forecastxgb` package. Visual inspection shows that the average values of MASE provided for the Theta and ARIMA models match those in the [`Tcomp` vignette](https://cran.r-project.org/web/packages/Tcomp/vignettes/tourism-comp.html). The results are easiest to understand graphically. 258 | 259 | ```{r, fig.width = 8, fig.height = 6} 260 | leg <- "f: Theta; forecast::thetaf\na: ARIMA; forecast::auto.arima 261 | n: Neural network; forecast::nnetar\nx: Extreme gradient boosting; forecastxgb::xgbar" 262 | 263 | Tcomp_results %>% 264 | ggplot(aes(x = model, y = MASE, colour = Frequency, label = model)) + 265 | geom_text(size = 4) + 266 | geom_line(aes(x = as.numeric(model)), alpha = 0.25) + 267 | scale_y_continuous("Mean scaled absolute error\n(smaller numbers are better)") + 268 | annotate("text", x = 2, y = 3.5, label = leg, hjust = 0) + 269 | ggtitle("Average error of four different timeseries forecasting methods\n2010 Tourism Forecasting Competition data") + 270 | labs(x = "Model, or ensemble of models\n(further to the left means better overall performance)") + 271 | theme_grey(9) 272 | ``` 273 | 274 | 275 | We see the overall best performing ensemble is the average of the Theta and ARIMA models - the two from the more traditional timeseries forecasting approach. The two machine learning methods (neural network and extreme gradient boosting) are not as effective, at least in these implementations. As individual methods, they are the two weakest, although the extreme gradient boosting method provided in `forecastxgb` performs noticeably better than `forecast::nnetar` for the annual and quarterly data. 276 | 277 | Theta by itself is the best performing with the annual data - simple methods work well when the dataset is small and highly aggregate. The best that can be said of the `xgbar` approach in this context is that it doesn't damage the Theta method much when included in a combination - several of the better performing ensembles have `xgbar` as one of their members. In contrast, the neural network models do badly with this collection of annual data. 278 | 279 | Adding `auto.arima` and `xgbar` to an ensemble of quarterly or monthly data definitely improves on Theta by itself. The best performing single model for quarterly or monthly data is `auto.arima` followed by `thetaf`. Again, neural networks are the poorest of the four individual models. 280 | 281 | Overall, I conclude that with univariate data, `xgbar` has little to add to an ensemble that already contains `auto.arima` and `thetaf` (or - not shown - the closely related `ets`). I believe however that inclusion of `xreg` external regressors would shift the balance in favour of `xgbar` and maybe even `nnetar` - the more complex and larger the dataset, the better the chance that these methods will have something to offer. If and when I find a large collection of timeseries competition data with external regressors I will probably add a second vignette, or at least a blog post at [http://ellisp.github.io](http://ellisp.github.io). -------------------------------------------------------------------------------- /pkg/man/Mcomp_results.Rd: -------------------------------------------------------------------------------- 1 | % Generated by roxygen2: do not edit by hand 2 | % Please edit documentation in R/extras.R 3 | \docType{data} 4 | \name{Mcomp_results} 5 | \alias{Mcomp_results} 6 | \title{M3 forecasting results} 7 | \format{A data frame with 75 rows and three columns.} 8 | \usage{ 9 | Mcomp_results 10 | } 11 | \description{ 12 | Summary data from four models, and 11 combinations of models, against the data from the M3 forecasting competition. 13 | } 14 | \details{ 15 | Full details are in the vignette of how a similar series with tourism competition data was generated. 16 | The data shows the average mean absolute scaled error 17 | (MASE) from using \code{xgbar} (x), \code{auto.arima} (a), \code{nnetar} (n) and \code{thetaf} (f) to 18 | generate forecasts of 3,003 data series from a range of sectors, in the M3 forecasting competition. 19 | 20 | \itemize{ 21 | \item MASE A mean mean absolute squared error 22 | \item model model, or ensemble of models, to which the MASE applies 23 | \item Frequency The frequency of the subset of data from which the mean MASE was calculated. 24 | } 25 | } 26 | \examples{ 27 | if(require(ggplot2)){ 28 | leg <- "f: Theta; forecast::thetaf\\na: ARIMA; forecast::auto.arima 29 | n: Neural network; forecast::nnetar\\nx: Extreme gradient boosting; forecastxgb::xgbar" 30 | 31 | ggplot(Mcomp_results, aes(x = model, y = MASE, colour = Frequency, label = model)) + 32 | geom_text(size = 4) + 33 | geom_line(aes(x = as.numeric(model)), alpha = 0.25) + 34 | annotate("text", x = 2, y = 3.5, label = leg, hjust = 0) + 35 | ggtitle("Average error of four different timeseries forecasting methods 36 | M3 Forecasting Competition data") + 37 | labs(x = "Model, or ensemble of models 38 | (further to the left means better overall performance)", 39 | y = "Mean scaled absolute error\\n(smaller numbers are better)") + 40 | theme_grey(9) 41 | } 42 | } 43 | \author{ 44 | Peter Ellis 45 | } 46 | \keyword{datasets} 47 | -------------------------------------------------------------------------------- /pkg/man/Tcomp_results.Rd: -------------------------------------------------------------------------------- 1 | % Generated by roxygen2: do not edit by hand 2 | % Please edit documentation in R/extras.R 3 | \docType{data} 4 | \name{Tcomp_results} 5 | \alias{Tcomp_results} 6 | \title{Tourism forecasting results} 7 | \format{A data frame with 60 rows and three columns.} 8 | \usage{ 9 | Tcomp_results 10 | } 11 | \description{ 12 | Summary data from four models, and 11 combinations of models, against the data from the 2010 tourism forecasting competition. 13 | } 14 | \details{ 15 | Full details of how this was generated are in the Vignette. This shows the average mean absolute scaled error 16 | (MASE) from using \code{xgbar} (x), \code{auto.arima} (a), \code{nnetar} (n) and \code{thetaf} (f) to generate forecasts of 1,311 tourism data series. 17 | 18 | \itemize{ 19 | \item MASE A mean mean absolute squared error 20 | \item model model, or ensemble of models, to which the MASE applies 21 | \item Frequency The frequency of the subset of data from which the mean MASE was calculated. 