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Model Selection and Adaptive Markov chain Monte Carlo for Bayesian Cointegrated VAR model

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  • Gareth W. Peters
  • Balakrishnan Kannan
  • Ben Lasscock
  • Chris Mellen
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    Abstract

    This paper develops a matrix-variate adaptive Markov chain Monte Carlo (MCMC) methodology for Bayesian Cointegrated Vector Auto Regressions (CVAR). We replace the popular approach to sampling Bayesian CVAR models, involving griddy Gibbs, with an automated efficient alternative, based on the Adaptive Metropolis algorithm of Roberts and Rosenthal, (2009). Developing the adaptive MCMC framework for Bayesian CVAR models allows for efficient estimation of posterior parameters in significantly higher dimensional CVAR series than previously possible with existing griddy Gibbs samplers. For a n-dimensional CVAR series, the matrix-variate posterior is in dimension $3n^2 + n$, with significant correlation present between the blocks of matrix random variables. 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 Bayes Factor analysis of rank. Practically the adaptive sampler also aids in the development of automated Bayesian cointegration models for algorithmic trading systems considering instruments made up of several assets, such as currency baskets. Previously the literature on financial applications of CVAR trading models typically only considers pairs trading (n=2) due to the computational cost of the griddy Gibbs. We are able to extend under our adaptive framework to $n >> 2$ and demonstrate an example with n = 10, resulting in a posterior distribution with parameters up to dimension 310. By also considering the rank as a random quantity we can ensure our resulting trading models are able to adjust to potentially time varying market conditions in a coherent statistical framework.

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    File URL: http://arxiv.org/pdf/1004.3830
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    Bibliographic Info

    Paper provided by arXiv.org in its series Papers with number 1004.3830.

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    Date of creation: Apr 2010
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    Handle: RePEc:arx:papers:1004.3830

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    1. Rodney Strachan & Herman K. van Dijk, . "Bayesian Model Averaging in Vector Autoregressive Processes with an Investigation of Stability of the US Great Ratios and Risk of a Liquidity Trap in the USA, UK and Japan," MRG Discussion Paper Series 1407, School of Economics, University of Queensland, Australia.
    2. Engle, Robert F & Granger, Clive W J, 1987. "Co-integration and Error Correction: Representation, Estimation, and Testing," Econometrica, Econometric Society, vol. 55(2), pages 251-76, March.
    3. John F. Geweke, 1995. "Bayesian reduced rank regression in econometrics," Working Papers 540, Federal Reserve Bank of Minneapolis.
    4. BAUWENS, Luc & LUBRANO , Michel, 1994. "Identification Restrictions and Posterior Densities in Cointegrated Gaussian VAR Systems," CORE Discussion Papers 1994018, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    5. J. Vermaak & C. Andrieu & A. Doucet & S. J. Godsill, 2004. "Reversible Jump Markov Chain Monte Carlo Strategies for Bayesian Model Selection in Autoregressive Processes," Journal of Time Series Analysis, Wiley Blackwell, vol. 25(6), pages 785-809, November.
    6. Strachan, Rodney W. & Inder, Brett, 2004. "Bayesian analysis of the error correction model," Journal of Econometrics, Elsevier, vol. 123(2), pages 307-325, December.
    7. Granger, C. W. J., 1981. "Some properties of time series data and their use in econometric model specification," Journal of Econometrics, Elsevier, vol. 16(1), pages 121-130, May.
    8. Sugita, Katsuhiro, 2002. "Testing for Cointegration Rank Using Bayes Factors," Royal Economic Society Annual Conference 2002 171, Royal Economic Society.
    9. BAUWENS, Luc & GIOT, Pierre, 1997. "A Gibbs sampling approach to cointegration," CORE Discussion Papers 1997016, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    10. Koop, G. & Strachan, R.W. & van Dijk, H.K. & Villani, M., 2005. "Bayesian approaches to cointegratrion," Econometric Institute Research Papers EI 2005-13, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    11. Kleibergen, F.R. & Paap, R., 1998. "Priors, posteriors and Bayes factors for a Bayesian analysis of cointegration," Econometric Institute Research Papers EI 9821, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    12. Katsuhiro Sugita, 2009. "A Monte Carlo comparison of Bayesian testing for cointegration rank," Economics Bulletin, AccessEcon, vol. 29(3), pages 2145-2151.
    13. Sugita, Katsuhiro, 2002. "Testing For Cointegration Rank Using Bayes Factors," The Warwick Economics Research Paper Series (TWERPS) 654, University of Warwick, Department of Economics.
    14. Kleibergen, Frank & van Dijk, Herman K., 1994. "On the Shape of the Likelihood/Posterior in Cointegration Models," Econometric Theory, Cambridge University Press, vol. 10(3-4), pages 514-551, August.
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