Consistency of maximum likelihood estimators for the regime-switching GARCH model

Xie, Yingfu

doi:10.1080/02331880701442619

Research article2009Peer reviewed

Consistency of maximum likelihood estimators for the regime-switching GARCH model

Xie, Yingfu

Abstract

The regime-switching GARCH (generalized autoregressive conditionally heteroscedastic) model incorporates the idea of Markov switching into the more restrictive GARCH model, which significantly extends the GARCH model. However, the statistical inference for such an extended model is rather difficult because observations at any time point then depend on the whole regime path and the likelihood becomes intractable quickly as the length of observations increases. In this paper, by transforming it into an infinite order ARCH model, we obtain the possibility of writing a likelihood which can be handled directly and the consistency of the maximum likelihood estimators is proved. Simulation studies to illustrate the consistency and asymptotic normality of the estimators (for both Gaussian and non-Gaussian innovations) and a model specification problem are presented.

Keywords

GARCH model; regime switching; MLE; consistency; asymptotic normality; model specification

Published in

Statistics
2009, volume: 43, number: 2, pages: 153-165
Publisher: TAYLOR & FRANCIS LTD

SLU Authors

Xie, Yingfu
- Department of Forest Economics, Swedish University of Agricultural Sciences

UKÄ Subject classification

Probability Theory and Statistics

Publication identifier

DOI: https://doi.org/10.1080/02331880701442619

Permanent link to this page (URI)

https://res.slu.se/id/publ/61231