22 | } 23 | } 24 | \examples{ 25 | if(require(ggplot2)){ 26 | leg <- "f: Theta; forecast::thetaf\\na: ARIMA; forecast::auto.arima 27 | n: Neural network; forecast::nnetar\\nx: Extreme gradient boosting; forecastxgb::xgbar" 28 | 29 | ggplot(Tcomp_results, aes(x = model, y = MASE, colour = Frequency, label = model)) + 30 | geom_text(size = 4) + 31 | geom_line(aes(x = as.numeric(model)), alpha = 0.25) + 32 | annotate("text", x = 2, y = 3.5, label = leg, hjust = 0) + 33 | ggtitle("Average error of four different timeseries forecasting methods 34 | 2010 Tourism Forecasting Competition data") + 35 | labs(x = "Model, or ensemble of models 36 | (further to the left means better overall performance)", 37 | y = "Mean scaled absolute error\\n(smaller numbers are better)") + 38 | theme_grey(9) 39 | } 40 | } 41 | \author{ 42 | Peter Ellis 43 | } 44 | \keyword{datasets} 45 | -------------------------------------------------------------------------------- /pkg/man/forecast.xgbar.Rd: -------------------------------------------------------------------------------- 1 | % Generated by roxygen2: do not edit by hand 2 | % Please edit documentation in R/forecast.xgbar.R 3 | \name{forecast.xgbar} 4 | \alias{forecast.xgbar} 5 | \title{Forecasting using xgboost models} 6 | \usage{ 7 | \method{forecast}{xgbar}(object, h = NULL, xreg = NULL, ...) 8 | } 9 | \arguments{ 10 | \item{object}{An object of class "\code{xgbar}". Usually the result of a call to \code{\link{xgbar}}.} 11 | 12 | \item{h}{Number of periods for forecasting. If \code{xreg} is provided, the number of rows of \code{xreg} will be 13 | used and \code{h} is ignored with a warning. If both \code{h} and \code{xreg} are \code{NULL} then 14 | \code{h = ifelse(frequency(object$y) > 1, 2 * frequency(object$y), 10)}} 15 | 16 | \item{xreg}{Future values of regression variables.} 17 | 18 | \item{...}{Ignored.} 19 | } 20 | \value{ 21 | An object of class \code{forecast} 22 | } 23 | \description{ 24 | Returns forecasts and other information for xgboost timeseries modesl fit with \code{xbgts} 25 | } 26 | \examples{ 27 | # Australian monthly gas production 28 | gas_model <- xgbar(gas) 29 | summary(gas_model) 30 | gas_fc <- forecast(gas_model, h = 12) 31 | plot(gas_fc) 32 | } 33 | \seealso{ 34 | \code{\link{xgbar}}, \code{\link[forecast]{forecast}} 35 | } 36 | \author{ 37 | Peter Ellis 38 | } 39 | -------------------------------------------------------------------------------- /pkg/man/forecastxgb-package.Rd: -------------------------------------------------------------------------------- 1 | % Generated by roxygen2: do not edit by hand 2 | % Please edit documentation in R/forecastxgb.R 3 | \docType{package} 4 | \name{forecastxgb-package} 5 | \alias{forecastxgb} 6 | \alias{forecastxgb-package} 7 | \title{Extreme gradient boosting time series forecasting} 8 | \description{ 9 | The \code{forecastxgb} package provides time series modelling and forecasting functions that combine 10 | the machine learning approach of Chen, He and Benesty's \code{xgboost} 11 | with the convenient handling of time series and familiar API of Rob Hyndman's \code{forecast}. 12 | } 13 | \details{ 14 | It applies to time series the Extreme Gradient Boosting proposed in \emph{Greedy Function Approximation: A 15 | Gradient Boosting Machine, by Jermoe Friedman in 2001} (http://www.jstor.org/stable/2699986). 16 | } 17 | \author{ 18 | \strong{Maintainer}: Peter Ellis \email{peter.ellis2013nz@gmail.com} 19 | 20 | } 21 | -------------------------------------------------------------------------------- /pkg/man/plot.xgbar.Rd: -------------------------------------------------------------------------------- 1 | % Generated by roxygen2: do not edit by hand 2 | % Please edit documentation in R/extras.R 3 | \name{plot.xgbar} 4 | \alias{plot.xgbar} 5 | \title{Plot xgbar object} 6 | \usage{ 7 | \method{plot}{xgbar}(x, ...) 8 | } 9 | \arguments{ 10 | \item{x}{An object created by \code{xgbar}} 11 | 12 | \item{...}{Additional arguments passed through to \code{plot()}} 13 | } 14 | \description{ 15 | plot method for an object created by xgbar 16 | } 17 | \examples{ 18 | model <- xgbar(AirPassengers) 19 | plot(model) 20 | } 21 | \seealso{ 22 | \code{\link{xgbar}} 23 | } 24 | \author{ 25 | Peter Ellis 26 | } 27 | -------------------------------------------------------------------------------- /pkg/man/seaice_ts.Rd: -------------------------------------------------------------------------------- 1 | % Generated by roxygen2: do not edit by hand 2 | % Please edit documentation in R/misc-doc.R 3 | \docType{data} 4 | \name{seaice_ts} 5 | \alias{seaice_ts} 6 | \title{Arctic sea ice} 7 | \format{An object of class \code{ts} of length 10647.} 8 | \source{ 9 | National Snow and Ice Data Center, \url{https://nsidc.org/data/docs/noaa/g02135_seaice_index/#daily_data_files"} 10 | } 11 | \usage{ 12 | seaice_ts 13 | } 14 | \description{ 15 | Extent in millions of square kilometres of sea ice in the Arctic from 21 August 1987 to 24 November 2016. 16 | } 17 | \examples{ 18 | plot(seaice_ts) 19 | } 20 | \keyword{datasets} 21 | -------------------------------------------------------------------------------- /pkg/man/summary.xgbar.Rd: -------------------------------------------------------------------------------- 1 | % Generated by roxygen2: do not edit by hand 2 | % Please edit documentation in R/extras.R 3 | \name{summary.xgbar} 4 | \alias{summary.xgbar} 5 | \alias{print.summary.xgbar} 6 | \title{Summary of an xgbar object} 7 | \usage{ 8 | \method{summary}{xgbar}(object, ...) 9 | } 10 | \arguments{ 11 | \item{object}{An object created by \code{\link{xgbar}}} 12 | 13 | \item{...}{Ignored.