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GENERALIZED LAPLACE INFERENCE IN MULTIPLE CHANGE-POINTS MODELS

Published online by Cambridge University Press:  23 February 2021

Alessandro Casini  and
Pierre Perron
Alessandro Casini*
Affiliation:
University of Rome Tor Vergata
Pierre Perron
Affiliation:
Boston University
*
Address Correspondence to Alessandro Casini, Department of Economics and Finance, University of Rome Tor Vergata, Via Columbia 2, Rome 00133, Italy; e-mail: alessandro.casini@uniroma2.it.
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Abstract

Under the classical long-span asymptotic framework, we develop a class of generalized laplace (GL) inference methods for the change-point dates in a linear time series regression model with multiple structural changes analyzed in, e.g., Bai and Perron (1998, Econometrica 66, 47–78). The GL estimator is defined by an integration rather than optimization-based method and relies on the LS criterion function. It is interpreted as a classical (non-Bayesian) estimator, and the inference methods proposed retain a frequentist interpretation. This approach provides a better approximation about the uncertainty in the data of the change-points relative to existing methods. On the theoretical side, depending on some input (smoothing) parameter, the class of GL estimators exhibits a dual limiting distribution, namely the classical shrinkage asymptotic distribution or a Bayes-type asymptotic distribution. We propose an inference method based on highest density regions using the latter distribution. We show that it has attractive theoretical properties not shared by the other popular alternatives, i.e., it is bet-proof. Simulations confirm that these theoretical properties translate to good finite-sample performance.

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Type
ARTICLES
Information
Econometric Theory , Volume 38 , Issue 1 , February 2022 , pp. 35 - 65
Copyright
© The Author(s), 2021. Published by Cambridge University Press

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Footnotes

This paper is based on the fourth chapter of the first author’s doctoral dissertation at Boston University. We thank the Editor and a Co-Editor for guiding the review, and three anonymous referees for constructive comments. We also thank Zhongjun Qu for useful comments.

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