├── .gitattributes ├── .idea ├── .gitignore ├── dictionaries │ └── User.xml ├── inspectionProfiles │ └── profiles_settings.xml ├── misc.xml ├── modules.xml ├── pybvar.iml └── vcs.xml ├── .travis.yml ├── LICENSE.txt ├── pybvar ├── __init__.py ├── __pycache__ │ ├── __init__.cpython-37.pyc │ ├── bvar.cpython-37.pyc │ └── priors.cpython-37.pyc ├── bvar.py └── priors.py ├── readme.md ├── setup.py └── tests ├── __init__.py └── test.py /.gitattributes: -------------------------------------------------------------------------------- 1 | # Auto detect text files and perform LF normalization 2 | * text=auto 3 | -------------------------------------------------------------------------------- /.idea/.gitignore: -------------------------------------------------------------------------------- 1 | 2 | # Default ignored files 3 | /workspace.xml -------------------------------------------------------------------------------- /.idea/dictionaries/User.xml: -------------------------------------------------------------------------------- 1 | 2 | 3 | 4 | mcmc 5 | 6 | 7 | -------------------------------------------------------------------------------- /.idea/inspectionProfiles/profiles_settings.xml: -------------------------------------------------------------------------------- 1 | 2 | 3 | 6 | -------------------------------------------------------------------------------- /.idea/misc.xml: -------------------------------------------------------------------------------- 1 | 2 | 3 | 4 | -------------------------------------------------------------------------------- /.idea/modules.xml: -------------------------------------------------------------------------------- 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | -------------------------------------------------------------------------------- /.idea/pybvar.iml: -------------------------------------------------------------------------------- 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 12 | -------------------------------------------------------------------------------- /.idea/vcs.xml: -------------------------------------------------------------------------------- 1 | 2 | 3 | 4 | 5 | 6 | -------------------------------------------------------------------------------- /.travis.yml: -------------------------------------------------------------------------------- 1 | language: python 2 | python: 3 | - "3.6" 4 | script: 5 | - pytest -------------------------------------------------------------------------------- /LICENSE.txt: -------------------------------------------------------------------------------- 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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It is safest 630 | to attach them to the start of each source file to most effectively 631 | state the exclusion of warranty; and each file should have at least 632 | the "copyright" line and a pointer to where the full notice is found. 633 | 634 | 635 | Copyright (C) 636 | 637 | This program is free software: you can redistribute it and/or modify 638 | it under the terms of the GNU General Public License as published by 639 | the Free Software Foundation, either version 3 of the License, or 640 | (at your option) any later version. 641 | 642 | This program is distributed in the hope that it will be useful, 643 | but WITHOUT ANY WARRANTY; without even the implied warranty of 644 | MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the 645 | GNU General Public License for more details. 646 | 647 | You should have received a copy of the GNU General Public License 648 | along with this program. If not, see . 649 | 650 | Also add information on how to contact you by electronic and paper mail. 651 | 652 | If the program does terminal interaction, make it output a short 653 | notice like this when it starts in an interactive mode: 654 | 655 | Copyright (C) 656 | This program comes with ABSOLUTELY NO WARRANTY; for details type `show w'. 