} 14 | } 15 | \description{ 16 | summary method for an object created by xgbar 17 | } 18 | \examples{ 19 | \dontrun{ 20 | # Half-hourly electricity demand in England and Wales, takes a few minutes 21 | electricity_model <- xgbar(taylor) 22 | summary(electricity_model) 23 | electricity_fc <- forecast(electricity_model, h = 500) 24 | plot(electricity_fc) 25 | } 26 | } 27 | \seealso{ 28 | \code{\link{xgbar}} 29 | } 30 | \author{ 31 | Peter Ellis 32 | } 33 | -------------------------------------------------------------------------------- /pkg/man/xgbar.Rd: -------------------------------------------------------------------------------- 1 | % Generated by roxygen2: do not edit by hand 2 | % Please edit documentation in R/xgbar.R 3 | \name{xgbar} 4 | \alias{xgbar} 5 | \alias{xgbts} 6 | \title{xgboost time series modelling} 7 | \usage{ 8 | xgbar(y, xreg = NULL, maxlag = max(8, 2 * frequency(y)), nrounds = 100, 9 | nrounds_method = c("cv", "v", "manual"), nfold = ifelse(length(y) > 30, 10 | 10, 5), lambda = 1, verbose = FALSE, seas_method = c("dummies", 11 | "decompose", "fourier", "none"), K = max(1, min(round(f/4 - 1), 10)), 12 | trend_method = c("none", "differencing"), ...) 13 | } 14 | \arguments{ 15 | \item{y}{A univariate time series.} 16 | 17 | \item{xreg}{Optionally, a vector or matrix of external regressors, which must have the same number of rows as y.} 18 | 19 | \item{maxlag}{The maximum number of lags of \code{y} and \code{xreg} (if included) to be considered as features.} 20 | 21 | \item{nrounds}{Maximum number of iterations \code{xgboost} will perform. If \code{nrounds_method = 'cv'}, 22 | the value of \code{nrounds} passed to \code{xgboost} is chosen by cross-validation; if it is \code{'v'} 23 | then the value of \code{nrounds} passed to \code{xgboost} is chosen by splitting the data into a training 24 | set (first 80 per cent) and test set (20 per cent) and choosing the number of iterations with the best value. 25 | If \code{nrounds_method = 'manual'} then \code{nrounds} iterations will be performed - unless you have chosen 26 | it carefully this is likely to lead to overfitting and poor forecasts.} 27 | 28 | \item{nrounds_method}{Method used to determine the value of nrounds actually given for \code{xgboost} for 29 | the final model. Options are \code{"cv"} for row-wise cross-validation, \code{"v"} for validation on a testing 30 | set of the most recent 20 per cent of data, \code{"manual"} in which case \code{nrounds} is passed through directly.} 31 | 32 | \item{nfold}{Number of equal size subsamples during cross validation, used if \code{nrounds_method = 'cv'}.} 33 | 34 | \item{lambda}{Value of lambda to be used for modulus power transformation of \code{y} (which is similar to Box-Cox transformation 35 | but works with negative values too), performed before using xgboost (and inverse transformed to the original scale afterwards). 36 | Set \code{lambda = 1} if no transformation is desired. 37 | The transformation is only applied to \code{y}, not \code{xreg}.} 38 | 39 | \item{verbose}{Passed on to \code{xgboost} and \code{xgb.cv}.} 40 | 41 | \item{seas_method}{Method for dealing with seasonality.} 42 | 43 | \item{K}{if \code{seas_method == 'fourier'}, the value of \code{K} passed through to \code{fourier} for order of Fourier series to be generated as seasonal regressor variables.} 44 | 45 | \item{trend_method}{How should the \code{xgboost} try to deal with trends? Currently the only options to \code{none} is 46 | \code{auto.arima}-style \code{differencing}, which is based on successive KPSS tests until there is no significant evidence the 47 | remaining series is non-stationary.} 48 | 49 | \item{...}{Additional arguments passed to \code{xgboost}. Only works if nrounds_method is "cv" or "manual".} 50 | } 51 | \value{ 52 | An object of class \code{xgbar}. These have a \code{forecast} method and are generally 53 | expected to be used in a way such as \code{forecast(my_xgbar_model, h = 24)}. But the \code{xgbar} 54 | object itself can be of use in model checking and diagnosis. It is list with the following elements: 55 | \describe{ 56 | \item{\code{y}}{The original value of \code{y} fed to \code{xgbar}} 57 | \item{\code{y2}}{\code{y} except for its first \code{maxlag} values. } 58 | \item{\code{x}}{The features used by \code{xgboost} to model \code{y2}. \code{x} is basically 59 | a matrix of numbers created by the automated feature generation of \code{xgbar}, in particular 60 | the differencing (if asked for), seasonal adjustment (if asked for), and creation of lagged 61 | values. If \code{y} is univariate, 62 | \code{x} will be just the lagged values of \code{y} and will have \code{length(y) - maxlag} rows 63 | and \code{maxlag} columns. If \code{xreg} was supplied, \code{x} will have \code{maxlag * (ncol(xreg) + 1)} 64 | columns - a set of columns for the lagged values of y, and a set of columns for each lagged value 65 | of the xreg matrix.} 66 | \item{\code{model}}{Object of class \code{xgb.Booster} returned by \code{xgboost}. The actual 67 | xgboost model that regressed \code{y2} on \code{x}.} 68 | \item{\code{fitted}}{Fitted values of \code{y}. The first \code{maxlag} values will be \code{NA}. 69 | The remainder are the predicted values of the xgboost regression of \code{y2} on \code{x}.} 70 | \item{\code{maxlag}}{The original user-supplied value of \code{maxlag}, stored for future use by 71 | \code{forecast.xgbar}.} 72 | \item{\code{seas_method}}{The original user-supplied value of \code{seas_method}, stored for future use by 73 | \code{forecast.xgbar}.} 74 | \item{\code{diffs}}{The number of rounds of differencing applied to y to make it stationary, if 75 | \code{trend_method = "differencing"} was used.} 76 | \item{\code{lambda}}{The original user-supplied value of \code{lambda} for modulus transformation, 77 | stored for future use by \code{forecast.xgbar}.} 78 | \item{\code{method}}{A character string summarising the key arguments to xgbar, of the structure 79 | \code{xgbar(maxlag, diffs, seas_method)}.} 80 | \item{\code{origxreg}}{The original user-supplied value of \code{origxreg}, 81 | stored for future use by \code{forecast.xgbar} (needed to create future values of lagged \code{xreg} 82 | for the forecast period) .} 83 | \item{code{ncolxreg}}{The number of columns in the original \code{xreg} matrix.} 84 | \item{\code{decomp}}{If \code{seas_method = "decompose"} was used, this will be a list of the output 85 | from \code{decompose}, which decomposes y (called \code{x} by \code{decompose}) into seasonal, trend 86 | and random components.} 87 | } 88 | } 89 | \description{ 90 | Fit a model to a time series using xgboost 91 | } 92 | \details{ 93 | This is the workhorse function for the \code{forecastxgb} package. 