Extension to the product partition model: computing the probability of a change

Abstract

The well-known product partition model (PPM) is considered for the identification of multiple change points in the means and variances of normal data sequences. In a natural fashion, the PPM may provide product estimates of these parameters at each instant of time, as well as the posterior distributions of the partitions and the number of change points. Prior distributions are assumed for the means, variances, and for the probability p that each individual time is a change point. The PPM is extended to generate the posterior distribution of p and the posterior probability that each instant of time is a change point. A Gibbs sampling scheme is used to compute all estimates of interest. The methodology is applied to an important time series from the Brazilian stock market. A sensitivity analysis is performed assuming different prior specifications of p.