GARCH volatility models with fixed parameters are too restrictive for long time series due to breaks in the  volatility process. Flexible alternatives are Markov-switching GARCH and
change-point GARCH models. They require estimation by MCMC methods due to the path dependence problem. An unsolved issue is the computation of their marginal likelihood, which is
essential for determining  the number of regimes or change-points. We solve the problem by using particle MCMC, a technique proposed by Andrieu, Doucet and Holenstein (2010). We examine the performance of this new method on simulated data, and we illustrate its use on several return series.