94 | It fits a model to a time series. Under the hood, it creates a matrix of explanatory variables 95 | based on lagged versions of the response time series, and (optionally) dummy variables (simple hot one encoding, or Fourier transforms) for seasons. That 96 | matrix is then fed as the feature set for \code{xgboost} to do its stuff. 97 | } 98 | \examples{ 99 | # Univariate example - quarterly production of woolen yarn in Australia 100 | woolmod <- xgbar(woolyrnq) 101 | summary(woolmod) 102 | plot(woolmod) 103 | fc <- forecast(woolmod, h = 8) 104 | plot(fc) 105 | 106 | # Bivariate example - quarterly income and consumption in the US 107 | if(require(fpp)){ 108 | consumption <- usconsumption[ ,1] 109 | income <- matrix(usconsumption[ ,2], dimnames = list(NULL, "Income")) 110 | consumption_model <- xgbar(y = consumption, xreg = income) 111 | summary(consumption_model) 112 | } 113 | } 114 | \references{ 115 | J. A. John and N. R. Draper (1980), "An Alternative Family of Transformations", \emph{Journal of the Royal Statistical 116 | Society}. 117 | } 118 | \seealso{ 119 | \code{\link{summary.xgbar}}, \code{\link{plot.xgbar}}, \code{\link{forecast.xgbar}}, \code{\link{xgbar_importance}}, 120 | \code{\link[xgboost]{xgboost}}. 121 | } 122 | \author{ 123 | Peter Ellis 124 | } 125 | -------------------------------------------------------------------------------- /pkg/man/xgbar_importance.Rd: -------------------------------------------------------------------------------- 1 | % Generated by roxygen2: do not edit by hand 2 | % Please edit documentation in R/extras.R 3 | \name{xgbar_importance} 4 | \alias{xgbar_importance} 5 | \title{Show importance of features in a xgbar model} 6 | \usage{ 7 | xgbar_importance(object, ...) 8 | } 9 | \arguments{ 10 | \item{object}{An object of class \code{xgbar}, usually created with \code{xgbar()}} 11 | 12 | \item{...}{Extra parameters passed through to \code{xgb.importance}} 13 | } 14 | \value{ 15 | A \code{data.table} of the features used in the model with their average gain 16 | (and their weight for boosted tree model) in the model. 17 | } 18 | \description{ 19 | This is a light wrapper for \code{xgboost::xbg.importance} to make it easier to use with objects of class \code{xgbar} 20 | } 21 | \seealso{ 22 | \code{\link[xgboost]{xgb.importance}}, \code{\link{summary.xgbar}}, \code{\link{xgbar}}. 23 | } 24 | \author{ 25 | Peter Ellis 26 | } 27 | -------------------------------------------------------------------------------- /pkg/pkg.Rproj: -------------------------------------------------------------------------------- 1 | Version: 1.0 2 | 3 | RestoreWorkspace: No 4 | SaveWorkspace: No 5 | AlwaysSaveHistory: Default 6 | 7 | EnableCodeIndexing: Yes 8 | Encoding: UTF-8 9 | 10 | AutoAppendNewline: Yes 11 | StripTrailingWhitespace: Yes 12 | 13 | BuildType: Package 14 | PackageUseDevtools: Yes 15 | PackageInstallArgs: --no-multiarch --with-keep.source 16 | PackageRoxygenize: rd,collate,namespace 17 | -------------------------------------------------------------------------------- /pkg/tests/testthat.R: -------------------------------------------------------------------------------- 1 | library(testthat) 2 | library(forecastxgb) 3 | 4 | test_check("forecastxgb") 5 | -------------------------------------------------------------------------------- /pkg/tests/testthat/test-correct-classes.R: -------------------------------------------------------------------------------- 1 | 2 | #=================seasonal===================== 3 | fc1 <- forecast(AirPassengers, level = FALSE) 4 | object <- xgbar(AirPassengers, maxlag = 30) 5 | fc2 <- forecast(object) 6 | 7 | 8 | expect_identical(fc1$x, fc2$x) 9 | expect_identical(class(fc1$x), class(fc2$x)) 10 | expect_identical(class(fc1$mean), class(fc2$mean)) 11 | expect_identical(frequency(fc1$mean), frequency(fc2$mean)) 12 | 13 | 14 | #=================non-seasonal================ 15 | fc1 <- forecast(Nile, level = FALSE) 16 | object <- xgbar(Nile, maxlag = 30) 17 | fc2 <- forecast(object) 18 | 19 | expect_identical(fc1$x, fc2$x) 20 | expect_identical(class(fc1$x), class(fc2$x)) 21 | expect_identical(class(fc1$mean), class(fc2$mean)) 22 | expect_identical(frequency(fc1$mean), frequency(fc2$mean)) 23 | 24 | 25 | -------------------------------------------------------------------------------- /pkg/tests/testthat/test-irregular-seasons.R: -------------------------------------------------------------------------------- 1 | 2 | test_that("differencing and decompose work togetherwith data with an irregular set of seasons", { 3 | y <- subset(Tcomp::tourism, "quarterly")[[36]]$x 4 | expect_error(mod1 <- xgbar(y, trend_method = "differencing", seas_method = "decompose"), NA) 5 | plot(forecast(mod1)) 6 | }) 7 | -------------------------------------------------------------------------------- /pkg/tests/testthat/test-modulus-transform.R: -------------------------------------------------------------------------------- 1 | 2 | test_that("Modulus transform and inverse work", { 3 | lambda <- BoxCox.lambda(AirPassengers) 4 | trans1 <- JDMod(AirPassengers, lambda = lambda) 5 | trans2 <- BoxCox(AirPassengers, lambda = lambda) # should be similar, not identical 6 | expect_lt(accuracy(trans1, trans2)[ ,"RMSE"], 0.002) 7 | 8 | return1 <- InvJDMod(trans1, lambda = lambda) 9 | expect_equal(AirPassengers, return1) 10 | }) 11 | 12 | test_that("Modulus transform works with negative and zero data", { 13 | y <- ts(round(rnorm(100), 1)) 14 | lambda <- BoxCox.lambda(abs(y)) 15 | expect_error(trans1 <- JDMod(y, lambda = lambda), NA) 16 | expect_error(return1 <- InvJDMod(trans1, lambda = lambda), NA) 17 | expect_equal(y, return1) 18 | }) 19 | 20 | test_that("Modulus transform works when lambda = 1 or 0",{ 21 | y <- ts(round(rnorm(100), 1)) 22 | expect_equal(y, JDMod(y, lambda = 1)) 23 | expect_equal(log(AirPassengers + 1), JDMod(AirPassengers, lambda = 0)) 24 | 25 | }) 26 | -------------------------------------------------------------------------------- /pkg/tests/testthat/test-ok-noninteger-frequency.R: -------------------------------------------------------------------------------- 1 | 2 | 3 | test_that("xgbar can fit models to time series with a non-integer frequency", { 4 | expect_error(model1 <- xgbar(seaice_ts, seas_method = "dummies"), NA) 5 | expect_error(model2 <- xgbar(seaice_ts, seas_method = "decompose"), NA) 6 | expect_error(model3 <- xgbar(seaice_ts, seas_method = "none"), NA) 7 | expect_error(model4 <- xgbar(seaice_ts, seas_method = "fourier", maxlag = 50), NA) 8 | expect_error(fc1 <- forecast(model1, h = 100), NA) 9 | expect_error(fc2 <- forecast(model2, h = 100), NA) 10 | expect_error(fc3 <- forecast(model2, h = 100), NA) 11 | expect_error(fc4 <- forecast(model2, h = 100), NA) 12 | }) 13 | 14 | 15 | -------------------------------------------------------------------------------- /pkg/tests/testthat/test-seasonal-methods.R: -------------------------------------------------------------------------------- 1 | 2 | test_that("different seasonal methods give different results", { 3 | y <- AirPassengers 4 | 5 | 6 | set.seed(123) 7 | obj1 <- xgbar(y, seas_method = "dummies") 8 | set.seed(123) 9 | obj2 <- xgbar(y, seas_method = "dummie") 10 | set.seed(123) 11 | obj3 <- xgbar(y, seas_method = "decompose") 12 | expect_equal(obj1, obj2) 13 | expect_false(isTRUE(all.equal(obj1, obj3))) 14 | expect_lt(accuracy(obj3$fitted, obj2$fitted)[ , "RMSE"], 8) 15 | }) -------------------------------------------------------------------------------- /pkg/tests/testthat/test-shorter-monthly-data.R: -------------------------------------------------------------------------------- 1 | 2 | test_that("works with series of 35 with frequency 12", { 3 | y <- ts(runif(35, min = 5000, max = 10000), start = c(2013, 12), frequency = 12) 4 | expect_error(bla_1_XGB_model <- xgbar(y = y), NA) 5 | }) -------------------------------------------------------------------------------- /pkg/tests/testthat/test-utils.R: -------------------------------------------------------------------------------- 1 | 2 | test_that("lagv produces the correct lagged matrix", { 3 | m <- cbind(6:10, 5:9, 4:8, 3:7, 2:6, 1:5) 4 | colnames(m) <- c("x", "x_lag1", "x_lag2", "x_lag3", "x_lag4", "x_lag5") 5 | x <- 1:10 6 | expect_equal(m, lagv(x, maxlag = 5)) 7 | }) 8 | 9 | 10 | test_that("lagvm produces the correct lagged matrix", { 11 | m <- cbind(3:4, 2:3, 1:2, 13:14, 12:13, 11:12) 12 | colnames(m) <- c("A_lag0", "A_lag1", "A_lag2", "B_lag0", "B_lag1","B_lag2") 13 | test <- cbind(1:4, 11:14) 14 | colnames(test) <- c("A", "B") 15 | expect_equal(m, lagvm(test, maxlag = 2)) 16 | }) 17 | 18 | -------------------------------------------------------------------------------- /pkg/tests/testthat/test-works-range-data.R: -------------------------------------------------------------------------------- 1 | 2 | 3 | test_that("works with larger high frequency data", { 4 | # electricity_model <- xgbar(taylor) 5 | # electricity_fc <- forecast(electricity_model, 500) 6 | # plot(electricity_fc) 7 | 8 | }) -------------------------------------------------------------------------------- /pkg/tests/testthat/tests-different-maxlags.R: -------------------------------------------------------------------------------- 1 | test_that("forecast works with maxlag = 1", { 2 | mod <- xgbar(Nile, maxlag = 1) 3 | expect_error(fc <- forecast(mod, h = 10), NA) 4 | }) 5 | 6 | 7 | test_that("forecast works with maxlag = 12", { 8 | mod <- xgbar(AirPassengers, maxlag = 12) 9 | expect_error(fc <- forecast(mod, h = 10), NA) 10 | }) 11 | 12 | 13 | test_that("forecast works with maxlag = 36", { 14 | mod <- xgbar(AirPassengers, maxlag = 36) 15 | expect_error(fc <- forecast(mod, h = 10), NA) 16 | }) 17 | 18 | 19 | 20 | test_that("forecast works with maxlag = 50", { 21 | mod <- xgbar(AirPassengers, maxlag = 36) 22 | expect_error(fc <- forecast(mod, h = 10), NA) 23 | }) 24 | 25 | -------------------------------------------------------------------------------- /pkg/vignettes/xgbar.Rmd: -------------------------------------------------------------------------------- 1 | --- 2 | title: "Extreme gradient boosting time series forecasting" 3 | author: "Peter Ellis" 4 | date: "26 November 2016" 5 | output: rmarkdown::html_vignette 6 | vignette: > 7 | %\VignetteIndexEntry{Extreme gradient boosting time series forecasting} 8 | %\VignetteEngine{knitr::rmarkdown} 9 | %\VignetteEncoding{UTF-8} 10 | --- 11 | 12 | The `forecastxgb` package provides time series modelling and forecasting functions that combine the machine learning approach of Chen, He and Benesty's [`xgboost`](https://CRAN.R-project.org/package=xgboost) with the convenient handling of time series and familiar API of Rob Hyndman's [`forecast`](http://github.com/robjhyndman/forecast). It applies to time series the Extreme Gradient Boosting proposed in [*Greedy Function Approximation: A Gradient Boosting Machine*, by Jerome Friedman in 2001](http://www.jstor.org/stable/2699986). xgboost has become an important machine learning algorithm; nicely explained in [this accessible documentation](http://xgboost.readthedocs.io/en/latest/model.html). 13 | 14 | **Warning: this package is under active development. The API and default settings should be expected to continue to change.** 15 | 16 | ## Basic usage 17 | 18 | The workhorse function is `xgbar`. This fits a model to a time series. Under the hood, it creates a matrix of explanatory variables based on lagged versions of the response time series, and (optionally) dummy variables of some sort for seasons. That matrix is then fed as the feature set for `xgboost` to do its stuff. 19 | 20 | ```{r echo = FALSE, cache = FALSE} 21 | set.seed(123) 22 | library(knitr) 23 | knit_hooks$set(mypar = function(before, options, envir) { 24 | if (before) par(bty = "l", family = "serif") 25 | }) 26 | opts_chunk$set(comment=NA, fig.width=7, fig.height=5, cache = FALSE, mypar = TRUE) 27 | ``` 28 | 29 | ### Univariate 30 | 31 | Usage with default values is straightforward. Here it is fit to Australian monthly gas production 1956-1995, an example dataset provided in `forecast`: 32 | ```{r message = FALSE} 33 | library(forecastxgb) 34 | model <- xgbar(gas) 35 | ``` 36 | (Note: the "Stopping. Best iteration..." to the screen is produced by `xgboost::xgb.cv`, which uses `cat()` rather than `message()` to print information on its processing.) 37 | 38 | By default, `xgbar` uses row-wise cross-validation to determine the best number of rounds of iterations for the boosting algorithm without overfitting. A final model is then fit on the full available dataset. The relative importance of the various features in the model can be inspected by `importance_xgb()` or, more conveniently, the `summary` method for objects of class `xgbar`. 