Hostname: page-component-cd9895bd7-gvvz8 Total loading time: 0 Render date: 2024-12-26T20:43:32.174Z Has data issue: false hasContentIssue false
  • English
  • Français

Markov Chain Monte Carlo Estimation of Regime Switching Vector Autoregressions

Published online by Cambridge University Press:  29 August 2014

Glen R. Harris
Glen R. Harris*
Affiliation:
Lend Lease Investment Management, Sydney
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Financial time series data are typically found to possess leptokurtic frequency distributions, time varying volatilities, outliers and correlation structures inconsistent with linear generating processes, nonlinear dependence, and dependencies between series that are not stable over time. Regime Switching Vector Autoregressions are of interest because they are capable of explaining the observed features of the data, can capture a variety of interactions between series, appear intuitively reasonable, are vector processes, and are now tractable.

This paper considers a vector autoregression subject to periodic structural changes. The parameters of a vector autoregression are modelled as the outcome of an unobserved discrete Markov process with unknown transition probabilities. The unobserved regimes, one for each time point, together with the regime transition probabilities, are determined in addition to the vector autoregression parameters within each regime.

A Bayesian Markov Chain Monte Carlo estimation procedure is developed which efficiently generates the posterior joint density of the parameters and the regimes. The complete likelihood surface is generated at the same time, enabling estimation of posterior model probabilities for use in non-nested model selection. The procedure can readily be extended to produce joint prediction densities for the variables, incorporating both parameter and model uncertainty.

Results using simulated and real data are provided. A clear separation of the variance between a stable and an unstable regime was observed. Ignoring regime shifts is very likely to produce misleading volatility estimates and is unlikely to be robust to outliers. A comparison with commonly used models suggests that Regime Switching Vector Autoregressions provide a particularly good description of the observed data.

Keywords

Vector regime switchingjoint parameter densityoutliersGibbs samplerMetropolis-Hastings algorithmMarkov Chain Monte Carloposterior model probabilitiesmodel selection
Type
Articles
Information
ASTIN Bulletin: The Journal of the IAA , Volume 29 , Issue 1 , May 1999 , pp. 47 - 79
Copyright
Copyright © International Actuarial Association 1999

References

Akgiray, V. (1989). Conditional Heteroscedasticity in Time Series of Stock Returns: Evidence and Forecasts. Journal of Business 62, 55–80.Google Scholar
Albert, J. H. and Chib, S. (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, 1–15.Google Scholar
Becker, D. (1991). Statistical Tests of the Lognormal Distribution as a Basis for Interest Rate Changes. Transactions of the Society of Actuaries XLIII.Google Scholar
Bollerslev, T. (1986). Generalized Autoregressive Conditional Heteroskedasticity. Journal of Econometrics 31 (June 1986), 307–327.Google Scholar
Carter, C. K. and Kohn, R. (1994). On Gibbs Sampling for State Space Models. Biometrika 81, 3, 541–553.Google Scholar
Chib, S. and Greenberg, E. (1995). Understanding the Metropolis-Hastings Algorithm. The American Statistician 49, No. 4, 327–335.Google Scholar
Engle, R. F. (1982). Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of U.K. Inflation. Econometrica 50, 987–1008.Google Scholar
Frees, E. W., Kung, Y-C., Rosenberg, M. A., Young, V. R. and Lai, S-W. (1996). Forecasting Social Security Actuarial Assumptions. North American Actuarial Journal 1, No. 4, 49–75.Google Scholar
Gray, S. F. (1996). Modeling the Conditional Distribution of Interest Rates as a Regime-Switching Process. Journal of Financial Economics 42, 27–62.Google Scholar
Hamilton, J. D. (1989). A New Approach to the Economic Analysis of Nonstationary Time Series and the Business Cycle. Econometrica, 57, 357–384.Google Scholar
Hamilton, J. D. (1990). Analysis of Time Series Subject to Changes in Regime. Journal of Econometrics, 45, 39–70.Google Scholar
Hamilton, J. D. and Susmel, R. (1994). Autoregressive Conditional Heteroskedasticity and Changes in Regime. Journal of Econometrics, 64, 307–333.CrossRefGoogle Scholar
Hamilton, J. D. and Lin, G. (1996). Stock Market Volatility and the Business Cycle. Journal of Applied Econometrics, 11, 573–593.Google Scholar
Harris, G. R. (1994). On Australian Stochastic Share Return Models for Actuarial Use. The Institute of Actuaries of Australia Quarterly Journal, September 1994, 34–54.Google Scholar
Harris, G. R. (1995a). Statistical Data Analysis and Stochastic Asset Model Validation. Transactions of the 25th International Congress of Actuaries 3, 313–331 (Brussels, Belgium).Google Scholar
Harris, G. R. (1995b). Low Frequency Statistical Interest Rate Models. Proceedings of the 5th AFIR International Colloquium 2, 799–831 (Brussels, Belgium).Google Scholar
Harris, G. R. (1995c). A Comparison of Stochastic Asset Models for Long Term Studies. The Institute of Actuaries of Australia Quarterly Journal, September 1995, 43–75.Google Scholar
Harris, G. R. (1996). Market Phases and Cycles? A Regime Switching Approach. The Institute of Actuaries of Australia Quarterly Journal, December 1996, Part 2, 28–44.Google Scholar
Kass, R. E. and Raftery, A. E. (1995). Bayes Factors. Journal of the American Statistical Association 90, 430, 773–795.Google Scholar
Kim, C. (1994). Dynamic Linear Models with Markov-Switching. Journal of Econometrics 60, 1–22.CrossRefGoogle Scholar
Lütkepohl, H. (1991). Introduction to Multiple Time Series Analysis. Springer-Verlag.CrossRefGoogle Scholar
Liu, J., Wong, W. H. and Kong, A. (1994). Covariance Structure of the Gibbs Sampler with Applications to the Comparison of Estimators and Augmentation Schemes. Biometrika 81, 27–40.Google Scholar
McNees, S. S. (1979). The Forecasting Record for the 1970's. New England Economic Review September/October 1979, 33–53.Google Scholar
Praetz, P. D. (1969). Australian Share Prices and the Random Walk Hypothesis. Australian Journal of Statistics 11, no. 3 (1969), 123–139.Google Scholar
Stock, J. H. and Watson, M. W. (1996). Evidence on Structural Instability in Macroeconomic Time Series Relations. Journal of Business and Economic Statistics 14, 1, 11–30.Google Scholar