Bayesian Analysis of Switching Arch Models

34 Pages Posted: 3 Dec 2002

See all articles by Sylvia Kaufmann

Sylvia Kaufmann

Oesterreichische Nationalbank - Economic Studies Division; University of Basel - WWZ

Sylvia Fruhwirth-Schnatter

Johannes Kepler University - Department of Applied Statistics and Econometrics


We consider a time series model with autoregressive conditional heteroscedasticity that is subject to changes in regime. The regimes evolve according to a multistate latent Markov switching process with unknown transition probabilities, and it is the constant in the variance process of the innovations that is subject to regime shifts. The joint estimation of the latent process and all model parameters is performed within a Bayesian framework using the method of Markov chain Monte Carlo (MCMC) simulation. We perform model selection with respect to the number of states and the number of autoregressive parameters in the variance process using Bayes factors and model likelihoods. To this aim, the model likelihood is estimated by the method of bridge sampling. The usefulness of the sampler is demonstrated by applying it to the data set previously used by Hamilton and Susmel (1994) who investigated models with switching autoregressive conditional heteroscedasticity using maximum likelihood methods. The paper concludes with some issues related to maximum likelihood methods, to classical model selection, and to potential straightforward extensions of the model presented here.

Keywords: Bayesian analysis, bridge sampling, MCMC estimation, model selection, switching ARCH-models

Suggested Citation

Kaufmann, Sylvia and Fruhwirth-Schnatter, Sylvia, Bayesian Analysis of Switching Arch Models. Journal of Time Series Analysis, Vol. 23, No. 4, pp. 425-458, 2002. Available at SSRN:

Sylvia Kaufmann (Contact Author)

Oesterreichische Nationalbank - Economic Studies Division ( email )

Otto Wagner-Platz 3
P.O. Box 61
Vienna, 1011
+43 1 40420-7221 (Phone)

University of Basel - WWZ ( email )

Basel, 4002

Sylvia Fruhwirth-Schnatter

Johannes Kepler University - Department of Applied Statistics and Econometrics ( email )

Altenbergerstrasse 69

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