Multiple change-point analysis for linear regression models

The product partition model (PPM) is a powerful tool for clustering and change point analysis mainly because it considers the number of blocks or segments as a random variable. We apply the PPM to identify multiple change points in linear regression models extending some previous works. In addition, we provide a predictivistic justification for the within-block linear model. This way of modeling provides a non ad-hoc procedure for treating piecewise regression models. We also modify the original algorithm proposed by Barry and Hartigan (1993) in order to obtain samples from the product distributions –posteriors of the parameters in the regression model, say– in the contiguous-block case. Consequently, posterior summaries (including the posterior means or product estimates) can be obtained in the usual way. The product estimates are obtained considering both the proposed and Barry and Hartigan’s algorithms, which are compared to least square estimates for the piecewise regression models. To illustrate the use of the proposed methodology, we analyze some financial data sets.

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