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HETEROSKEDASTIC TIME SERIES WITH A UNIT ROOT

Published online by Cambridge University Press:  01 October 2009

Giuseppe Cavaliere  and
A.M. Robert Taylor
Giuseppe Cavaliere
Affiliation:
University of Bologna
A.M. Robert Taylor*
Affiliation:
University of Nottingham
*
*Address correspondence to Robert Taylor, School of Economics, The Sir Clive Granger Building, University of Nottingham, Nottingham NG7 2RD, United Kingdom; e-mail: Robert.Taylor@nottingham.ac.uk.
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Abstract

In this paper we provide a unified theory, and associated invariance principle, for the large-sample distributions of the Dickey–Fuller class of statistics when applied to unit root processes driven by innovations displaying nonstationary stochastic volatility of a very general form. These distributions are shown to depend on both the spot volatility and the integrated variation associated with the innovation process. We propose a partial solution (requiring any leverage effects to be asymptotically negligible) to the identified inference problem using a wild bootstrap–based approach. Results are initially presented in the context of martingale differences and are later generalized to allow for weak dependence. Monte Carlo evidence is also provided that suggests that our proposed bootstrap tests perform very well in finite samples in the presence of a range of innovation processes displaying nonstationary volatility and/or weak dependence.

Type
ARTICLES
Information
Econometric Theory , Volume 25 , Issue 5 , October 2009 , pp. 1228 - 1276
Copyright
Copyright © Cambridge University Press 2009

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