Detection of High and Low States in Stock Market Returns with MCMC Method in a Markov Switching Model

Clément Rey (1) , Serge Rey (2) , Jean-Renaud Viala (3)

1 CERMICS - Centre d'Enseignement et de Recherche en Mathématiques et Calcul Scientifique
2 CATT - Centre d'Analyse Théorique et de Traitement des données économiques
3 AMUNDI Asset Management

To detect abnormal states in stock market returns, this study considers seven indices over an 21-year period, the Dow Jones, S&P500, Nasdaq, Nikkei225, the 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. Third, the associations between the Nikkei and the other markets indices are systematically lower, indicating the relative disconnection of the Japanese market.

Mots clés: Markov switching; MCMC method; Abnormal stock returns; Contingency table

Domaines: Economies et finances

Clément Rey, Serge Rey, Jean-Renaud Viala. Detection of High and Low States in Stock Market Returns with MCMC Method in a Markov Switching Model. Economic Modelling, 2014, 41, pp.145-155. ⟨10.1016/j.econmod.2014.05.003⟩. ⟨hal-01880340⟩