├── __init__.py ├── README.md ├── regimechange.py └── readme.ipynb /__init__.py: -------------------------------------------------------------------------------- 1 | from .regimechange import * 2 | 3 | __all__ = ['kernel_split', 'successive_split', 'METRICS', 'KERNELS'] 4 | -------------------------------------------------------------------------------- /README.md: -------------------------------------------------------------------------------- 1 | 2 | # DETECTING REGIME CHANGES WITH KERNELS 3 | 4 | This package contains tools for the local, semi-parametric detection of regime changes in a bivariate time series setting. Regime changes can be defined with respect to a given bivariate mapping (eg. correlation, tracking error) and a kernel weighting parameter that controls the fidelity of the estimator to local changes. 5 | 6 | 7 | ```python 8 | import regimechange as rg 9 | ``` 10 | 11 | The `METRICS` dictionary contains a set of pre-defined metric functions that define a state change. 12 | 13 | 14 | ```python 15 | print('Pre-defined metrics include: ' + ', '.join(rg.METRICS.keys()) + '.') 16 | ``` 17 | 18 | Pre-defined metrics include: excess return, excess volatility, correlation, tracking error. 19 | 20 | 21 | The `KERNELS` dictionary contains a set of pre-defined kernels that control sensitivity to local information. 22 | 23 | 24 | ```python 25 | print('Pre-defined kernels include: ' + ', '.join(rg.KERNELS.keys()) + '.') 26 | ``` 27 | 28 | Pre-defined kernels include: hyperbolic, gaussian, triangular, uniform. 29 | 30 | 31 | The Gaussian and Uniform (aka k-nearest-neighbor) kernels are well known. We provide the other two for completeness. The hyperbolic kernel $\kappa_h:\mathbb{R}^n\times\mathbb{R}^n \mapsto \mathbb{R}_{++}$ with bandwidth $b$ is of the form 32 | 33 | $$\kappa_h(x, y) = \left(\frac{1}{1 + \|x - y\|}\right)^{b}$$ 34 | 35 | while the triangular kernel $\kappa_t:\mathbb{R}^n\times\mathbb{R}^n \mapsto \mathbb{R}_{++}$ with bandwidth $b$ is of the form 36 | 37 | $$\kappa_t(x, y) = \left(1 - \frac{\|x - y\|}{b} \right)_+$$ 38 | 39 | ### Usage 40 | 41 | We demonstrate the use of this package and its effectiveness in the following examples. 42 | 43 | 44 | ```python 45 | from matplotlib import pyplot as plt 46 | import regimechange as rg 47 | import numpy as np 48 | 49 | plt.style.use('ggplot') 50 | %matplotlib inline 51 | ``` 52 | 53 | Consider a discrete regime change that occurs in with respect to the Pearson correlation coefficient. Specifically, we'll generate data where one time series is almost perfectly correlated with the other and then, at day 68, the correlation flips signs. 54 | 55 | 56 | ```python 57 | benchmark = np.random.normal(size=(100,1)) # some benchmark index 58 | tracking = benchmark.copy() + .5*np.random.normal(size=(100,1)) # fund tracking benchmark 59 | tracking[68:] = -1*tracking[68:] # flip relationship at day 68 60 | 61 | plt.figure(figsize=(12, 6)) 62 | plt.axvline(x=68, color = 'orange', label='regime change', linewidth=3) 63 | plt.plot(np.cumsum(benchmark), label='benchmark index', linewidth=2) 64 | plt.plot(np.cumsum(tracking), label='tracking fund', linestyle='--') 65 | plt.legend() 66 | plt.show() 67 | ``` 68 | 69 | 70 | ![correlation_regime](https://cloud.githubusercontent.com/assets/13667067/25038748/0b48b722-20b5-11e7-88de-0bf85c061fcd.png) 71 | 72 | 73 | We can estimate when this regime change occurred using the `kernel_split` method: 74 | 75 | 76 | ```python 77 | data = np.hstack((benchmark, tracking)) 78 | rg.kernel_split( 79 | time_series=data, 80 | metric=rg.METRICS['correlation'], 81 | kernel=rg.KERNELS['uniform'], 82 | bandwidth=25, 83 | pad=1 84 | ) 85 | ``` 86 | 87 | 88 | 89 | 90 | (68, 1.8800332588540651) 91 | 92 | 93 | 94 | Suppose there are multiple correlation regime changes. 