657 | This is free software, and you are welcome to redistribute it 658 | under certain conditions; type `show c' for details. 659 | 660 | The hypothetical commands `show w' and `show c' should show the appropriate 661 | parts of the General Public License. Of course, your program's commands 662 | might be different; for a GUI interface, you would use an "about box". 663 | 664 | You should also get your employer (if you work as a programmer) or school, 665 | if any, to sign a "copyright disclaimer" for the program, if necessary. 666 | For more information on this, and how to apply and follow the GNU GPL, see 667 | . 668 | 669 | The GNU General Public License does not permit incorporating your program 670 | into proprietary programs. If your program is a subroutine library, you 671 | may consider it more useful to permit linking proprietary applications with 672 | the library. If this is what you want to do, use the GNU Lesser General 673 | Public License instead of this License. But first, please read 674 | . -------------------------------------------------------------------------------- /pybvar/__init__.py: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/joergrieger/pybvar/65bf5cd9f25b670f418efc795c528cc934c390ec/pybvar/__init__.py -------------------------------------------------------------------------------- /pybvar/__pycache__/__init__.cpython-37.pyc: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/joergrieger/pybvar/65bf5cd9f25b670f418efc795c528cc934c390ec/pybvar/__pycache__/__init__.cpython-37.pyc -------------------------------------------------------------------------------- /pybvar/__pycache__/bvar.cpython-37.pyc: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/joergrieger/pybvar/65bf5cd9f25b670f418efc795c528cc934c390ec/pybvar/__pycache__/bvar.cpython-37.pyc -------------------------------------------------------------------------------- /pybvar/__pycache__/priors.cpython-37.pyc: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/joergrieger/pybvar/65bf5cd9f25b670f418efc795c528cc934c390ec/pybvar/__pycache__/priors.cpython-37.pyc -------------------------------------------------------------------------------- /pybvar/bvar.py: -------------------------------------------------------------------------------- 1 | import numpy as np 2 | 3 | def lagdata(data, p, intercept): 4 | """ Create lagged data. 5 | Parameter data: The data to be lagged. 6 | Parameter p: The number of lags. 7 | Parameter intercept: A boolean variable indicating whether the model has an intercept or not. 8 | Returns: A matrix with the lagged data. 9 | """ 10 | # preliminary stuff 11 | nl = data.shape[0] 12 | nv = data.shape[1] 13 | 14 | # check for intercept 15 | if intercept: 16 | constant = 1 17 | else: 18 | constant = 0 19 | 20 | # create new matrix of the appropriate dimension 21 | ndim = nv * p + constant 22 | laggeddata = np.empty((nl-p-1, ndim)) 23 | 24 | if intercept: 25 | laggeddata[:, 0] = 1 26 | 27 | for i in range(1, (p+1)): 28 | ind1 = (i-1)*nv+constant 29 | ind2 = i*nv+constant 30 | laggeddata[:, ind1:ind2] = data[(p-i):(nl-1-i), :] 31 | 32 | return laggeddata 33 | 34 | 35 | class bvar: 36 | """Class for the bayesian VAR model. 37 | """ 38 | def __init__(self, data, prior): 39 | """Initializes the VAR model. 40 | Parameter data: The data used in the model. 41 | Parameter prior: The prior used for inference. 42 | """ 43 | # Store model information 44 | self.data = data 45 | self.p = prior.p 46 | self.intercept = prior.intercept 47 | self.nv = prior.nv 48 | 49 | if self.intercept: 50 | constant = 1 51 | else: 52 | constant = 0 53 | 54 | self.nk = self.nv * self.p + constant 55 | 56 | # Store data 57 | self.y = data[(self.p+1):, :] 58 | self.x = lagdata(data, self.p, self.intercept) 59 | 60 | self.prior = prior 61 | 62 | def mcmc(self, nreps, burnin, nthin=1): 63 | """Estimate a bayesian VAR model using Gibbs-sampling. 64 | Parameter nreps: total number of draws. 65 | Parameter burning: number of burn-in draws. 66 | Parameter nthin: Thinning parameter 67 | Return: 0 if there were no problems during the run of the MCMC algorithm. 