Publication Type
Journal Article
Version
publishedVersion
Publication Date
5-2021
Abstract
This article obtains the exact distribution of the maximum likelihood estimator of structural break point in the Ornstein–Uhlenbeck process when a continuous record is available. The exact distribution is asymmetric, trimodal, dependent on the initial condition. These three properties are also found in the finite sample distribution of the least squares (LS) estimator of structural break point in autoregressive (AR) models. Motivated by these observations, the article then develops an in-fill asymptotic theory for the LS estimator of structural break point in the AR(1) coefficient. The in-fill asymptotic distribution is also asymmetric, tri-modal, dependent on the initial condition, and delivers excellent approximations to the finite sampledistribution. Unlike the long-span asymptotic theory, which depends on the underlying AR roots and hence is tailor-made but is only available in a rather limited number of cases, the in-fill asymptotic theory is continuous in the underlying roots. Monte Carlo studies show that the in-fill asymptotic theory performs better than the long-span asymptotic theory for cases where the long-span theory is available and performs very well for cases where no long-span theory is available. The article also proposes to use the highest density region to construct confidence intervals for structural break point.
Keywords
asymmetry, exact distribution, highest density region, long-span asymptotics, in-fill asymptotics, trimodality
Discipline
Econometrics
Research Areas
Econometrics
Publication
Econometric Reviews
Volume
40
Issue
4
First Page
359
Last Page
386
ISSN
0747-4938
Identifier
10.1080/07474938.2020.1788822
Publisher
Taylor & Francis: STM, Behavioural Science and Public Health Titles
Citation
JIANG, Liang; WANG, Xiaohu; and Jun YU.
In-fill asymptotic theory for structural break point in autoregression. (2021). Econometric Reviews. 40, (4), 359-386.
Available at: https://ink.library.smu.edu.sg/soe_research/2551
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