ON THE ASYMPTOTIC EXPECTATIONS OF SOME UNIT ROOT TESTS IN A FIRST ORDER AUTOREGRESSIVE

PROCESS IN THE PRESENCE OF TREND

ROLF LARSSON

Department of Mathematics, Uppsala University, P.O. Box 480, S-751 06 Uppsala, Sweden

(Received September 8, 1995; revised September 11, 1996)

Abstract. Estimation in a first order autoregressive process with trend is considered. Integral expressions for the asymptotic bias of the estimator under a unit root and for the expectation of the limit distribution of the log likelihood ratio test for a unit root are given, and evaluated numerically.

Key words and phrases: Autoregression with trend, unit root test.