68 | """ 69 | 70 | # Declare variables for storage 71 | self.Betadraws = np.empty((self.nk, self.nv, int((nreps-burnin)/nthin))) 72 | self.Sigmadraws = np.empty((self.nv, self.nv, int((nreps-burnin)/nthin))) 73 | 74 | # Initialize the Gibbs-Sampler 75 | draw = self.prior.init_mcmc(self.y, self.x) 76 | alpha = draw[0] 77 | sigma = draw[1] 78 | 79 | # Gibbs sampling 80 | for ireps in range(1, (nreps + 1)): 81 | 82 | # print progress 83 | if ireps % 100 == 0: 84 | print(ireps) 85 | 86 | # Draw posterior 87 | draw = self.prior.draw_posterior(self.y, self.x, alpha, sigma) 88 | alpha = draw[0] 89 | sigma = draw[1] 90 | 91 | # Store results 92 | if ireps > burnin and (ireps-burnin) % nthin == 0: 93 | i = int((ireps - burnin)/nthin - 1) 94 | self.Betadraws[:, :, i] = alpha.reshape((self.nk, self.nv)) 95 | self.Sigmadraws[:, :, i] = sigma 96 | ret = 0 97 | return ret -------------------------------------------------------------------------------- /pybvar/priors.py: -------------------------------------------------------------------------------- 1 | import numpy as np 2 | from scipy.stats import wishart 3 | 4 | class Uninformative: 5 | """Class for the uninformative prior.""" 6 | def __init__(self, data, p, intercept): 7 | """Initialize the uninformative prior. 8 | Parameter data: A matrix of dimension Txk containing the data. 9 | Parameter p: The number of lags in the model. 10 | Parameter intercept: Boolean variable whether the model contains an intercept or not 11 | """ 12 | # Model information 13 | self.intercept = intercept 14 | self.T = data.shape[0] 15 | self.p = p 16 | self.nv = data.shape[1] 17 | 18 | 19 | def draw_posterior(self, y, x, alpha, sigma): 20 | """One draw from the posterior for the uninformative prior. 21 | Parameter y: A (T-p)xk matrix with the LHS of the model. With T being the length of the original data set, p the number of lags and k the number of variables in the model. 22 | Parameter x: A (T-p)x(k*p+constant) matrix with the RHS of the model. With T being the length of the original data, p the number of lags, k the number of variables in the model and constant is either 0 or 1 depending whether the model has an intercept (constant = 1) or not (constant = 0). 23 | Parameter alpha: The regression coefficients of the previous draw. 24 | Parameter sigma: The variance-covariance matrix from the previous draw. 25 | Returns: One draw of the mcmc consists of the draw for the coefficients and a draw for the variance-covariance matrix. 26 | """ 27 | # get OLS estimates 28 | tmp1 = np.linalg.inv(np.matmul(np.transpose(x), x)) 29 | tmp2 = np.matmul(np.transpose(x), y) 30 | olsestim = np.matmul(tmp1, tmp2) 31 | 32 | # residuals 33 | resids = y - np.matmul(x, olsestim) 34 | sse = np.matmul(np.transpose(resids), resids) 35 | 36 | # Draw coefficients (beta) 37 | vpost = np.kron(sigma, np.linalg.inv(np.matmul(np.transpose(x), x))) 38 | alpha = np.random.multivariate_normal(np.ndarray.flatten(olsestim), vpost) 39 | 40 | # Draw variance-covariance matrix 41 | sigma = wishart.rvs(self.T, np.linalg.inv(sse)) 42 | 43 | # Return Values 44 | return alpha, sigma 45 | 46 | def init_mcmc(self, y, x): 47 | """ Initializes the mcmc algorithm for the uninformative prior. 48 | Parameter y: A (T-p)xk matrix with the LHS of the model. With T being the length of the original data set, p the number of lags and k the number of variables in the model. 49 | Parameter x: A (T-p)x(k*p+constant) matrix with the RHS of the model. With T being the length of the original data, p the number of lags, k the number of variables in the model and constant is either 0 or 1 depending whether the model has an intercept (constant = 1) or not (constant = 0). 50 | Returns: The initial draw of the mcmc algorithm for a model with uninformative prior. 