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A Powerful Test for Changing Trends in Time Series Models
Author(s) -
Wu Jilin,
Xiao Zhijie
Publication year - 2018
Publication title -
journal of time series analysis
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.576
H-Index - 54
eISSN - 1467-9892
pISSN - 0143-9782
DOI - 10.1111/jtsa.12282
Subject(s) - mathematics , parametric statistics , heteroscedasticity , variance (accounting) , monotonic function , series (stratigraphy) , distortion (music) , parametric model , econometrics , monte carlo method , algorithm , mathematical optimization , statistics , computer science , mathematical analysis , paleontology , amplifier , computer network , accounting , bandwidth (computing) , business , biology
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.