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ASYMPTOTIC PROPERTIES OF THE CUSUM ESTIMATOR FOR THE TIME OF CHANGE IN LINEAR PANEL DATA MODELS

Published online by Cambridge University Press:  22 January 2016

Lajos Horváth ,
Marie Hušková ,
Gregory Rice  and
Jia Wang
Lajos Horváth*
Affiliation:
University of Utah
Marie Hušková
Affiliation:
Charles University
Gregory Rice
Affiliation:
University of Waterloo
Jia Wang
Affiliation:
University of Utah
*
*Address correspondence to Lajos Horváth, Department of Mathematics, University of Utah, Salt Lake City, UT 84112–0090 USA; email: horvath@math.utah.edu.
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Abstract

We consider the problem of estimating the common time of a change in the mean parameters of panel data when dependence is allowed between the cross-sectional units in the form of a common factor. A CUSUM type estimator is proposed, and we establish first and second order asymptotics that can be used to derive consistent confidence intervals for the time of change. Our results improve upon existing theory in two primary directions. Firstly, the conditions we impose on the model errors only pertain to the order of their long run moments, and hence our results hold for nearly all stationary time series models of interest, including nonlinear time series like the ARCH and GARCH processes. Secondly, we study how the asymptotic distribution and norming sequences of the estimator depend on the magnitude of the changes in each cross-section and the common factor loadings. The performance of our results in finite samples is demonstrated with a Monte Carlo simulation study, and we consider applications to two real data sets: the exchange rates of 23 currencies with respect to the US dollar, and the GDP per capita in 113 countries.

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Type
ARTICLES
Information
Econometric Theory , Volume 33 , Issue 2 , April 2017 , pp. 366 - 412
Copyright
Copyright © Cambridge University Press 2016 

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