51 | """ 52 | # get OLS estimates 53 | tmp1 = np.linalg.inv(np.matmul(np.transpose(x), x)) 54 | tmp2 = np.matmul(np.transpose(x), y) 55 | olsestim = np.matmul(tmp1, tmp2) 56 | 57 | # residuals 58 | resids = y - np.matmul(x,olsestim) 59 | sse = np.matmul(np.transpose(resids), resids) 60 | 61 | # Draw Sigma 62 | sigma = wishart.rvs(self.T, np.linalg.inv(sse)) 63 | alpha = None 64 | retlist = (alpha, sigma) 65 | return retlist 66 | 67 | class ConjugateNormal: 68 | """ 69 | Class for the Conjugate-Normal prior. 70 | Parameter data: A matrix of dimension Txk containing the data. 71 | Parameter p: The number of lags in the model. 72 | Parameter intercept: Boolean variable whether the model contains an intercept or not 73 | Parameter coefprior prior on the VAR-coefficients (scalar) 74 | Parameter coefpriorvar prior on the variance of the VAR-coefficients (scalar) 75 | Parameter varprior prior on the variance (scalar) 76 | Parameter varpriordof degree of freedom of the variance 77 | """ 78 | def __init__(self, data, p, intercept, coefprior, coefpriorvar, varprior, varpriordof): 79 | self.intercept = intercept 80 | self.p = p 81 | self.T = data.shape[0] 82 | self.nv = data.shape[1] 83 | 84 | if intercept: 85 | constant = 1 86 | else: 87 | constant = 0 88 | 89 | self.coefprior = coefprior * np.ones((self.nv * self.p + constant, self.nv)) 90 | self.coefpriorvar = coefpriorvar * np.eye(self.nv * self.p + constant) 91 | 92 | self.varprior = np.eye(self.nv) 93 | self.varpriordof = varpriordof 94 | 95 | def init_mcmc(self, y, x): 96 | """ Initializes the mcmc algorithm for the Conjugate-Normal prior. 97 | Parameter y: A (T-p)xk matrix with the LHS of the model. With T being the length of the original data set, p the number of lags and k the number of variables in the model. 98 | Parameter x: A (T-p)x(k*p+constant) matrix with the RHS of the model. With T being the length of the original data, p the number of lags, k the number of variables in the model and constant is either 0 or 1 depending whether the model has an intercept (constant = 1) or not (constant = 0). 99 | Returns: The initial draw of the mcmc algorithm for a model with uninformative prior. 100 | """ 101 | # get OLS estimates 102 | tmp1 = np.linalg.inv(np.matmul(np.transpose(x), x)) 103 | tmp2 = np.matmul(np.transpose(x), y) 104 | olsestim = np.matmul(tmp1, tmp2) 105 | 106 | # residuals 107 | resids = y - np.matmul(x, olsestim) 108 | sse = np.matmul(np.transpose(resids), resids) 109 | 110 | # Draw Sigma 111 | sigma = wishart.rvs(self.T, np.linalg.inv(sse)) 112 | alpha = np.ndarray.flatten(olsestim) 113 | retlist = (alpha, sigma) 114 | return retlist 115 | 116 | def draw_posterior(self, y, x, alpha, sigma): 117 | """One draw from the posterior for the Conjugate-Normal prior. 118 | Parameter y: A (T-p)xk matrix with the LHS of the model. With T being the length of the original data set, p the number of lags and k the number of variables in the model. 119 | Parameter x: A (T-p)x(k*p+constant) matrix with the RHS of the model. With T being the length of the original data, p the number of lags, k the number of variables in the model and constant is either 0 or 1 depending whether the model has an intercept (constant = 1) or not (constant = 0). 120 | Parameter alpha: The regression coefficients of the previous draw. 121 | Parameter sigma: The variance-covariance matrix from the previous draw. 122 | Returns: One draw of the mcmc consists of the draw for the coefficients and a draw for the variance-covariance matrix. 123 | """ 124 | # OLS estimates 125 | tmp1 = np.linalg.inv(np.matmul(np.transpose(x), x)) 126 | tmp2 = np.matmul(np.transpose(x), y) 127 | olsestim = np.matmul(tmp1, tmp2) 128 | resids = y - np.matmul(x, olsestim) 129 | sse = np.matmul(np.transpose(resids), resids) 130 | 131 | # Posterior for coefficients 132 | vpost = np.linalg.inv(np.linalg.inv(self.coefpriorvar) + np.matmul(np.transpose(x), x)) 133 | apost = np.matmul(vpost, np.matmul(np.linalg.inv(self.coefpriorvar), self.coefprior) + np.matmul(np.matmul(np.transpose(x), x), olsestim)) 134 | cova = np.kron(sigma, vpost) 135 | alpha = np.random.multivariate_normal(np.ndarray.flatten(apost), cova) 