95 | 96 | 97 | ```python 98 | data = np.vstack((data, data)) 99 | 100 | plt.figure(figsize=(12, 6)) 101 | plt.axvline(x=68, color = 'orange', label='regime change 1', linewidth=3) 102 | plt.axvline(x=100, color = 'purple', label='regime change 2', linewidth=3) 103 | plt.axvline(x=169, color = 'green', label='regime change 2', linewidth=3) 104 | plt.plot(np.cumsum(data[:, 0]), label='benchmark index', linewidth=2) 105 | plt.plot(np.cumsum(data[:, 1]), label='tracking fund', linestyle='--') 106 | plt.legend() 107 | plt.show() 108 | ``` 109 | 110 | 111 | ![multiple correlation regimes](https://cloud.githubusercontent.com/assets/13667067/25038750/0b693d6c-20b5-11e7-9b10-790c004daf96.png) 112 | 113 | 114 | For detecting these several regime changes, we can turn to the `successive_split` method which implements some regime change mechanism (like `kernel_split`) recursively. For this, we'll need a univariate function that outputs the location of a regime change such as the following. 115 | 116 | 117 | ```python 118 | ks = lambda time_series: rg.kernel_split( 119 | time_series, 120 | metric=rg.METRICS['correlation'], 121 | kernel=rg.KERNELS['triangular'], 122 | bandwidth=25, 123 | pad=1 124 | ) 125 | ``` 126 | 127 | Then we can run the `successive_split` method, specifying a hypothesis number of splits in the argument `num_splits`. The `successive_split` method works by identifying a regime change, dividing the time series into two partitions, then re-performing detection recursively on each partition. By this logic, $\mathcal{O}\left(2^{\lceil \log_2(n) \rceil}\right)$ regime changes will be computed and the top $n$ most drastic estimated regime changes will be returned, where $n$ represents `num_splits`. Better results are thus obtained by choosing a conservatively high `num_splits` so that enough exploration takes place before the results are ranked. 128 | 129 | For this case, we'll set `num_splits` to 5, an upper bound for how many regimes we expect to have in the data. 130 | 131 | 132 | ```python 133 | rg.successive_split( 134 | time_series=data, 135 | kernel_splitter=ks, 136 | num_splits=5 137 | ) 138 | ``` 139 | 140 | 141 | 142 | 143 | [(168, 1.9005015889472829), 144 | (68, 1.9005015889472827), 145 | (100, 1.8256333481430742), 146 | (31, 0.095901802064368602), 147 | (131, 0.095901802064368602)] 148 | 149 | 150 | 151 | As can be seen, the three regime changes are identified and ranked at the top with large values while the latter two returned items have significantly lower values, signifying that a regime change likely did not occur at those times. 152 | 153 | Another example is with the metric tracking error. We'll generate data where one time series tracks the other well then suddenly tracks poorly starting on day 40. 154 | 155 | 156 | ```python 157 | benchmark = np.random.normal(size=(100,1)) # some benchmark index 158 | tracking = benchmark.copy() + .5*np.random.normal(size=(100,1)) # fund tracking benchmark 159 | tracking[40:] = tracking[40:] + np.random.normal(size=(60,1)) # tracking error blows up at day 40 160 | 161 | plt.figure(figsize=(12, 6)) 162 | plt.axvline(x=41, color = 'orange', label='regime change', linewidth=3) 163 | plt.plot(np.cumsum(benchmark), label='benchmark index', linewidth=2) 164 | plt.plot(np.cumsum(tracking), label='tracking fund', linestyle='--') 165 | plt.legend() 166 | plt.show() 167 | ``` 168 | 169 | 170 | ![tracking error](https://cloud.githubusercontent.com/assets/13667067/25038749/0b65c880-20b5-11e7-9b2f-a67707b91785.png) 171 | 172 | 173 | We can again estimate when this regime change occurred using the `kernel_split` method: 174 | 175 | 176 | ```python 177 | data = np.hstack((benchmark, tracking)) 178 | rg.kernel_split( 179 | time_series=data, 180 | metric=rg.METRICS['tracking error'], 181 | kernel=rg.KERNELS['gaussian'], 182 | bandwidth=10 183 | ) 184 | ``` 185 | 186 | 187 | 188 | 189 | (41, 0.58183784971618535) 190 | 191 | 192 | 193 | ### Speed Test 194 | 195 | 196 | ```python 197 | %timeit rg.kernel_split(\ 198 | time_series=data,\ 199 | metric=rg.METRICS['tracking error'],\ 200 | kernel=rg.KERNELS['hyperbolic'],\ 201 | bandwidth=10,\ 202 | pad=1\ 203 | ) 204 | ``` 205 | 206 | 100 loops, best of 3: 16.6 ms per loop 207 | 208 | -------------------------------------------------------------------------------- /regimechange.py: -------------------------------------------------------------------------------- 1 | """Local, semi-parametric methods for identifying when discrete regime 2 | changes have occurred in a bivariate time series setting.""" 3 | 4 | from operator import add 5 | import numpy as np 6 | from scipy.stats import norm as gaussian 7 | 8 | METRICS = { # library of common metrics which define a state change 9 | 'correlation': lambda ts, w: _weighted_corr(ts[:, 0], ts[:, 1], w), 10 | 'tracking error': lambda ts, w: _weighted_std(ts[:, 0] - ts[:, 1], w), 11 | 'excess return': lambda ts, w: np.average(ts[:, 0] - ts[:, 1], weights=w), 12 | 'excess volatility': lambda ts, w: _weighted_2ndmom(ts[:, 0] - ts[:, 1], w) 13 | } 14 | 15 | KERNELS = { # library of kernels for estimating local regime changes 16 | 'gaussian': lambda age, bw: gaussian.pdf(range(age), scale=bw), 17 | 'hyperbolic': lambda age, bw: 1/np.arange(1, age+1)**(1/bw), 18 | 'triangular': lambda age, bw: np.maximum(0, 1-(1/bw)*np.arange(age)), 19 | 'uniform': lambda age, bw: np.array([1]*min(int(bw), age) + \ 20 | [0]*max(0, age-int(bw))) 21 | } 22 | 23 | def _weighted_2ndmom(array, weights): 24 | """Weighted uncentralized second moment.""" 25 | 26 | weighted_var = np.average(array**2, weights=weights) 27 | return np.sqrt(weighted_var) 28 | 29 | def _weighted_std(array, weights): 30 | """Weighted standard deviation.""" 31 | 32 | weighted_mean = np.average(array, weights=weights) 33 | weighted_var = np.average((array - weighted_mean)**2, weights=weights) 34 | return np.sqrt((array.shape[0]/(array.shape[0]-1)) * weighted_var) 35 | 36 | def _weighted_corr(array_x, array_y, weights): 37 | """Weighted standard deviation.""" 38 | 39 | mean_x = np.average(array_x, weights=weights) 40 | mean_y = np.average(array_y, weights=weights) 41 | 42 | rss_x = np.linalg.norm(np.sqrt(weights)*(array_x - mean_x), 2) 43 | rss_y = np.linalg.norm(np.sqrt(weights)*(array_y - mean_y), 2) 44 | 45 | inner_prod = (array_x - mean_x).T.dot(weights * (array_y - mean_y)) 46 | 47 | return inner_prod/(rss_x * rss_y) 48 | 49 | def kernel_split(time_series, metric, kernel, bandwidth=10, pad=1): 50 | """Detection of some instantaneous, potentially local state change. 51 | 52 | Given a bivariate time series, metric defining a state change, and 53 | a weighting kernel controling fidelity to local information, 54 | estimates the date at which a regime change has occurred with respect 55 | to the provided metric. Specifically, the function returns the date a 56 | the new regime begins. 57 | 58 | @arg {np.array} time_series 2D array containing time series data 59 | with dates in ascending order along 60 | axis 0 and covariates along axis 1. 61 | 62 | @arg {function} metric A metric of interest that will define 63 | the state change between the two time 64 | series. 65 | 66 | @arg {np.array} Bivariate time series; same format as 67 | time_series above. Will be used as 68 | data for which metric is calculated. 69 | 70 | @arg {np.array} Flat np.array of same length as 71 | previous argument; used to weight 72 | observations in calculation of metric 73 | of interest. 