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UNIT ROOT INFERENCE FOR NON-STATIONARY LINEAR PROCESSES DRIVEN BY INFINITE VARIANCE INNOVATIONS

Published online by Cambridge University Press:  03 May 2016

Giuseppe Cavaliere ,
Iliyan Georgiev  and
A.M.Robert Taylor
Giuseppe Cavaliere
Affiliation:
University of Bologna
Iliyan Georgiev
Affiliation:
University of Bologna
A.M.Robert Taylor*
Affiliation:
University of Essex
*
*Address correspondence to Robert Taylor, Essex Business School, University of Essex, Wivenhoe Park, Colchester, CO4 3SQ, UK; e-mail: rtaylor@essex.ac.uk
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Abstract

The contribution of this paper is two-fold. First, we derive the asymptotic null distribution of the familiar augmented Dickey-Fuller [ADF] statistics in the case where the shocks follow a linear process driven by infinite variance innovations. We show that these distributions are free of serial correlation nuisance parameters but depend on the tail index of the infinite variance process. These distributions are shown to coincide with the corresponding results for the case where the shocks follow a finite autoregression, provided the lag length in the ADF regression satisfies the same o(T1/3) rate condition as is required in the finite variance case. In addition, we establish the rates of consistency and (where they exist) the asymptotic distributions of the ordinary least squares sieve estimates from the ADF regression. Given the dependence of their null distributions on the unknown tail index, our second contribution is to explore sieve wild bootstrap implementations of the ADF tests. Under the assumption of symmetry, we demonstrate the asymptotic validity (bootstrap consistency) of the wild bootstrap ADF tests. This is done by establishing that (conditional on the data) the wild bootstrap ADF statistics attain the same limiting distribution as that of the original ADF statistics taken conditional on the magnitude of the innovations.

Type
ARTICLES
Information
Econometric Theory , Volume 34 , Issue 2 , April 2018 , pp. 302 - 348
Copyright
Copyright © Cambridge University Press 2016 

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Footnotes

We thank two anonymous referees, the Editor, Peter Phillips, and the Co-Editor, Michael Jansson, for their helpful and constructive comments on previous versions of the paper. Cavaliere and Georgiev gratefully acknowledge financial support provided by the Fundação para a Ciência e a Tecnologia, Portugal, through grant PTDC/EGE-ECO/108620/2008. Cavaliere thanks the Italian Ministry of Education, University and Research (MIUR) for financial support (PRIN project: “Multivariate statistical models for risk assessment”). Cavaliere and Taylor would also like to thank the Danish Council for Independent Research, Sapere Aude | DFF Advanced Grant (Grant nr: 12-124980) for financial support.

References

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