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Unit root testing with stationary covariates and a structural break in the trend function
Author(s) -
Fossati Sebastian
Publication year - 2013
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.12020
Subject(s) - unit root , mathematics , univariate , structural break , unit root test , covariate , statistical hypothesis testing , statistics , function (biology) , sample size determination , asymptotic distribution , sample (material) , focus (optics) , power (physics) , power function , econometrics , mathematical analysis , cointegration , multivariate statistics , chemistry , physics , chromatography , quantum mechanics , evolutionary biology , estimator , biology , optics
The issue of testing for a unit root allowing for a structural break in the trend function is considered. The focus is on the construction of more powerful tests using the information in relevant multi‐variate data sets. The proposed test adopts the generalized least squares detrending approach and uses correlated stationary covariates to improve power. As it is standard in the literature, the break date is treated as unknown. Asymptotic distributions are derived, and a set of asymptotic and finite sample critical values are tabulated. Asymptotic local power functions show that power gains can be large. Finite sample results show that the test exhibits small‐size distortions and power that can be far beyond what is achievable by univariate tests.