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Unit root inference for non-stationary linear processes driven by infinite variance innovations

Cavaliere, Giuseppe and Georgiev, Iliyan and Taylor, AM Robert (2018) 'Unit root inference for non-stationary linear processes driven by infinite variance innovations.' Econometric Theory, 34 (02). 302 - 348. ISSN 0266-4666

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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.

Item Type: Article
Subjects: H Social Sciences > HB Economic Theory
Divisions: Faculty of Social Sciences > Essex Business School
Faculty of Social Sciences > Essex Business School > Essex Finance Centre
Depositing User: Jim Jamieson
Date Deposited: 16 Feb 2016 13:00
Last Modified: 02 Oct 2018 12:15
URI: http://repository.essex.ac.uk/id/eprint/16083

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