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Time-varying GARCH-M models are commonly used in econometrics and financial economics. Yet the recursive nature of the conditional variance makes exact likelihoodanalysis 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 () computational operations, where  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

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