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STATIONARITY TESTS UNDER TIME-VARYING SECOND MOMENTS

Published online by Cambridge University Press:  23 September 2005

Giuseppe Cavaliere  and
A.M. Robert Taylor
Giuseppe Cavaliere
Affiliation:
University of Bologna
A.M. Robert Taylor
Affiliation:
University of Birmingham
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Abstract

In this paper we analyze the effects of a very general class of time-varying variances on well-known “stationarity” tests of the I(0) null hypothesis. Our setup allows, among other things, for both single and multiple breaks in variance, smooth transition variance breaks, and (piecewise-) linear trending variances. We derive representations for the limiting distributions of the test statistics under variance breaks in the errors of I(0), I(1), and near-I(1) data generating processes, demonstrating the dependence of these representations on the precise pattern followed by the variance processes. Monte Carlo methods are used to quantify the effects of fixed and smooth transition single breaks and trending variances on the size and power properties of the tests. Finally, bootstrap versions of the tests are proposed that provide a solution to the inference problem.We are grateful to Peter Phillips, a co-editor, and two anonymous referees whose comments on an earlier draft have led to a considerable improvement in the paper.

Type
Research Article
Information
Econometric Theory , Volume 21 , Issue 6 , December 2005 , pp. 1112 - 1129
Copyright
© 2005 Cambridge University Press

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