39 | 40 | 41 | ```{r} 42 | summary(model) 43 | ``` 44 | We see in the case of the gas data that the most important feature in explaining gas production is the production 12 months previously; and then other features decrease in importance from there but still have an impact. 45 | 46 | Forecasting is the main purpose of this package, and a `forecast` method is supplied. The resulting objects are of class `forecast` and familiar generic functions work with them. 47 | 48 | ```{r} 49 | fc <- forecast(model, h = 12) 50 | plot(fc) 51 | ``` 52 | Note that prediction intervals are not currently available. 53 | 54 | ### With external regressors 55 | External regressors can be added by using the `xreg` argument familiar from other forecast functions like `auto.arima` and `nnetar`. `xreg` can be a vector or `ts` object but is easiest to integrate into the analysis if it is a matrix (even a matrix with one column) with well-chosen column names; that way feature names persist meaningfully. 56 | 57 | The example below, with data taken from the `fpp` package supporting Athanasopoulos and Hyndman's [Forecasting Principles and Practice](https://www.otexts.org/fpp) book, shows income being used to explain consumption. In the same way that the response variable `y` is expanded into lagged versions of itself, each column in `xreg` is expanded into lagged versions, which are then treated as individual features for `xgboost`. 58 | 59 | ```{r message = FALSE} 60 | library(fpp) 61 | consumption <- usconsumption[ ,1] 62 | income <- matrix(usconsumption[ ,2], dimnames = list(NULL, "Income")) 63 | consumption_model <- xgbar(y = consumption, xreg = income) 64 | summary(consumption_model) 65 | ``` 66 | We see that the two most important features explaining consumption are the two previous quarters' values of consumption; followed by the income in this quarter; and so on. 67 | 68 | 69 | The challenge of using external regressors in a forecasting environment is that to forecast, you need values of the future external regressors. One way this is sometimes done is by first forecasting the individual regressors. In the example below we do this, making sure the data structure is the same as the original `xreg`. When the new value of `xreg` is given to `forecast`, it forecasts forward the number of rows of the new `xreg`. 70 | ```{r} 71 | income_future <- matrix(forecast(xgbar(usconsumption[,2]), h = 10)$mean, 72 | dimnames = list(NULL, "Income")) 73 | plot(forecast(consumption_model, xreg = income_future)) 74 | ``` 75 | 76 | 77 | ## Advanced usage 78 | The default settings for `xgbar` give reasonable results. The key things that can be changed by the user include: 79 | 80 | - the maximum number of lags to include as explanatory variables. There is a trade-off here, as each number higher this gets, the less rows of data you have. Generally at least two full seasonal cycles are desired, and the default is `max(8, 2 * frequency(y))`. When the data gets very short this value is sometimes forced lower, with a warning. 81 | - the method for choosing the maximum number of boosting iterations. The default is row-wise cross validation, after the matrix of lagged explanatory variables has been created. This is not a traditional approach for cross validation of time series, because the resampling does not preserve the original ordering. However, the presence of the lagged values means this is less of an issue. The main alternative (`nrounds_method = "v"`) is to set aside the final 20% of data and use that for validation of the various numbers of rounds of iterations of the first 80% of training data. Experiments so far suggest that both methods give similar results; if anything the cross-validation method generally recommends a slightly lower number of iterations than does the alternative. 82 | 83 | ## Options 84 | 85 | ### Seasonality 86 | 87 | Currently there are three methods of treating seasonality. 88 | 89 | - The current default method is to throw dummy variables for each season into the mix of features for `xgboost` to work with. 90 | - An alternative is to perform classic multiplicative seasonal adjustment on the series before feeding it to `xgboost`. This seems to work better. 91 | - A third option is to create a set of pairs of Fourier transform variables and use them as x regressors 92 | 93 | ```{r echo = FALSE} 94 | model1 <- xgbar(co2, seas_method = "dummies") 95 | model2 <- xgbar(co2, seas_method = "decompose") 96 | model3 <- xgbar(co2, seas_method = "fourier") 97 | plot(forecast(model1), main = "Dummy variables for seasonality") 98 | plot(forecast(model2), main = "Decomposition seasonal adjustment for seasonality") 99 | plot(forecast(model3), main = "Fourier transform pairs as x regressors") 100 | ``` 101 | 102 | All methods perform quite poorly at the moment, suffering from the difficulty the default settings have in dealing with non-stationary data (see below). 103 | 104 | ### Transformations 105 | 106 | The data can be transformed by a modulus power transformation (as per John and Draper, 1980) before feeding to `xgboost`. This transformation is similar to a Box-Cox transformation, but works with negative data. Leaving the `lambda` parameter as 1 will effectively switch off this transformation. 107 | ```{r echo = FALSE} 108 | model1 <- xgbar(co2, seas_method = "decompose", lambda = 1) 109 | model2 <- xgbar(co2, seas_method = "decompose", lambda = BoxCox.lambda(co2)) 110 | plot(forecast(model1), main = "No transformation") 111 | plot(forecast(model2), main = "With transformation") 112 | ``` 113 | 114 | Version 0.0.9 of `forecastxgb` gave `lambda` the default value of `BoxCox.lambda(abs(y))`. This returned spectacularly bad forecasting results. Forcing this to be between 0 and 1 helped a little, but still gave very bad results. So far there isn't evidence (but neither is there enough investigation) that a Box Cox transformation helps xgbar do its model fitting at all. 115 | 116 | ### Non-stationarity 117 | From experiments so far, it seems the basic idea of `xgboost` struggles in this context with extrapolation into a new range of variables not in the training set. This suggests better results might be obtained by transforming the series into a stationary one before modelling - a similar approach to that taken by `forecast::auto.arima`. This option is available by `trend_method = "differencing"` and seems to perform well - certainly better than without - and it will probably be made a default setting once more experience is available. 