A change point analysis of BOVESPA and BOVMESB indexes using the Bayeian approach

In this paper we present a Bayesian solution to the multiple change point problems in the mean m and variance s2 of two Brazilian indexes: Índice Geral da Bolsa de Valores de São Paulo (IBOVESPA) and Índice da Bolsa de Valores de Minas Gerais, Espírito Santo e Brasília (IBOVMESB), both expressed in terms of returns calculated on closing prices. The product partition model defined by Hartigan (1990) is used to obtain the posterior behavior of m and s2 and to construct the posterior distributions of the number of change points. The Gibbs sampling scheme is reviewed and implemented to estimate the posterior distribution of the number of change points. The results are used to analyze the behavior of IBOVESPA and IBOVMESB within the period from 1991 to 1999.