74 | 75 | @arg {float} The metric of interest returned as a 76 | scalar. 77 | 78 | @arg {function} kernel A kernel of defining fidelity to 79 | local regime changes. 80 | 81 | @arg {int} The length of the sequence of weights 82 | outputted by the kernel function. 83 | 84 | @arg {float} Bandwidth controlling fidelity of 85 | the kernel to local information. 86 | 87 | @return {np.array} Array of positive floats defining 88 | sequence of (typically decaying) 89 | kernel weights. Need not be 90 | normalized as kernel_split method 91 | will perform the normalization 92 | internally. 93 | 94 | @arg {float} bandwidth Kernel bandwidth to be passed to the 95 | supplied kernel function. Forced to 96 | be be greater than or equal to two so 97 | that statistical estimators of 98 | correlation and standard deviation 99 | have sufficient degrees of freedom. 100 | 101 | @arg {int} pad round(pad * bandwidth) is the number 102 | of observations on each end of the 103 | time series that are not considered 104 | to be candidate points of 105 | statechange. Maximum is such that 106 | there after padding, there are at 107 | least two dates under consideration 108 | as points of state change. 109 | 110 | @return {tuple} Pair with index of split point in first position 111 | and kernel-weighted metric difference in second 112 | position. 113 | """ 114 | 115 | # typechecks and fail safety: 116 | 117 | assert bandwidth >= 2, 'Bandwidth parameter must be greater than or equal '\ 118 | 'to two.' 119 | 120 | assert isinstance(time_series, np.ndarray), 'Time series must be numpy ' \ 121 | 'array.' 122 | assert np.issubdtype(time_series.dtype, np.number), 'Time series array ' \ 123 | 'can only contain only numerical values.' 124 | assert time_series.ndim == 2, 'Time series array must be 2D with dates ' \ 125 | 'ascending along axis 0 and covariates along axis 1.' 126 | assert (time_series != np.nan).all() and (time_series != np.infty).all(), \ 127 | 'Time series array cannot contain missing or infinite values.' 128 | num_dates, num_covariates = time_series.shape # dimensions of data 129 | assert num_covariates == 2, 'Time series array can only contain two '\ 130 | 'covariates.' 131 | 132 | pad = round(pad*bandwidth) # redefine pad as a constant number of obs 133 | assert pad >= 2, 'At least two observations must be padded on each end ' \ 134 | 'of the time series array.' 135 | assert num_dates - 2*pad >= 3, 'Time series must have at least three ' \ 136 | 'observations after padding.' 137 | 138 | # estimating breakpoint 139 | 140 | regime_discrepancy = [] # will store diff between every split of regimes 141 | 142 | for partition in range(pad, num_dates-pad): 143 | 144 | regime_a = time_series[:partition] # left partition of time series 145 | weights_a = kernel(partition, bandwidth)[::-1] 146 | 147 | regime_b = time_series[partition:] # right partition of time series 148 | weights_b = kernel(num_dates - partition, bandwidth) 149 | 150 | # print((metric(regime_a, weights_a), metric(regime_b, weights_b))) 151 | 152 | regime_discrepancy.append( 153 | abs( 154 | metric(regime_a, weights_a) - metric(regime_b, weights_b) 155 | ) 156 | ) 157 | 158 | split_date = np.argmax(regime_discrepancy) 159 | 160 | return (split_date + pad, regime_discrepancy[split_date]) 161 | 162 | def successive_split(time_series, kernel_splitter, num_splits): 163 | """Detects multiple points of regime change in bivariate time series. 164 | 165 | Splits given bivariate time series several times at regime change 166 | points defined by the provided kernel_splitter function. If number 167 | of desired splits is greater than detectable regime changes, then all 168 | detected regime changes are returned. 