Modeling

ARTICLE IN PRESS

Journal of Econometrics 127 (2005) 179–199 www.elsevier.com/locate/jeconom

A nonparametric test for changing trends

Ted JuhlÃ, Zhijie Xiao

Department of Economics, University of Kansas, 213 Summerfield Hall, Lawrence, KS 66045, USA Accepted 12 May 2004 Available online 18 October 2004

Abstract Many tests of parameter change in dynamic models exhibit nonmonotonic power. An important source of the nonmonotonic power comes from the bias in estimating parameters when there is a change in the deterministic component. To avoid this bias, we propose a nonparametric test for changing trends based on nonparametrically detrended data. The tests are similar in spirit to nonparametric conditional moment tests such as Fan and Li (J. Nonparametr. Stat. 10 (1999a) 245; 11 (1999b) 251) and Zheng (J. Econometrics 75 (1996) 263). The resulting statistics have a standard normal distribution. A Monte Carlo experiment suggests that the tests have good power against changes in the deterministic component. r 2004 Elsevier B.V. All rights reserved.

JEL Classification: C12; C14; C22 Keywords: Nonparametric; Partially linear models; Structural change

1. Introduction Trend stationary processes, or stationary time series with shifted mean or broken trends, are important models in analyzing economic time series. In the last 15 years, a great deal of research attention has been devoted to the development of statistical tests for structural change in the trend function of a time series. Some recent tests

ÃCorresponding author. Tel.: +1-785-864-2849; fax: +1-785-864-5270.

E-mail addresses: juhl@ku.edu (T. Juhl), zxiao@uiuc.edu (Z. Xiao). 0304-4076/$ - see front matter r 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.jeconom.2004.05.014

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180 T. Juhl, Z. Xiao / Journal of Econometrics 127 (2005) 179–199

that can be applied to test structural change in deterministic trend regressors include Bai (1996), Chu and White (1992), Ploberger...