Frequentist and Bayesian Change-Point Models: A Missing Link

We show that the minimum description length (MDL) criterion widely used to estimate lin- ear change-point (CP) models corresponds to the marginal likelihood of a Bayesian model with a specific class of prior distributions. This allows for results from the frequentist and Bayesian literatures to be bridged together. In this estimation framework, one can rely on the consistency of the number and locations of the estimated CPs and the computational efficiency of frequentist methods, and obtain a probability of observing a CP at a given time, compute model posterior probabilities, and select or combine CP methods via Bayesian posteriors. This approach is further extended to other popular information criteria (such as Akaike, Bayes, and Hannan-Quinn’s). Moreover, we propose several CP methods that take advantage of the MDL probabilistic representation. Based on simulated and macroeconomic data, the novel methods detect and date structural breaks with the same or improved level of accuracy than state-of-the- art approaches. Finally, we highlight the usefulness of combining CP methods for long time series, both in terms of improved detection accuracy and reduced computational cost.