Testing for a unit root in time series regression¶
Why this mattered¶
TBD
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.
Related¶
- cite → Distribution of the Estimators for Autoregressive Time Series with a Unit Root — Phillips and Perron build on Dickey and Fuller's unit-root asymptotics for autoregressive estimators to test nonstationarity in time-series regressions.
- cite → Likelihood Ratio Statistics for Autoregressive Time Series with a Unit Root — Phillips and Perron extend Dickey and Fuller's likelihood-ratio unit-root testing framework to allow more general serial correlation and heteroskedasticity.
- cite → A Simple, Positive Semi-Definite, Heteroskedasticity and Autocorrelation Consistent Covariance Matrix — Phillips and Perron use Newey and West's HAC covariance idea to make unit-root test statistics robust to autocorrelation and heteroskedasticity.
- cite ← Testing the null hypothesis of stationarity against the alternative of a unit root — KPSS positions its stationarity-null test as the reverse-null complement to Phillips and Perron's unit-root regression test.
- enables ← Distribution of the Estimators for Autoregressive Time Series with a Unit Root — Fuller's unit-root estimator distributions supplied the nonstandard asymptotic theory underlying Phillips-Perron style unit-root regression tests.
- enables ← Likelihood Ratio Statistics for Autoregressive Time Series with a Unit Root — Dickey and Fuller's likelihood-ratio unit-root statistics provided the testing framework that Phillips-Perron generalized to serially correlated and heteroskedastic errors.