A segmented regime-switching model with its application to stock market indices

This paper evaluates the ability of a Markov regime-switching log-normal (RSLN) model to capture the time-varying features of stock return and volatility. The model displays a better ability to depict a fat tail distribution as compared with using a log-normal model, which means that the RSLN model can describe observed market behavior better. Our major objective is to explore the capability of the model to capture stock market behavior over time. By analyzing the behavior of calibrated regime-switching parameters over different lengths of time intervals, the change-point concept is introduced and an algorithm is proposed for identifying the change-points in the series corresponding to the times when there are changes in parameter estimates. This algorithm for identifying change-points is tested on the Standard and Poor's 500 monthly index data from 1971 to 2008, and the Nikkei 225 monthly index data from 1984 to 2008. It is evident that the change-points we identify match the big events observed in the US stock market and the Japan stock market (e.g., the October 1987 stock market crash), and that the segmentations of stock index series, which are defined as the periods between change-points, match the observed bear-bull market phases.