Testing for a unit root in time series regression
1988/01/01 by PETER C. B. PHILLIPS, Peter C.B. Phillips, PIERRE PERRON +1 · 18,074 citations
Economics, Econometrics and Finance · Mathematics · #Applied mathematics #Asymptotic distribution #Augmented Dickey–Fuller test #Cointegration #Complex Systems and Time Series Analysis #Computer science #Data mining #Econometrics #Financial Risk and Volatility Modeling #Limiting #Mathematics #Monetary Policy and Economic Impact #Nonparametric statistics #Nuisance parameter #Null (SQL) #Null hypothesis #Regression #Series (stratigraphy) #Statistical hypothesis testing #Statistics #Time series #Unit root #Unit root test
paper · doi:10.1093/biomet/75.2.335
published in Biometrika 75(2), 335-346 (Oxford University Press)
openalex publication_date 1988/01/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Abstract
This paper proposes new tests for detecting the presence of a unit root in quite general time series models. Our approach is nonparametric with respect to nuisance parameters and thereby allows for a very wide class of weakly dependent and possibly heterogeneously distributed data. The tests accommodate models with a fitted drift and a time trend so that they may be used to discriminate between unit root nonstationarity and stationarity about a deterministic trend. The limiting distributions of the statistics are obtained under both the unit root null and a sequence of local alternatives. The latter noncentral distribution theory yields local asymptotic power functions for the tests and facilitates comparisons with alternative procedures due to Dickey & Fuller. Simulations are reported on the performance of the new tests in finite samples.
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