Time Series Regression with a Unit Root

Peter Phillips

Econometrica, 1987, vol. 55, issue 2, 277-301

Abstract: This paper studies the random walk in a general time series setting that allows for weakly dependent and heterogeneously distributed innovations. It is shown that simple least squares regression consistently estimates a unit root under very general conditions in spite of the presence of autocorrelated errors. The limiting distribution of the standardized estimator and the associated regression t statistic are found using functional central limit theory. New tests of the random walk hypothesis are developed which permit a wide class of dependent and heterogeneous innovation sequences. A new limiting distribution theory is constructed based on the concept of continuous data recording. This theory, together with an asymptotic expansion that is developed in the paper for the unit root case, explain many of the interesting experimental results recently reported in Evans and Savin (1981, 1984). Copyright 1987 by The Econometric Society.

Date: 1987
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Related works:
Working Paper: Testing for a Unit Root in Time Series Regression (1987)
Working Paper: Time Series Regression with a Unit Root (1986)
Software Item: PPUNIT: RATS procedure to perform Phillips-Perron Unit Root test
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