169 | 170 | @arg {np.array} time_series 2D array containing time series 171 | data with dates in ascending 172 | order along axis 0 and covariates 173 | along axis 1. 174 | 175 | @arg {function} kernel_splitter One-argument function that takes 176 | a bivariate time series of the 177 | same format as the previous arg 178 | and returns the index defining 179 | a regime change point (eg. 180 | `kernel_splitter = lambda x: 181 | kernel_split(x, ...)`). 182 | 183 | @arg {np.array} Bivariate time series, same form 184 | as time_series arg above. 185 | 186 | @arg {int} num_splits The number of desired regime 187 | changes to be detected via 188 | kernel_splitter. 189 | 190 | @return {list} List of tuples specifying regime change points. 191 | Each tuple is of the form (index of split point, 192 | kernel-weighted metric difference). 193 | """ 194 | 195 | assert isinstance(num_splits, int) 196 | assert num_splits >= 1 197 | 198 | if num_splits == 1: 199 | return [kernel_splitter(time_series)] 200 | else: 201 | breakpoints = [(0, None), (time_series.shape[0], None)] 202 | 203 | def index_map(date_pair): 204 | """Runs kernel_splitter on slice of time_series defined by 205 | date_pair.""" 206 | 207 | try: 208 | return tuple(map( 209 | add, 210 | (date_pair[0], 0), 211 | kernel_splitter(time_series[date_pair[0]:date_pair[1]]) 212 | )) 213 | except AssertionError: 214 | return None 215 | 216 | while len(breakpoints) - 2 < num_splits: 217 | 218 | dates = sorted([date for date, value in breakpoints]) # just dates 219 | windows = zip(dates[:-1], dates[1:]) # snippets 220 | new_breakpoints = [ # new regime change points 221 | pair for pair in map(index_map, windows) if pair is not None 222 | ] 223 | if len(new_breakpoints) == 0: 224 | break 225 | else: 226 | breakpoints += new_breakpoints 227 | 228 | breakpoints = sorted( 229 | breakpoints[2:], 230 | key=lambda pair: pair[1], 231 | reverse=True 232 | ) 233 | 234 | return breakpoints[:num_splits] 235 | -------------------------------------------------------------------------------- /readme.ipynb: -------------------------------------------------------------------------------- 1 | { 2 | "cells": [ 3 | { 4 | "cell_type": "markdown", 5 | "metadata": {}, 6 | "source": [ 7 | "# REGIME CHANGE\n", 8 | "**MUSTAFA S EISA** \\ 14 APRIL 2017" 9 | ] 10 | }, 11 | { 12 | "cell_type": "markdown", 13 | "metadata": {}, 14 | "source": [ 15 | "This package contains tools for the local, semi-parametric detection of regime changes in a bivariate time series setting. Regime changes can be defined with respect to a given bivariate mapping (eg. correlation, tracking error) and a kernel weighting parameter that controls the fidelity of the estimator to local changes." 16 | ] 17 | }, 18 | { 19 | "cell_type": "code", 20 | "execution_count": 35, 21 | "metadata": { 22 | "scrolled": false 23 | }, 24 | "outputs": [], 25 | "source": [ 26 | "import regimechange as rg" 27 | ] 28 | }, 29 | { 30 | "cell_type": "markdown", 31 | "metadata": {}, 32 | "source": [ 33 | "The `METRICS` dictionary contains a set of pre-defined metric functions that define a state change." 34 | ] 35 | }, 36 | { 37 | "cell_type": "code", 38 | "execution_count": 36, 39 | "metadata": {}, 40 | "outputs": [ 41 | { 42 | "name": "stdout", 43 | "output_type": "stream", 44 | "text": [ 45 | "Pre-defined metrics include: excess return, excess volatility, correlation, tracking error.\n" 46 | ] 47 | } 48 | ], 49 | "source": [ 50 | "print('Pre-defined metrics include: ' + ', '.join(rg.METRICS.keys()) + '.')" 51 | ] 52 | }, 53 | { 54 | "cell_type": "markdown", 55 | "metadata": {}, 56 | "source": [ 57 | "The `KERNELS` dictionary contains a set of pre-defined kernels that control sensitivity to local information." 