Detection of high and low states in stock market returns with MCMC method in a Markov switching model

To detect abnormal states in stock market returns, this study considers seven indices, over a 21-year period, the Dow Jones, S&P500, Nasdaq, Nikkei225, FTSE100, DAX, and CAC40. Three states are possible, namely a state of high rate of return, a state of low rate of return, both with high volatility and an intermediate state with low volatility. To determine the state of the market at each date, we study the returns using Markov chain Monte Carlo method (Metropolis–Hastings algorithm). Then at a second time, using a Cramer's coefficient, we deduce association coefficients or “correlations” among the different states of the major stock exchange markets around the world. First, the associations were globally stronger during the subprime crisis than during the dot-com bubble period. Second, among European markets Cramer's V is higher regardless of the period. Third, the associations between the Nikkei and the other market indices are systematically lower, indicating the relative disconnection of the Japanese market.