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Reversible Jump Markov Chain Monte Carlo Strategies for Bayesian Model Selection in Autoregressive Processes

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  • J. Vermaak
  • C. Andrieu
  • A. Doucet
  • S. J. Godsill

Abstract

. This paper addresses the problem of Bayesian inference in autoregressive (AR) processes in the case where the correct model order is unknown. Original hierarchical prior models that allow the stationarity of the model to be enforced are proposed. Obtaining the quantities of interest, such as parameter estimates, predictions of future values of the time series, posterior model‐order probabilities, etc., requires integration with respect to the full posterior distribution, an operation which is analytically intractable. Reversible jump Markov chain Monte Carlo (MCMC) algorithms are developed to perform the required integration implicitly by simulating from the posterior distribution. The methods developed are evaluated in simulation studies on a number of synthetic and real data sets.

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  • 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.
    • Handle: RePEc:bla:jtsera:v:25:y:2004:i:6:p:785-809
    DOI: 10.1111/j.1467-9892.2004.00380.x
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    References listed on IDEAS

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    2. Knut Are Aastveit & Anne Sofie Jore & Francesco Ravazzolo, 2014. "Forecasting recessions in real time," Working Paper 2014/02, Norges Bank.
    3. Philippe, Anne, 2006. "Bayesian analysis of autoregressive moving average processes with unknown orders," Computational Statistics & Data Analysis, Elsevier, vol. 51(3), pages 1904-1923, December.
    4. Alexander Meyer-Gohde & Daniel Neuhoff, 2015. "Generalized Exogenous Processes in DSGE: A Bayesian Approach," SFB 649 Discussion Papers SFB649DP2015-014, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    5. Ricardo S. Ehlers & Stephen P. Brooks, 2008. "Adaptive Proposal Construction for Reversible Jump MCMC," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 35(4), pages 677-690, December.
    6. Gareth W. Peters & Balakrishnan Kannan & Ben Lasscock & Chris Mellen, 2010. "Model Selection and Adaptive Markov chain Monte Carlo for Bayesian Cointegrated VAR model," Papers 1004.3830, arXiv.org.
    7. Drovandi, Christopher C. & Pettitt, Anthony N. & Henderson, Robert D. & McCombe, Pamela A., 2014. "Marginal reversible jump Markov chain Monte Carlo with application to motor unit number estimation," Computational Statistics & Data Analysis, Elsevier, vol. 72(C), pages 128-146.
    8. Guillermo Ferreira & Jorge Figueroa-Zúñiga & Mário Castro, 2015. "Partially linear beta regression model with autoregressive errors," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 24(4), pages 752-775, December.
    9. Billio, Monica & Casarin, Roberto & Ravazzolo, Francesco & van Dijk, Herman K., 2012. "Combination schemes for turning point predictions," The Quarterly Review of Economics and Finance, Elsevier, vol. 52(4), pages 402-412.
    10. Daniel Felix Ahelegbey & Monica Billio & Roberto Casarin, 2016. "Sparse Graphical Vector Autoregression: A Bayesian Approach," Annals of Economics and Statistics, GENES, issue 123-124, pages 333-361.
    11. Tang, Yongqiang & Ghosal, Subhashis, 2007. "A consistent nonparametric Bayesian procedure for estimating autoregressive conditional densities," Computational Statistics & Data Analysis, Elsevier, vol. 51(9), pages 4424-4437, May.
    12. João Henrique Gonçalves Mazzeu & Esther Ruiz & Helena Veiga, 2018. "Uncertainty And Density Forecasts Of Arma Models: Comparison Of Asymptotic, Bayesian, And Bootstrap Procedures," Journal of Economic Surveys, Wiley Blackwell, vol. 32(2), pages 388-419, April.
    13. Vosseler, Alexander, 2016. "Bayesian model selection for unit root testing with multiple structural breaks," Computational Statistics & Data Analysis, Elsevier, vol. 100(C), pages 616-630.
    14. Glen Livingston & Darfiana Nur, 2020. "Bayesian inference of smooth transition autoregressive (STAR)(k)–GARCH(l, m) models," Statistical Papers, Springer, vol. 61(6), pages 2449-2482, December.
    15. Gonçalves Mazzeu, Joao Henrique & Ruiz Ortega, Esther & Veiga, Helena, 2015. "Model uncertainty and the forecast accuracy of ARMA models: A survey," DES - Working Papers. Statistics and Econometrics. WS ws1508, Universidad Carlos III de Madrid. Departamento de Estadística.
    16. Ringwald, Leopold & Zörner, Thomas O., 2023. "The money-inflation nexus revisited," Journal of Empirical Finance, Elsevier, vol. 73(C), pages 293-333.

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