Distribution of the Estimators for Autoregressive Time Series with a Unit Root¶
Why this mattered¶
TBD
Abstract¶
Abstract Let n observations Y 1, Y 2, ···, Y n be generated by the model Y t = pY t−1 + e t , where Y 0 is a fixed constant and {e t } t-1 n is a sequence of independent normal random variables with mean 0 and variance σ2. Properties of the regression estimator of p are obtained under the assumption that p = ±1. Representations for the limit distributions of the estimator of p and of the regression t test are derived. The estimator of p and the regression t test furnish methods of testing the hypothesis that p = 1.
Related¶
- enables → Statistical analysis of cointegration vectors — Dickey and Fuller's unit-root asymptotics supplied the nonstationary time-series foundation Johansen needed to derive likelihood tests for cointegration vectors.
- enables → Testing for a unit root in time series regression — Fuller's unit-root estimator distributions supplied the nonstandard asymptotic theory underlying Phillips-Perron style unit-root regression tests.
- enables → Testing the null hypothesis of stationarity against the alternative of a unit root — Dickey and Fuller's unit-root asymptotics supplied the nonstationary time-series testing framework that KPSS inverted by making stationarity the null hypothesis.
- cite ← Statistical analysis of cointegration vectors — Johansen's cointegration analysis cites Dickey-Fuller unit-root theory as the time-series foundation for testing nonstationarity.
- cite ← Likelihood Ratio Statistics for Autoregressive Time Series with a Unit Root — Dickey and Fuller's likelihood-ratio tests build directly on their earlier unit-root autoregressive estimator distributions.
- cite ← Testing for a unit root in time series regression — Phillips and Perron build on Dickey and Fuller's unit-root asymptotics for autoregressive estimators to test nonstationarity in time-series regressions.
- cite ← Testing the null hypothesis of stationarity against the alternative of a unit root — KPSS contrasts its stationarity-null test with Dickey and Fuller's unit-root asymptotics for autoregressive time-series estimators.