The New Palgrave Dictionary of Economics

2018 Edition
| Editors: Macmillan Publishers Ltd

Regime Switching Models

  • James D. Hamilton
Reference work entry
DOI: https://doi.org/10.1057/978-1-349-95189-5_2459

Abstract

If the parameters of a time-series process are subject to change over time, then a full description of the data-generating process must include a specification of the probability law governing these changes, for example, postulating that the parameters evolve according to the realization of an unobserved Markov chain. This article describes classical and Bayesian algorithms for estimation and inference in such models and discusses some of the issues that arise in particular cases such as GARCH and state-space models.

Keywords

ARMA models Asset prices Econometrics GARCH models Gaussian densities Gibbs sampler Kalman filter Markov chain Monte Carlo methods Markov processes Maximum likelihood Numerical optimization methods in economics Regime-switching models State-space models Vector autoregressions 

JEL Classifications

C1 
This is a preview of subscription content, log in to check access.

Bibliography

  1. Albert, J., and S. Chib. 1993. Bayes inference via Gibbs sampling of autoregressive time series subject to Markov mean and variance shifts. Journal of Business and Economic Statistics 11: 1–15.Google Scholar
  2. Ang, A., and G. Bekaert. 2002a. International asset allocation with regime shifts. Review of Financial Studies 15: 1137–1187.CrossRefGoogle Scholar
  3. Ang, A., and G. Bekaert. 2002b. Regime switches in interest rates. Journal of Business and Economic Statistics 20: 163–182.CrossRefGoogle Scholar
  4. Baum, L., E. Petrie, G. Soules, and N. Weiss. 1980. A maximization technique occurring in the statistical analysis of probabilistic functions of Markov chains. Annals of Mathematical Statistics 41: 164–171.CrossRefGoogle Scholar
  5. Calvet, L., and A. Fisher. 2004. How to forecast long-run volatility: Regime-switching and the estimation of multifractal processes. Journal of Financial Econometrics 2: 49–83.CrossRefGoogle Scholar
  6. Carrasco, M., L. Hu, and W. Ploberger. 2004. Optimal test for Markov switching. Working paper. University of Rochester.Google Scholar
  7. Cerra, V., and S. Saxena. 2005. Did output recover from the Asian crisis? IMF Staff Papers 52: 1–23.Google Scholar
  8. Chauvet, M., and J. Hamilton. 2006. Dating business cycle turning points. In Nonlinear time series analysis of business cycles, ed. C. Milas, P. Rothman, and D. van Dijk. Amsterdam: Elsevier.Google Scholar
  9. Chib, S. 1998. Estimation and comparison of multiple change-point models. Journal of Econometrics 86: 221–241.CrossRefGoogle Scholar
  10. Cosslett, S., and L.-F. Lee. 1985. Serial correlation in discrete variable models. Journal of Econometrics 27: 79–97.CrossRefGoogle Scholar
  11. Dai, Q., K. Singleton, and W. Yang. 2003. Regime shifts in a dynamic term structure model of U.S. Treasury bonds. Working paper, Stanford University.Google Scholar
  12. Davig, T. 2004. Regime-switching debt and taxation. Journal of Monetary Economics 51: 837–859.CrossRefGoogle Scholar
  13. Diebold, F., J.-H. Lee, and G. Weinbach. 1994. Regime switching with time-varying transition probabilities. In Nonstationary time series analysis and cointegration, ed. C. Hargreaves. Oxford: Oxford University Press.Google Scholar
  14. Dueker, M. 1997. Markov switching in GARCH processes and mean-reverting stockmarket volatility. Journal of Business and Economic Statistics 15: 26–34.Google Scholar
  15. Filardo, A. 1994. Business cycle phases and their transitional dynamics. Journal of Business and Economic Statistics 12: 299–308.Google Scholar
  16. Filardo, A., and S. Gordon. 1998. Business cycle durations. Journal of Econometrics 85: 99–123.CrossRefGoogle Scholar
  17. Francq, C., and J.-M. Zakoïan. 2001. Stationarity of multivariate Markov-switching ARMA models. Journal of Econometrics 102: 339–364.CrossRefGoogle Scholar
  18. Garcia, R. 1998. Asymptotic null distribution of the likelihood ratio test in Markov switching models. International Economic Review 39: 763–788.CrossRefGoogle Scholar
  19. Garcia, R., R. Luger, and E. Renault. 2003. Empirical assessment of an intertemporal option pricing model with latent variables. Journal of Econometrics 116: 49–83.CrossRefGoogle Scholar