58 | ] 59 | }, 60 | { 61 | "cell_type": "code", 62 | "execution_count": 37, 63 | "metadata": {}, 64 | "outputs": [ 65 | { 66 | "name": "stdout", 67 | "output_type": "stream", 68 | "text": [ 69 | "Pre-defined kernels include: hyperbolic, gaussian, triangular, uniform.\n" 70 | ] 71 | } 72 | ], 73 | "source": [ 74 | "print('Pre-defined kernels include: ' + ', '.join(rg.KERNELS.keys()) + '.')" 75 | ] 76 | }, 77 | { 78 | "cell_type": "markdown", 79 | "metadata": {}, 80 | "source": [ 81 | "The Gaussian and Uniform (aka K-nearest-neighbor) kernels are well known. We provide the other two for completeness. The hyperbolic kernel $\\kappa_h:\\mathbb{R}^n\\times\\mathbb{R}^n \\mapsto \\mathbb{R}_{++}$ with bandwidth $b$ is of the form\n", 82 | "\n", 83 | "$$\\kappa_h(x, y) = \\left(\\frac{1}{1 + \\|x - y\\|}\\right)^{b}$$\n", 84 | "\n", 85 | "while the triangular kernel $\\kappa_t:\\mathbb{R}^n\\times\\mathbb{R}^n \\mapsto \\mathbb{R}_{++}$ with bandwidth $b$ is of the form\n", 86 | "\n", 87 | "$$\\kappa_t(x, y) = \\left(1 - \\frac{\\|x - y\\|}{b} \\right)_+$$" 88 | ] 89 | }, 90 | { 91 | "cell_type": "markdown", 92 | "metadata": {}, 93 | "source": [ 94 | "### Usage\n", 95 | "\n", 96 | "We demonstrate the use of this package and its effectiveness in the following examples." 97 | ] 98 | }, 99 | { 100 | "cell_type": "code", 101 | "execution_count": 38, 102 | "metadata": { 103 | "collapsed": true 104 | }, 105 | "outputs": [], 106 | "source": [ 107 | "from matplotlib import pyplot as plt\n", 108 | "import regimechange as rg\n", 109 | "import numpy as np\n", 110 | "\n", 111 | "plt.style.use('ggplot')\n", 112 | "%matplotlib inline" 113 | ] 114 | }, 115 | { 116 | "cell_type": "markdown", 117 | "metadata": {}, 118 | "source": [ 119 | "Consider a discrete regime change that occurs in with respect to the Pearson correlation coefficient. Specifically, we'll generate data where one time series is almost perfectly correlated with the other and then, at day 68, the correlation flips signs." 120 | ] 121 | }, 122 | { 123 | "cell_type": "code", 124 | "execution_count": 62, 125 | "metadata": {}, 126 | "outputs": [ 127 | { 128 | "data": { 129 | "image/png": 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htBjzyQesOmuzYWUrQgghmoYk1QH2yqZcbltXSmX/YVBRYX0ZCyECqtKt2ZlX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\n", 130 | "text/plain": [ 131 | "" 132 | ] 133 | }, 134 | "metadata": {}, 135 | "output_type": "display_data" 136 | } 137 | ], 138 | "source": [ 139 | "benchmark = np.random.normal(size=(100,1)) # some benchmark index\n", 140 | "tracking = benchmark.copy() + .5*np.random.normal(size=(100,1)) # fund tracking benchmark\n", 141 | "tracking[68:] = -1*tracking[68:] # flip relationship at day 68\n", 142 | "\n", 143 | "plt.figure(figsize=(12, 6))\n", 144 | "plt.axvline(x=68, color = 'orange', label='regime change', linewidth=3)\n", 145 | "plt.plot(np.cumsum(benchmark), label='benchmark index', linewidth=2)\n", 146 | "plt.plot(np.cumsum(tracking), label='tracking fund', linestyle='--')\n", 147 | "plt.legend()\n", 148 | "plt.show()" 149 | ] 150 | }, 151 | { 152 | "cell_type": "markdown", 153 | "metadata": {}, 154 | "source": [ 155 | "We can estimate when this regime change occurred using the `kernel_split` method:" 156 | ] 157 | }, 158 | { 159 | "cell_type": "code", 160 | "execution_count": 63, 161 | "metadata": {}, 162 | "outputs": [ 163 | { 164 | "data": { 165 | "text/plain": [ 166 | "(68, 1.8800332588540651)" 167 | ] 168 | }, 169 | "execution_count": 63, 170 | "metadata": {}, 171 | "output_type": "execute_result" 172 | } 173 | ], 174 | "source": [ 175 | "data = np.hstack((benchmark, tracking))\n", 176 | "rg.kernel_split(\n", 177 | " time_series=data,\n", 178 | " metric=rg.METRICS['correlation'],\n", 179 | " kernel=rg.KERNELS['uniform'],\n", 180 | " bandwidth=25,\n", 181 | " pad=1\n", 182 | ")\n", 183 | "\n", 184 | "# 68" 185 | ] 186 | }, 187 | { 188 | "cell_type": "markdown", 189 | "metadata": {}, 190 | "source": [ 191 | "Suppose there are multiple correlation regime changes." 