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A flexible prior distribution for Markov switching autoregressions with Student-t errors

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Abstract

This paper proposes an empirical Bayes approach for Markov switching autoregressions that can constrain some of the state-dependent parameters (regression coefficients and error variances) to be approximately equal across regimes. By flexibly reducing the dimension of the parameter space, this can help to ensure regime separation and to detect the Markov switching nature of the data. The permutation sampler with a hierarchical prior is used for choosing the prior moments, the identification constraint, and the parameters governing prior state dependence. The empirical relevance of the methodology is illustrated with an application to quarterly and monthly real interest rate data.

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Bibliographic Info

Paper provided by Department of Quantitative Economics, University of Freiburg/Fribourg Switzerland in its series DQE Working Papers with number 2.

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Length: 43 pages
Date of creation: 15 Jun 2004
Date of revision: 12 Nov 2011
Publication status: Published in Journal of Econometrics, 2006, vol. 133, no. 1, pp. 153-190.
Handle: RePEc:fri:dqewps:wp0002

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Keywords: Hidden Markov models; empirical Bayes prior; truncated inverted gamma; permutation sampler; real interest rate;

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  1. Geweke, J, 1993. "Bayesian Treatment of the Independent Student- t Linear Model," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 8(S), pages S19-40, Suppl. De.
  2. John Geweke, 1995. "Monte Carlo simulation and numerical integration," Staff Report 192, Federal Reserve Bank of Minneapolis.
  3. Hamilton, James D, 1989. "A New Approach to the Economic Analysis of Nonstationary Time Series and the Business Cycle," Econometrica, Econometric Society, vol. 57(2), pages 357-84, March.
  4. Garcia, R. & Perron, P., 1994. "An Analysis of the Real Interest rate Under Regime Shifts," Cahiers de recherche 9428, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
  5. van Dijk, Dick & Teräsvirta, Timo & Franses, Philip Hans, 2000. "Smooth Transition Autoregressive Models - A Survey of Recent Developments," Working Paper Series in Economics and Finance 380, Stockholm School of Economics, revised 17 Jan 2001.
  6. Engel, Charles & Hamilton, James D, 1990. "Long Swings in the Dollar: Are They in the Data and Do Markets Know It?," American Economic Review, American Economic Association, vol. 80(4), pages 689-713, September.
  7. Fruhwirth-Schnatter S., 2001. "Markov Chain Monte Carlo Estimation of Classical and Dynamic Switching and Mixture Models," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 194-209, March.
  8. Andrews, Donald W K, 1991. "Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimation," Econometrica, Econometric Society, vol. 59(3), pages 817-58, May.
  9. John Geweke, 2004. "Getting It Right: Joint Distribution Tests of Posterior Simulators," Journal of the American Statistical Association, American Statistical Association, vol. 99, pages 799-804, January.
  10. Kim, Sangjoon & Shephard, Neil & Chib, Siddhartha, 1998. "Stochastic Volatility: Likelihood Inference and Comparison with ARCH Models," Review of Economic Studies, Wiley Blackwell, vol. 65(3), pages 361-93, July.
  11. Chib, Siddhartha, 1996. "Calculating posterior distributions and modal estimates in Markov mixture models," Journal of Econometrics, Elsevier, vol. 75(1), pages 79-97, November.
  12. Donald W.K. Andrews & Christopher J. Monahan, 1990. "An Improved Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimator," Cowles Foundation Discussion Papers 942, Cowles Foundation for Research in Economics, Yale University.
  13. Hans M. Amman & David A. Kendrick, . "Computational Economics," Online economics textbooks, SUNY-Oswego, Department of Economics, number comp1, Spring.
  14. C. P. Robert & T. Rydén & D. M. Titterington, 2000. "Bayesian inference in hidden Markov models through the reversible jump Markov chain Monte Carlo method," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 62(1), pages 57-75.
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Cited by:
  1. Philippe J. Deschamps, 2008. "Comparing smooth transition and Markov switching autoregressive models of US unemployment," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 23(4), pages 435-462.
  2. Ardia, David, 2007. "Bayesian Estimation of a Markov-Switching Threshold Asymmetric GARCH Model with Student-t Innovations," DQE Working Papers 6, Department of Quantitative Economics, University of Freiburg/Fribourg Switzerland, revised 08 Jul 2008.
  3. Tomasz Wozniak, 2012. "Testing Causality Between Two Vectors in Multivariate GARCH Models," Economics Working Papers ECO2012/20, European University Institute.
  4. Ardia, David, 2009. "Bayesian Estimation of the GARCH(1,1) Model with Student-t Innovations in R," MPRA Paper 17414, University Library of Munich, Germany.
  5. Tomasz Wozniak, 2012. "Granger-causal analysis of VARMA-GARCH models," Economics Working Papers ECO2012/19, European University Institute.

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