  20. Goldfeld, S., and R. Quandt. 1973. A Markov model for switching regressions. Journal of Econometrics 1: 3–16.CrossRefGoogle Scholar
  21. Gray, S. 1996. Modeling the conditional distribution of interest rates as a regime-switching process. Journal of Financial Economics 42: 27–62.CrossRefGoogle Scholar
  22. Haas, M., S. Mittnik, and M. Paolella. 2004. A new approach to Markov-switching GARCH models. Journal of Financial Econometrics 2: 493–530.CrossRefGoogle Scholar
  23. Hamilton, J. 1988. Rational-expectations econometric analysis of changes in regime: An investigation of the term structure of interest rates. Journal of Economic Dynamics and Control 12: 385–423.CrossRefGoogle Scholar
  24. Hamilton, J. 1989. A new approach to the economic analysis of nonstationary time series and the business cycle. Econometrica 57: 357–384.CrossRefGoogle Scholar
  25. Hamilton, J. 1994. Time series analysis. Princeton: Princeton University Press.Google Scholar
  26. Hamilton, J. 1996. Specification testing in Markov-switching time-series models. Journal of Econometrics 70: 127–157.CrossRefGoogle Scholar
  27. Hamilton, J. 2005. What’s real about the business cycle? Federal Reserve Bank of St. Louis Review 87: 435–452.Google Scholar
  28. Hamilton, J., and G. Lin. 1996. Stock market volatility and the business cycle. Journal of Applied Econometrics 11: 573–593.CrossRefGoogle Scholar
  29. Hamilton, J., and G. Perez-Quiros. 1996. What do the leading indicators lead? Journal of Business 69: 27–49.CrossRefGoogle Scholar
  30. Hamilton, J., and R. Susmel. 1994. Autoregressive conditional heteroskedasticity and changes in regime. Journal of Econometrics 64: 307–333.CrossRefGoogle Scholar
  31. Hansen, B. 1992. The likelihood ratio test under non-standard conditions. Journal of Applied Econometrics 7: S61–S82. Erratum, 11(1996), 195–198.Google Scholar
  32. Jeanne, O., and P. Masson. 2000. Currency crises, sunspots, and Markov-switching regimes. Journal of International Economics 50: 327–350.CrossRefGoogle Scholar
  33. Juang, B.-H., and L. Rabiner. 1985. Mixture autoregressive hidden Markov models for speech signals. IEEE Transactions on Acoustics, Speech, and Signal Processing 30: 1404–1413.CrossRefGoogle Scholar
  34. Kim, C. 1994. Dynamic linear models with Markov-switching. Journal of Econometrics 60: 1–22.CrossRefGoogle Scholar
  35. Kim, C., and C. Nelson. 1999. State-space models with regime switching. Cambridge, MA: MIT Press.Google Scholar
  36. Koop, G., and S. Potter. 1999. Bayes factors and nonlinearity: Evidence from economic time series. Journal of Econometrics 88: 251–281.CrossRefGoogle Scholar
  37. Krolzig, H.-M. 1997. Markov-switching vector autoregressions: Modelling, statistical inference, and application to business cycle analysis. Berlin: Springer.CrossRefGoogle Scholar
  38. Lindgren, G. 1978. Markov regime models for mixed distributions and switching regressions. Scandinavian Journal of Statistics 5: 81–91.Google Scholar
  39. Peria, M. 2002. A regime-switching approach to the study of speculative attacks: A focus on EMS crises. In Advances in Markov-switching models, ed. J. Hamilton and B. Raj. Heidelberg: Physica Verlag.Google Scholar
  40. Poritz, A. 1982. Linear predictive hidden Markov models and the speech signal. Acoustics, Speech and Signal Processing, IEEE Conference on ICASSP ’82 7: 1291–1294.CrossRefGoogle Scholar
  41. Rabiner, L. 1989. A tutorial on hidden Markov models and selected applications in speech recognition. Proceedings of the IEEE 77: 257–286.CrossRefGoogle Scholar
  42. Sims, C., and T. Zha. 2006. Were there switches in U.S. monetary policy? American Economic Review 96: 54–81.CrossRefGoogle Scholar
  43. Timmermann, A. 2000. Moments of Markov switching models. Journal of Econometrics 96: 75–111.CrossRefGoogle Scholar
  44. Tjøstheim, D. 1986. Some doubly stochastic time series models. Journal of Time Series Analysis 7: 51–72.CrossRefGoogle Scholar
  45. Yang, M. 2000. Some properties of vector autoregressive processes with Markov-switching coefficients. Econometric Theory 16: 23–43.CrossRefGoogle Scholar

Copyright information

© Macmillan Publishers Ltd. 2018

Authors and Affiliations

  • James D. Hamilton
    • 1
  1. 1.