192 | ] 193 | }, 194 | { 195 | "cell_type": "code", 196 | "execution_count": 64, 197 | "metadata": {}, 198 | "outputs": [ 199 | { 200 | "data": { 201 | "image/png": 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17IpfQrMtdELPcdkNkiMctDvCIDsferpg/9u+fZom5usvoA9MrgqF1poWw0VU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3AAAg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\n0jC/xi1BbbVa+eBoJvt/y7vis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202 | "text/plain": [ 203 | "" 204 | ] 205 | }, 206 | "metadata": {}, 207 | "output_type": "display_data" 208 | } 209 | ], 210 | "source": [ 211 | "data = np.vstack((data, data))\n", 212 | "\n", 213 | "plt.figure(figsize=(12, 6))\n", 214 | "plt.axvline(x=68, color = 'orange', label='regime change 1', linewidth=3)\n", 215 | "plt.axvline(x=100, color = 'purple', label='regime change 2', linewidth=3)\n", 216 | "plt.axvline(x=169, color = 'green', label='regime change 2', linewidth=3)\n", 217 | "plt.plot(np.cumsum(data[:, 0]), label='benchmark index', linewidth=2)\n", 218 | "plt.plot(np.cumsum(data[:, 1]), label='tracking fund', linestyle='--')\n", 219 | "plt.legend()\n", 220 | "plt.show()" 221 | ] 222 | }, 223 | { 224 | "cell_type": "markdown", 225 | "metadata": {}, 226 | "source": [ 227 | "For detecting these several regime changes, we can turn to the `successive_split` method which implements some regime change mechanism (like `kernel_split`) recursively. For this, we'll need a univariate function that outputs the location of a regime change such as the following." 228 | ] 229 | }, 230 | { 231 | "cell_type": "code", 232 | "execution_count": 70, 233 | "metadata": { 234 | "collapsed": true 235 | }, 236 | "outputs": [], 237 | "source": [ 238 | "ks = lambda time_series: rg.kernel_split(\n", 239 | " time_series,\n", 240 | " metric=rg.METRICS['correlation'],\n", 241 | " kernel=rg.KERNELS['triangular'],\n", 242 | " bandwidth=25,\n", 243 | " pad=1\n", 244 | ")" 245 | ] 246 | }, 247 | { 248 | "cell_type": "markdown", 249 | "metadata": {}, 250 | "source": [ 251 | "Then we can run the `successive_split` method, specifying a hypothesis number of splits in the argument `num_splits`. The `successive_split` method works by identifying a regime change, dividing the time series into two partitions, then re-performing detection recursively on each partition. By this logic, $\\mathcal{O}\\left(2^{\\lceil \\log_2(n) \\rceil}\\right)$ regime changes will be computed and the top $n$ most drastic estimated regime changes will be returned, where $n$ represents `num_splits`. Better results are thus obtained by choosing a conservatively high `num_splits` so that enough exploration takes place before the results are ranked.\n", 252 | "\n", 253 | "For this case, we'll set `num_splits` to 5, an upper bound for how many regimes we expect to have in the data." 254 | ] 255 | }, 256 | { 257 | "cell_type": "code", 258 | "execution_count": 71, 259 | "metadata": {}, 260 | "outputs": [ 261 | { 262 | "data": { 263 | "text/plain": [ 264 | "[(168, 1.9005015889472829),\n", 265 | " (68, 1.9005015889472827),\n", 266 | " (100, 1.8256333481430742),\n", 267 | " (31, 0.095901802064368602),\n", 268 | " (131, 0.095901802064368602)]" 269 | ] 270 | }, 271 | "execution_count": 71, 272 | "metadata": {}, 273 | "output_type": "execute_result" 274 | } 275 | ], 276 | "source": [ 277 | "rg.successive_split(\n", 278 | " time_series=data,\n", 279 | " kernel_splitter=ks,\n", 280 | " num_splits=5\n", 281 | ")" 282 | ] 283 | }, 284 | { 285 | "cell_type": "markdown", 286 | "metadata": {}, 287 | "source": [ 288 | "As can be seen, the three regime changes are identified and ranked at the top with large values while the latter two returned items have significantly lower values, signifying that a regime change likely did not occur at those times.