Model Selection and Adaptive Markov Chain Monte Carlo for Bayesian Cointegrated VAR Model

24 Pages Posted: 5 Jun 2017

See all articles by Gareth Peters

Gareth Peters

Department of Actuarial Mathematics and Statistics, Heriot-Watt University; University College London - Department of Statistical Science; University of Oxford - Oxford-Man Institute of Quantitative Finance; London School of Economics & Political Science (LSE) - Systemic Risk Centre; University of New South Wales (UNSW) - Faculty of Science

Balakrishnan Kannan

affiliation not provided to SSRN

Ben Lasscock

affiliation not provided to SSRN

Chris Mellen

affiliation not provided to SSRN

Date Written: 2009

Abstract

In this paper, we develop novel Markov chain Monte Carlo sampling methodology for Bayesian Cointegrated Vector Auto Regression (CVAR) models. Here we focus on two novel exten sions to the sampling methodology for the CVAR posterior distribution. The first extension we develop replaces the popular sampling methodology of the griddy Gibbs sampler with an automated alternative which is based on an Adaptive Metropolis-Hastings algorithm. This is particularly relevant to automate the proposal mechanism in the MCMC algorithm in settings where griddy Gibbs is impractical such as when the dimension of the CVAR series is large, e.g. d > 5.

We also treat the rank of the CVAR model as a random variable and perform joint inference on the rank and model parameters. This is achieved with a Bayesian posterior distribution defined over both the rank and the CVAR model parameters, and inference is made via a Savage-Dickey density estimator for the Bayes Factor analysis of rank.

Keywords: Cointegrated Vector Auto Regression, Adaptive Markov chain Monte Carlo, Bayesian Inference, Bayes Factors, Savage-Dickey

Suggested Citation

Peters, Gareth and Kannan, Balakrishnan and Lasscock, Ben and Mellen, Chris, Model Selection and Adaptive Markov Chain Monte Carlo for Bayesian Cointegrated VAR Model (2009). Available at SSRN: https://ssrn.com/abstract=2980412 or http://dx.doi.org/10.2139/ssrn.2980412

Gareth Peters (Contact Author)

Department of Actuarial Mathematics and Statistics, Heriot-Watt University ( email )

Edinburgh Campus
Edinburgh, EH14 4AS
United Kingdom

HOME PAGE: http://garethpeters78.wixsite.com/garethwpeters

University College London - Department of Statistical Science ( email )

1-19 Torrington Place
London, WC1 7HB
United Kingdom

University of Oxford - Oxford-Man Institute of Quantitative Finance ( email )

University of Oxford Eagle House
Walton Well Road
Oxford, OX2 6ED
United Kingdom

London School of Economics & Political Science (LSE) - Systemic Risk Centre ( email )

Houghton St
London
United Kingdom

University of New South Wales (UNSW) - Faculty of Science ( email )

Australia

Balakrishnan Kannan

affiliation not provided to SSRN

Ben Lasscock

affiliation not provided to SSRN

Chris Mellen

affiliation not provided to SSRN

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