An Estimation Methodology For Markov Regime Switching Stochastic Volatility Model Using A Modified EM Algorithm

Economists have long recognized the possibility that parameters may not be constant through time, but rather that structural shifts may occur in parameters. Dynamic models with Markov switching between regimes is a tool for dealing with such structural shifts. The number of published papers that apply Markov switching models has been enormous in the field of volatility studies. In this paper, we propose a model of volatility using a Markov regime switching stochastic volatility(MRSV) model that includes Markovian state transition matrix in the state equation. For estimating the volatility of this MRSV, we now describe a modified filter, smoother, and EM algorithm using Bayes theorem(Kim, H. Y., 1998) and a quasi maximum likelihood approach. The proposed algorithm is tested for stock price index return data, KOSPI200 and S&P500. By comparisons with a GARCH model, this algorithm provides better results in terms of the MSE criterion.