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ESTIMATION OF CHANGE-POINTS IN LINEAR AND NONLINEAR TIME SERIES MODELS

Published online by Cambridge University Press:  04 December 2014

Shiqing Ling
Shiqing Ling*
Affiliation:
Hong Kong University of Science and Technology
*
*Address correspondence to Shiqing Ling, Department of Mathematics, Hong Kong University of Science and Technology, Hong Kong; e-mail : maling@ust.hk.
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Abstract

This paper develops an asymptotic theory for estimated change-points in linear and nonlinear time series models. Based on a measurable objective function, it is shown that the estimated change-point converges weakly to the location of the maxima of a double-sided random walk and other estimated parameters are asymptotically normal. When the magnitude d of changed parameters is small, it is shown that the limiting distribution can be approximated by the known distribution as in Yao (1987, Annals of Statistics 15, 1321–1328). This provides a channel to connect our results with those in Picard (1985, Advances in Applied Probability 17, 841–867) and Bai, Lumsdaine, and Stock (1998, Review of Economic Studies 65, 395–432), where the magnitude of changed parameters depends on the sample size n and tends to zero as n → ∞. The theory is applied for the self-weighted QMLE and the local QMLE of change-points in ARMA-GARCH/IGARCH models. A simulation study is carried out to evaluate the performance of these estimators in the finite sample.

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ARTICLES
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Econometric Theory , Volume 32 , Issue 2 , April 2016 , pp. 402 - 430
Copyright
Copyright © Cambridge University Press 2014 

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