136 | 137 | # Posterior for variance - covariance matrix 138 | vpost = self.T + self.varpriordof 139 | tmp1 = sse + self.varprior + np.matmul(np.transpose(olsestim), np.matmul(np.transpose(x), np.matmul(x, olsestim))) 140 | tmp2 = np.matmul(np.matmul(np.transpose(self.coefprior), np.linalg.inv(self.coefpriorvar)), self.coefprior) 141 | tmp3 = np.matmul(np.matmul(np.transpose(apost), np.linalg.inv(self.coefpriorvar) + np.matmul(np.transpose(x), x)), apost) 142 | spost = tmp1 + tmp2 + tmp3 143 | sigma = wishart.rvs(vpost,np.linalg.inv(spost)) 144 | 145 | # Return estimates 146 | retlist = (alpha,sigma) 147 | return(retlist) 148 | 149 | 150 | 151 | class Minnesota: 152 | def __init__(self, data, p, intercept): 153 | 154 | -------------------------------------------------------------------------------- /readme.md: -------------------------------------------------------------------------------- 1 | # pybvar 2 | 3 | 'pybvar' is a package for bayesian vector autoregression in Python. This package is similar to [bvars](https://github.com/joergrieger/bvars). 4 | 5 | This readme contains some examples on the usage of the package. 6 | 7 | The package is in a very preliminary stage of its development. 8 | 9 | # Examples 10 | 11 | Let's say that we would like to estimate a bayesian VAR with an uninformative prior. 12 | 13 | The following code sets up the uninformative prior for a VAR model with lag p=2 and an intercept 14 | 15 | ``` 16 | prior = uninformative(data,2,True) 17 | ``` 18 | 19 | In the next step we have to create a bvar object and pass the prior to it. This is done using the following code: 20 | 21 | ``` 22 | bv = bvar(data,prior) 23 | ``` 24 | 25 | To start the mcmc algorithm with 10,000 draws and 5,000 burn-in draws and we only want to keep every 5th draw we have to use the following code 26 | 27 | ``` 28 | results = bv.mcmc(10000,5000,5) 29 | ``` -------------------------------------------------------------------------------- /setup.py: -------------------------------------------------------------------------------- 1 | from distutils.core import setup 2 | setup( 3 | name = "pybvar", 4 | packages = ["pybvar"], 5 | version = "0.0.1", 6 | description = "Bayesian Vector Autoregressions", 7 | author = "Joerg Rieger", 8 | author_email = "joerg.rieger.jr@gmail.com", 9 | url = "https://github.com/joergrieger/pybvar.git", 10 | keywords = ["statistics","vector autoregression","bayes","inference"] 11 | classifiers = [ 12 | "Programming Language :: Python", 13 | "Intended Audience :: Science/Research", 14 | "Topic :: Software Development :: Libraries :: Python Modules", 15 | "Topic :: Scientific/Engineering", 16 | "Operating System :: OS Independent", 17 | "Topic :: Scientific/Engineering :: Mathematics" 18 | ], 19 | long_description = """pybvar is a package for bayesian vector autoregression. For more information about this package and its usage, visit https://github.com/joergrieger/pybvar.""" 20 | ) 21 | 22 | 23 | 24 | -------------------------------------------------------------------------------- /tests/__init__.py: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/joergrieger/pybvar/65bf5cd9f25b670f418efc795c528cc934c390ec/tests/__init__.py -------------------------------------------------------------------------------- /tests/test.py: -------------------------------------------------------------------------------- 1 | import numpy as np 2 | from pybvar.bvar import bvar 3 | from pybvar.priors import Uninformative 4 | from pybvar.priors import ConjugateNormal 5 | 6 | # Create Testdata 7 | TestData = np.random.standard_normal((150, 4)) 8 | 9 | # Test uninformative prior 10 | prior1 = Uninformative(TestData, 2, False) 11 | bv = bvar(TestData, prior1) 12 | bv.mcmc(1000, 200, 1) 13 | 14 | # Test conjugate-normal prior 15 | prior2 = ConjugateNormal(TestData, 2, False, 1, 0.1, 0.1, 10) 16 | bv2 = bvar(TestData, prior2) 17 | bv2.mcmc(1000, 200, 1) 18 | --------------------------------------------------------------------------------