Linking Frequentist and Bayesian Change-Point Methods
51 Pages Posted: 8 Jan 2020 Last revised: 9 Jun 2022
Date Written: December 6, 2019
We show that the two-stage minimum description length (MDL) criterion widely used to estimate linear change-point (CP) models corresponds to the marginal likelihood of a Bayesian model with a specific class of prior distributions. This allows results from the frequentist and Bayesian paradigms to be bridged together. Thanks to this link, 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. The approach is extended to other popular information criteria (Akaike, Schwarz, and Hannan-Quinn’s). Furthermore, we adapt several CP methods to take advantage of the MDL probabilistic representation. Based on simulated and macroeconomic data, we show that the adapted CP methods can improve structural break detection compared to state-of-the-art approaches. Finally, we highlight the usefulness of combining CP methods for long time series in terms of improved detection accuracy and reduced computational cost.
Keywords: change-point, model selection/combination, structural change, minimum description length
JEL Classification: C11, C12, C22, C32, C52, C53
Suggested Citation: Suggested Citation