Journal of Probability and Statistics
Volume 2011 (2011), Article ID 718647, 39 pages
Research Article

Estimation and Properties of a Time-Varying GQARCH(1,1)-M Model

Athens University of Economics and Business, Department of International and European Economic Studies, 10434 Athens, Greece

Received 16 May 2011; Accepted 14 July 2011

Academic Editor: Mike Tsionas

Copyright © 2011 Sofia Anyfantaki and Antonis Demos. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Time-varying GARCH-M models are commonly used in econometrics and financial economics. Yet the recursive nature of the conditional variance makes exact likelihood analysis of these models computationally infeasible. This paper outlines the issues and suggests to employ a Markov chain Monte Carlo algorithm which allows the calculation of a classical estimator via the simulated EM algorithm or a simulated Bayesian solution in only 𝑂 ( 𝑇 ) computational operations, where 𝑇 is the sample size. Furthermore, the theoretical dynamic properties of a time-varying GQARCH(1,1)-M are derived. We discuss them and apply the suggested Bayesian estimation to three major stock markets.