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In-fill Asymptotic Theory for Structural Break Point in Autoregression: A Unified Theory

Liang Jiang (), Xiaohu Wang () and Jun Yu ()
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Liang Jiang: School of Economics, Singapore Management University
Xiaohu Wang: The Chinese University of Hong Kong

No 10-2017, Economics and Statistics Working Papers from Singapore Management University, School of Economics

Abstract: This paper 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, tri-modal, dependent on the initial condition. These three properties are also found in the finite sam- ple distribution of the least squares (LS) estimator of structural break point in autoregressive (AR) models. Motivated by these observations, the paper 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 sample distribution. Unlike the long-span asymptotic theory, which depends on the underlying AR root 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.

Keywords: Asymmetry; Bias; Exact distribution; Long-span asymptotics; In-fill asymptotics; Trimodality. (search for similar items in EconPapers)
JEL-codes: C11 C46 (search for similar items in EconPapers)
Pages: 38 pages
Date: 2017-05-19
New Economics Papers: this item is included in nep-ecm, nep-ets, nep-ore and nep-sea
Note: Paper available on: http://ink.library.smu.edu.sg/soe_research/1968/
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