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Asymptotic Distributions of the Least-Squares Estimators and Test Statistics in the Near Unit Root Model with Non-Zero Initial Value and Local Drift and Trend

Published online by Cambridge University Press:  11 February 2009

Seiji Nabeya  and
Bent E. Sørensen
Seiji Nabeya
Affiliation:
Tokyo International University
Bent E. Sørensen
Affiliation:
Brown University
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Abstract

This paper considers the distribution of the Dickey-Fuller test in a model with non-zero initial value and drift and trend. We show how stochastic integral representations for the limiting distribution can be derived either from the local to unity approach with local drift and trend or from the continuous record asymptotic results of Sørensen [29]. We also show how the stochastic integral representations can be utilized as the basis for finding the corresponding characteristic functions via the Fredholm approach of Nabeya and Tanaka [16,17], This “link” between those two approaches may be of general interest. We further tabulate the asymptotic distribution by inverting the characteristic function. Using the same methods, we also find the characteristic function for the asymptotic distribution for the Schmidt-Phillips [26] unit root test. Our results show very clearly the dependence of the various tests on the initial value of the time series.

Type
Articles
Information
Econometric Theory , Volume 10 , Issue 5 , December 1994 , pp. 937 - 966
Copyright
Copyright © Cambridge University Press 1994

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