Frequentist and Bayesian Change-Point Models: A Missing Link

46 Pages Posted: 8 Jan 2020 Last revised: 11 Mar 2020

See all articles by David Ardia

David Ardia

HEC Montreal - Department of Decision Sciences

Arnaud Dufays

CeReFiM. Université de Namur.; Université Laval

Carlos Ordás Criado

Université Laval - Département d'Économique

Date Written: December 6, 2019

Abstract

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.

Keywords: change point, model selection, model combination, structural change

JEL Classification: C11, C12, C22, C32, C52, C53

Suggested Citation

Ardia, David and Dufays, Arnaud and Criado, Carlos Ordás, Frequentist and Bayesian Change-Point Models: A Missing Link (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)

CeReFiM. Université de Namur. ( email )

Rempart de la Vierge 8
Namur, Namur 5000
Belgium

Université Laval ( email )

2214 Pavillon J-A. DeSeve
Quebec, Quebec G1K 7P4
Canada

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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