Testing for a unit root in time series regression. (English) Zbl 0644.62094

Phillips, Peter C. B.; Perron, Pierre

Biometrika 75, No. 2, 335-346 (1988).

Summary: 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 D. A. Dickey and W. A. Fuller [see Econometrica 49, 1057-1072 (1981; Zbl 0471.62090)]. Simulations are reported on the performance of the new tests in finite samples.

MSC:

62M10	Time series, auto-correlation, regression, etc. in statistics (GARCH)
62E20	Asymptotic distribution theory in statistics
62G10	Nonparametric hypothesis testing

Keywords:

Brownian motion; weak convergence; asymptotic null distribution; least squares regression estimation; unit root; time series models; nuisance parameters; heterogeneously distributed data; unit root nonstationarity; stationarity; sequence of local alternatives; noncentral distribution theory; local asymptotic power functions; Simulations

Citations:

Zbl 0471.62090