Theory and Inference for a Markov Switching GARCH Model

CORE Discussion Paper No. 2007/55

26 Pages Posted: 6 Sep 2007

See all articles by Luc Bauwens

Luc Bauwens

Université catholique de Louvain

Arie Preminger

University of Haifa - Department of Economics; Catholic University of Louvain (UCL) - Center for Operations Research and Econometrics (CORE)

J. V. K. Rombouts

HEC Montreal; Catholic University of Louvain (UCL) - Center for Operations Research and Econometrics (CORE); Centre interuniversitaire sur le risque, les politiques économiques et l'emploi (CIRPÉE); Center for Interuniversity Research and Analysis on Organization (CIRANO)

Date Written: August 2007

Abstract

We develop a Markov-switching GARCH model (MS-GARCH) wherein the conditional mean and variance switch in time from one GARCH process to another. The switching is governed by a hidden Markov chain. We provide sufficient conditions for geometric ergodicity and existence of moments of the process. Because of path dependence, maximum likelihood estimation is not feasible. By enlarging the parameter space to include the state variables, Bayesian estimation using a Gibbs sampling algorithm is feasible. We illustrate the model on SP500 daily returns.

Keywords: GARCH, Markov-switching, Bayesian inference

JEL Classification: C11, C22, C52

Suggested Citation

Bauwens, Luc and Preminger, Arie and Rombouts, Jeroen, Theory and Inference for a Markov Switching GARCH Model (August 2007). CORE Discussion Paper No. 2007/55, Available at SSRN: https://ssrn.com/abstract=1011623 or http://dx.doi.org/10.2139/ssrn.1011623

Luc Bauwens (Contact Author)

Université catholique de Louvain ( email )

CORE
34 Voie du Roman Pays
B-1348 Louvain-la-Neuve, b-1348
Belgium
32 10 474321 (Phone)
32 10 474301 (Fax)

Arie Preminger

University of Haifa - Department of Economics ( email )

Haifa 31905
Israel

Catholic University of Louvain (UCL) - Center for Operations Research and Econometrics (CORE) ( email )

34 Voie du Roman Pays
B-1348 Louvain-la-Neuve, b-1348
Belgium

Jeroen Rombouts

HEC Montreal ( email )

3000, Chemin de la Côte-Sainte-Catherine
Montreal, Quebec H3T 2A7
Canada

Catholic University of Louvain (UCL) - Center for Operations Research and Econometrics (CORE) ( email )

34 Voie du Roman Pays
B-1348 Louvain-la-Neuve, b-1348
Belgium

Centre interuniversitaire sur le risque, les politiques économiques et l'emploi (CIRPÉE) ( email )

Pavillon De Sève
Ste-Foy, Quebec G1K 7P4
Canada

Center for Interuniversity Research and Analysis on Organization (CIRANO) ( email )

2020 rue University, 25th floor
Montreal H3C 3J7, Quebec
Canada

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