Markov switching in stochastic variance. Bayesian comparison of two simple models

Abstract

In the paper two particular Markov Switching Stochastic Volatility models (MSSV) are under consideration: one with a switching intercept in the Iog-volatility equation, and the other — with a regime-dependent autoregression parameter. While the former one is fairly common in the literature (as a tool of taking account for regimes of different mean volatility level), the latter has not been paid almost any attention so far. We note the fact, that state-varying mean volatility may arise from switches in the intercept or in the autoregression parameter. Hence, we aim to compare these two models in respect of goodness of fit to the data from the Polish financial market, employing Bayesian techniques of estimation and model comparison. Clear evidence of structural shifts in the volatility pattern is found. Two different regimes of the economy are characterized in terms of the mean volatility level and the variance of volatility.