118 | 119 | ```{r} 120 | model <- xgbar(AirPassengers, trend_method = "differencing", seas_method = "fourier") 121 | plot(forecast(model, 24)) 122 | ``` 123 | 124 | 125 | ## Future developments 126 | Future work might include: 127 | 128 | * additional automated time-dependent features (eg dummy variables for trading days, Easter, etc) 129 | * ability to include xreg values that don't get lagged 130 | * some kind of automated multiple variable forecasting, similar to a vector-autoregression. 131 | * better choices of defaults for values such as `lambda` (for power transformations), `K` (for Fourier transforms) and, most likely to be effective, `maxlag`. 132 | 133 | ## Tourism forecasting competition 134 | Here is a more substantive example. I use the 1,311 datasets from the 2010 Tourism Forecasting Competition described in 135 | in [Athanasopoulos et al (2011)](http://robjhyndman.com/papers/forecompijf.pdf), originally in the International Journal of Forecasting (2011) 27(3), 822-844. The data are available in the CRAN package [Tcomp](https://cran.r-project.org/package=Tcomp). Each data object is a list, with elements inlcuding `x` (the original training data), `h` (the forecasting period) and `xx` (the test data of length `h`). Only univariate time series are included. 136 | 137 | To give the `xgbar` model a good test, I am going to compare its performance in forecasting the 1,311 `xx` time series from the matching `x` series with three other modelling approaches: 138 | 139 | - Auto-regressive integrated moving average (ARIMA) 140 | - Theta 141 | - Neural networks 142 | 143 | Those three are all from Rob Hyndman's `forecast` package. I am also going to look at the performance of ensembles of the four model types. With all combinations this means 15 models in total. 144 | 145 | Because all four models use the `forecast` paradigm it is relatively straightforward to structure the analysis. The code below is a little repetitive but should be fairly transparent. Because of the scale and the embarrassingly parallel nature of the work (ie no particular reason to do it in any particular order, so easy to split into tasks for different processes to do in parallel), I use `foreach` and `doParallel` to make the best use of my 8 logical processors. The code below sets up a cluster for the parallel computing and a function `competition` which will work on any object of class `Mcomp`, which `Tcomp` inherits from the `Mcomp` package providing the first three "M" forecasting competition data collections. 146 | 147 | ```{r message = FALSE} 148 | #=============prep====================== 149 | library(Tcomp) 150 | library(foreach) 151 | library(doParallel) 152 | library(forecastxgb) 153 | library(dplyr) 154 | library(ggplot2) 155 | library(scales) 156 | ``` 157 | ```{r eval = FALSE} 158 | #============set up cluster for parallel computing=========== 159 | cluster <- makeCluster(7) # only any good if you have at least 7 processors :) 160 | registerDoParallel(cluster) 161 | 162 | clusterEvalQ(cluster, { 163 | library(Tcomp) 164 | library(forecastxgb) 165 | }) 166 | 167 | 168 | #===============the actual analytical function============== 169 | competition <- function(collection, maxfors = length(collection)){ 170 | if(class(collection) != "Mcomp"){ 171 | stop("This function only works on objects of class Mcomp, eg from the Mcomp or Tcomp packages.") 172 | } 173 | nseries <- length(collection) 174 | mases <- foreach(i = 1:maxfors, .combine = "rbind") %dopar% { 175 | thedata <- collection[[i]] 176 | seas_method <- ifelse(frequency(thedata$x) < 6, "dummies", "fourier") 177 | mod1 <- xgbar(thedata$x, trend_method = "differencing", seas_method = seas_method, lambda = 1, K = 2) 178 | fc1 <- forecast(mod1, h = thedata$h) 179 | fc2 <- thetaf(thedata$x, h = thedata$h) 180 | fc3 <- forecast(auto.arima(thedata$x), h = thedata$h) 181 | fc4 <- forecast(nnetar(thedata$x), h = thedata$h) 182 | # copy the skeleton of fc1 over for ensembles: 183 | fc12 <- fc13 <- fc14 <- fc23 <- fc24 <- fc34 <- fc123 <- fc124 <- fc134 <- fc234 <- fc1234 <- fc1 184 | # replace the point forecasts with averages of member forecasts: 185 | fc12$mean <- (fc1$mean + fc2$mean) / 2 186 | fc13$mean <- (fc1$mean + fc3$mean) / 2 187 | fc14$mean <- (fc1$mean + fc4$mean) / 2 188 | fc23$mean <- (fc2$mean + fc3$mean) / 2 189 | fc24$mean <- (fc2$mean + fc4$mean) / 2 190 | fc34$mean <- (fc3$mean + fc4$mean) / 2 191 | fc123$mean <- (fc1$mean + fc2$mean + fc3$mean) / 3 192 | fc124$mean <- (fc1$mean + fc2$mean + fc4$mean) / 3 193 | fc134$mean <- (fc1$mean + fc3$mean + fc4$mean) / 3 194 | fc234$mean <- (fc2$mean + fc3$mean + fc4$mean) / 3 195 | fc1234$mean <- (fc1$mean + fc2$mean + fc3$mean + fc4$mean) / 4 196 | mase <- c(accuracy(fc1, thedata$xx)[2, 6], 197 | accuracy(fc2, thedata$xx)[2, 6], 198 | accuracy(fc3, thedata$xx)[2, 6], 199 | accuracy(fc4, thedata$xx)[2, 6], 200 | accuracy(fc12, thedata$xx)[2, 6], 201 | accuracy(fc13, thedata$xx)[2, 6], 202 | accuracy(fc14, thedata$xx)[2, 6], 203 | accuracy(fc23, thedata$xx)[2, 6], 204 | accuracy(fc24, thedata$xx)[2, 6], 205 | accuracy(fc34, thedata$xx)[2, 6], 206 | accuracy(fc123, thedata$xx)[2, 6], 207 | accuracy(fc124, thedata$xx)[2, 6], 208 | accuracy(fc134, thedata$xx)[2, 6], 209 | accuracy(fc234, thedata$xx)[2, 6], 210 | accuracy(fc1234, thedata$xx)[2, 6]) 211 | mase 212 | } 213 | message("Finished fitting models") 214 | colnames(mases) <- c("x", "f", "a", "n", "xf", "xa", "xn", "fa", "fn", "an", 215 | "xfa", "xfn", "xan", "fan", "xfan") 216 | return(mases) 217 | } 218 | ``` 219 | 220 | Applying this function to the three different subsets of tourism data (by different frequency) is straightforward but takes a few minutes to run: 221 | 222 | ```{r eval = FALSE} 223 | #========Fit models============== 224 | system.time(t1 <- competition(subset(tourism, "yearly"))) 225 | system.time(t4 <- competition(subset(tourism, "quarterly"))) 226 | system.time(t12 <- competition(subset(tourism, "monthly"))) 227 | 228 | # shut down cluster to avoid any mess: 229 | stopCluster(cluster) 230 | ``` 231 | 232 | The `competition` function returns the mean absolute scaled error (MASE) of every model combination for every dataset. The following code creates a summary object from the objects `t1`, `t4` and `t12` that hold those individual results: 233 | 234 | ```{r eval = FALSE} 235 | #==============present results================ 236 | results <- c(apply(t1, 2, mean), 237 | apply(t4, 2, mean), 238 | apply(t12, 2, mean)) 239 | 240 | results_df <- data.frame(MASE = results) 241 | results_df$model <- as.character(names(results)) 242 | periods <- c("Annual", "Quarterly", "Monthly") 243 | results_df$Frequency <- rep.int(periods, times = c(15, 15, 15)) 244 | 245 | best <- results_df %>% 246 | group_by(model) %>% 247 | summarise(MASE = mean(MASE)) %>% 248 | arrange(MASE) %>% 249 | mutate(Frequency = "Average") 250 | 251 | Tcomp_results <- results_df %>% 252 | rbind(best) %>% 253 | mutate(model = factor(model, levels = best$model)) %>% 254 | mutate(Frequency = factor(Frequency, levels = c("Annual", "Average", "Quarterly", "Monthly"))) 255 | ``` 256 | 257 | The resulting object, `Tcomp_results`, is provided with the `forecastxgb` package. Visual inspection shows that the average values of MASE provided for the Theta and ARIMA models match those in the [`Tcomp` vignette](https://cran.r-project.org/web/packages/Tcomp/vignettes/tourism-comp.html). The results are easiest to understand graphically. 258 | 259 | ```{r, fig.width = 8, fig.height = 6} 260 | leg <- "f: Theta; forecast::thetaf\na: ARIMA; forecast::auto.arima 261 | n: Neural network; forecast::nnetar\nx: Extreme gradient boosting; forecastxgb::xgbar" 262 | 263 | Tcomp_results %>% 264 | ggplot(aes(x = model, y = MASE, colour = Frequency, label = model)) + 265 | geom_text(size = 4) + 266 | geom_line(aes(x = as.numeric(model)), alpha = 0.25) + 267 | scale_y_continuous("Mean scaled absolute error\n(smaller numbers are better)") + 268 | annotate("text", x = 2, y = 3.5, label = leg, hjust = 0) + 269 | ggtitle("Average error of four different timeseries forecasting methods\n2010 Tourism Forecasting Competition data") + 270 | labs(x = "Model, or ensemble of models\n(further to the left means better overall performance)") + 271 | theme_grey(9) 272 | ``` 273 | 274 | 275 | We see the overall best performing ensemble is the average of the Theta and ARIMA models - the two from the more traditional timeseries forecasting approach. The two machine learning methods (neural network and extreme gradient boosting) are not as effective, at least in these implementations. As individual methods, they are the two weakest, although the extreme gradient boosting method provided in `forecastxgb` performs noticeably better than `forecast::nnetar` for the annual and quarterly data. 276 | 277 | Theta by itself is the best performing with the annual data - simple methods work well when the dataset is small and highly aggregate. The best that can be said of the `xgbar` approach in this context is that it doesn't damage the Theta method much when included in a combination - several of the better performing ensembles have `xgbar` as one of their members. In contrast, the neural network models do badly with this collection of annual data. 278 | 279 | Adding `auto.arima` and `xgbar` to an ensemble of quarterly or monthly data definitely improves on Theta by itself. The best performing single model for quarterly or monthly data is `auto.arima` followed by `thetaf`. Again, neural networks are the poorest of the four individual models. 280 | 281 | Overall, I conclude that with univariate data, `xgbar` has little to add to an ensemble that already contains `auto.arima` and `thetaf` (or - not shown - the closely related `ets`). I believe however that inclusion of `xreg` external regressors would shift the balance in favour of `xgbar` and maybe even `nnetar` - the more complex and larger the dataset, the better the chance that these methods will have something to offer. If and when I find a large collection of timeseries competition data with external regressors I will probably add a second vignette, or at least a blog post at [http://ellisp.github.io](http://ellisp.github.io). -------------------------------------------------------------------------------- /prep/get-seaice-data.R: -------------------------------------------------------------------------------- 1 | # This script gets the example Arctic sea ice data 2 | library(dplyr) 3 | library(testthat) 4 | library(lubridate) 5 | 6 | mon <- c("Jan", "Feb", "Mar", "Apr", "May", "Jun", "Jul", "Aug", "Sep", "Oct", "Nov", "Dec") 7 | 8 | # https://nsidc.org/data/docs/noaa/g02135_seaice_index/#daily_data_files 9 | 10 | # This is the latest incomplete year's "near real time" data: 11 | download.file("ftp://sidads.colorado.edu/DATASETS/NOAA/G02135/north/daily/data/NH_seaice_extent_nrt_v2.csv", 12 | destfile = "seaice_nrt.csv") 13 | 14 | # And this is the earlier, fully definitive years' data 15 | download.file("ftp://sidads.colorado.edu/DATASETS/NOAA/G02135/north/daily/data/NH_seaice_extent_final_v2.csv", 16 | destfile = "seaice_final.csv") 17 | 18 | seaice_nrt <- read.csv("seaice_nrt.csv", skip = 2, header = FALSE)[ , 1:5] 19 | seaice_final <- read.csv("seaice_final.csv", skip = 2, header = FALSE)[ , 1:5] 20 | 21 | seaice <- rbind(seaice_final, seaice_nrt) 22 | names(seaice) <- c("year", "month", "day", "extent", "missing") 23 | expect_equal(sum(seaice$missing == 0), nrow(seaice)) 24 | 25 | seaice <- seaice %>% 26 | mutate(date = as.Date(paste(year, month, day, sep = "-"))) %>% 27 | group_by(month) %>% 28 | mutate(monthday = month + day / max(day)) %>% 29 | ungroup() %>% 30 | mutate(month = factor(month, labels = mon)) %>% 31 | arrange(year, month, day) %>% 32 | mutate(timediff = c(NA, diff(date)), 33 | dayofyear = yday(date)) %>% 34 | filter(timediff == 1) 35 | 36 | 37 | 38 | seaice_ts <- ts(seaice$extent, frequency = 365.25, start = c(1987, 233)) 39 | save(seaice_ts, file = "pkg/data/seaice_ts.rda") 40 | 41 | # clean up (unless you want to keep the csvs) 42 | unlink("seaice_nrt.csv") 43 | unlink("seaice_final.csv") --------------------------------------------------------------------------------