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A POWERFUL TEST OF THE AUTOREGRESSIVE UNIT ROOT HYPOTHESIS BASED ON A TUNING PARAMETER FREE STATISTIC

Published online by Cambridge University Press:  01 December 2009

Morten Ørregaard Nielsen
Morten Ørregaard Nielsen*
Affiliation:
Queen’s University and CREATES
*
*Address correspondence to Morten Ørregaard Nielsen, Department of Economics, Dunning Hall, room 307, 94 University Avenue, Queen’s University, Kingston, Ontario, K7L 3N6, Canada; e-mail: [email protected].
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Abstract

This paper presents a family of simple nonparametric unit root tests indexed by one parameter, d, and containing the Breitung (2002, Journal of Econometrics 108, 342–363) test as the special case d = 1. It is shown that (a) each member of the family with d > 0 is consistent, (b) the asymptotic distribution depends on d and thus reflects the parameter chosen to implement the test, and (c) because the asymptotic distribution depends on d and the test remains consistent for all d > 0, it is possible to analyze the power of the test for different values of d. The usual Phillips–Perron and Dickey–Fuller type tests are indexed by bandwidth, lag length, etc., but have none of these three properties.

It is shown that members of the family with d < 1 have higher asymptotic local power than the Breitung (2002) test, and when d is small the asymptotic local power of the proposed nonparametric test is relatively close to the parametric power envelope, particularly in the case with a linear time trend. Furthermore, generalized least squares (GLS) detrending is shown to improve power when d is small, which is not the case for the Breitung (2002) test. Simulations demonstrate that when applying a sieve bootstrap procedure, the proposed variance ratio test has very good size properties, with finite-sample power that is higher than that of the Breitung (2002) test and even rivals the (nearly) optimal parametric GLS detrended augmented Dickey–Fuller test with lag length chosen by an information criterion.

Type
ARTICLES
Information
Econometric Theory , Volume 25 , Issue 6: Newbold Conference Special Issue , December 2009 , pp. 1515 - 1544
Copyright
Copyright © Cambridge University Press 2009

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