Linking Frequentist and Bayesian Change-Point Methods

51 Pages Posted: 8 Jan 2020 Last revised: 9 Jun 2022

See all articles by David Ardia

David Ardia

HEC Montreal - Department of Decision Sciences

Arnaud Dufays

EDHEC Business school

Carlos Ordás Criado

Université Laval - Département d'Économique

Date Written: December 6, 2019

Abstract

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

Ardia, David and Dufays, Arnaud and Criado, Carlos Ordás, Linking Frequentist and Bayesian Change-Point Methods (December 6, 2019). Available at SSRN: https://ssrn.com/abstract=3499824 or http://dx.doi.org/10.2139/ssrn.3499824

David Ardia

HEC Montreal - Department of Decision Sciences ( email )

3000 Côte-Sainte-Catherine Road
Montreal, QC H2S1L4
Canada

Arnaud Dufays (Contact Author)

EDHEC Business school ( email )

24 Avenue Gustave Delory
Roubaix, 59100
France

Carlos Ordás Criado

Université Laval - Département d'Économique ( email )

2325 Rue de l'Université
Ste-Foy, Quebec G1K 7P4 G1K 7P4
Canada

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