\n", 289 | "\n", 290 | "Another example is with the metric tracking error. We'll generate data where one time series tracks the other well then suddenly tracks poorly starting on day 40." 291 | ] 292 | }, 293 | { 294 | "cell_type": "code", 295 | "execution_count": 92, 296 | "metadata": {}, 297 | "outputs": [ 298 | { 299 | "data": { 300 | "image/png": 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wJ4xXmchwX87l2tiXml3hc1VQCJZn52J57l8Yd07C6DsM1bApymol8WwuJzLy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301 | "text/plain": [ 302 | "" 303 | ] 304 | }, 305 | "metadata": {}, 306 | "output_type": "display_data" 307 | } 308 | ], 309 | "source": [ 310 | "benchmark = np.random.normal(size=(100,1)) # some benchmark index\n", 311 | "tracking = benchmark.copy() + .5*np.random.normal(size=(100,1)) # fund tracking benchmark\n", 312 | "tracking[40:] = tracking[40:] + np.random.normal(size=(60,1)) # tracking error blows up at day 40\n", 313 | "\n", 314 | "plt.figure(figsize=(12, 6))\n", 315 | "plt.axvline(x=41, color = 'orange', label='regime change', linewidth=3)\n", 316 | "plt.plot(np.cumsum(benchmark), label='benchmark index', linewidth=2)\n", 317 | "plt.plot(np.cumsum(tracking), label='tracking fund', linestyle='--')\n", 318 | "plt.legend()\n", 319 | "plt.show()" 320 | ] 321 | }, 322 | { 323 | "cell_type": "markdown", 324 | "metadata": {}, 325 | "source": [ 326 | "We can again estimate when this regime change occurred using the `kernel_split` method:" 327 | ] 328 | }, 329 | { 330 | "cell_type": "code", 331 | "execution_count": 93, 332 | "metadata": { 333 | "scrolled": true 334 | }, 335 | "outputs": [ 336 | { 337 | "data": { 338 | "text/plain": [ 339 | "(41, 0.58183784971618535)" 340 | ] 341 | }, 342 | "execution_count": 93, 343 | "metadata": {}, 344 | "output_type": "execute_result" 345 | } 346 | ], 347 | "source": [ 348 | "data = np.hstack((benchmark, tracking))\n", 349 | "rg.kernel_split(\n", 350 | " time_series=data,\n", 351 | " metric=rg.METRICS['tracking error'],\n", 352 | " kernel=rg.KERNELS['gaussian'],\n", 353 | " bandwidth=10\n", 354 | ")\n", 355 | "\n", 356 | "# 41" 357 | ] 358 | }, 359 | { 360 | "cell_type": "markdown", 361 | "metadata": {}, 362 | "source": [ 363 | "### Speed Test" 364 | ] 365 | }, 366 | { 367 | "cell_type": "code", 368 | "execution_count": 75, 369 | "metadata": {}, 370 | "outputs": [ 371 | { 372 | "name": "stdout", 373 | "output_type": "stream", 374 | "text": [ 375 | "100 loops, best of 3: 16.6 ms per loop\n" 376 | ] 377 | } 378 | ], 379 | "source": [ 380 | "%timeit rg.kernel_split(\\\n", 381 | " time_series=data,\\\n", 382 | " metric=rg.METRICS['tracking error'],\\\n", 383 | " kernel=rg.KERNELS['hyperbolic'],\\\n", 384 | " bandwidth=10,\\\n", 385 | " pad=1\\\n", 386 | ")" 387 | ] 388 | } 389 | ], 390 | "metadata": { 391 | "kernelspec": { 392 | "display_name": "Python 3", 393 | "language": "python", 394 | "name": "python3" 395 | }, 396 | "language_info": { 397 | "codemirror_mode": { 398 | "name": "ipython", 399 | "version": 3 400 | }, 401 | "file_extension": ".py", 402 | "mimetype": "text/x-python", 403 | "name": "python", 404 | "nbconvert_exporter": "python", 405 | "pygments_lexer": "ipython3", 406 | "version": "3.5.3" 407 | } 408 | }, 409 | "nbformat": 4, 410 | "nbformat_minor": 2 411 | } 412 | --------------------------------------------------------------------------------