A Powerful Test for Changing Trends in Time Series Models

14 Pages Posted: 12 Jun 2018

See all articles by Jilin Wu

Jilin Wu

Shandong University - Center for Economic Research

Zhijie Xiao

Boston College - Department of Finance and Department of Economics

Date Written: July 2018

Abstract

We propose a non‐parametric test for trend specification with improved properties. Many existing tests in the literature exhibit non‐monotonic power. To deal with this problem, Juhl and Xiao [Juhl T, 2005] proposed a non‐parametric test with good power by detrending the data non‐parametrically. However, their test is developed for smooth changing trends and is constructed under the assumption of correct specification in the dynamics. In addition, their test suffers from size distortion in finite samples and imposes restrictive assumptions on the variance structure. The current article tries to address these issues. First, the proposed test allows for both abrupt breaks and smooth structural changes in deterministic trends. Second, the test employs a sieve approach to avoid the misspecification problem. Third, the extended test can be applied to the data with conditional heteroskedasticity and time‐varying variance. Fourth, the power properties under alternatives are also investigated. Finally, a partial plug‐in method is proposed to alleviate size distortion. Monte Carlo simulations show that the new test not only has good size but also has monotonic power in finite samples.

Keywords: non‐monotonic power, structural change, bandwidth selection, local power

Suggested Citation

Wu, Jilin and Xiao, Zhijie, A Powerful Test for Changing Trends in Time Series Models (July 2018). Journal of Time Series Analysis, Vol. 39, Issue 4, pp. 488-501, 2018, Available at SSRN: https://ssrn.com/abstract=3192255 or http://dx.doi.org/10.1111/jtsa.12282

Jilin Wu (Contact Author)

Shandong University - Center for Economic Research ( email )

Jinan, Shandong 250100
China

Zhijie Xiao

Boston College - Department of Finance and Department of Economics ( email )

United States

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