Research Repository

Sieve-based inference for infinite-variance linear processes

Cavaliere, Giuseppe and Georgiev, Iliyan and Taylor, AM Robert (2016) 'Sieve-based inference for infinite-variance linear processes.' Annals of Statistics, 44 (4). 1467 - 1494. ISSN 0090-5364

[img]
Preview
Text
euclid.aos.1467894705.pdf - Published Version

Download (307kB) | Preview

Abstract

We extend the available asymptotic theory for autoregressive sieve estimators to cover the case of stationary and invertible linear processes driven by independent identically distributed (i.i.d.) infinite variance (IV) innovations. We show that the ordinary least squares sieve estimates, together with estimates of the impulse responses derived from these, obtained from an autoregression whose order is an increasing function of the sample size, are consistent and exhibit asymptotic properties analogous to those which obtain for a finite-order autoregressive process driven by i.i.d. IV errors. As these limit distributions cannot be directly employed for inference because they either may not exist or, where they do, depend on unknown parameters, a second contribution of the paper is to investigate the usefulness of bootstrap methods in this setting. Focusing on three sieve bootstraps: the wild and permutation bootstraps, and a hybrid of the two, we show that, in contrast to the case of finite variance innovations, the wild bootstrap requires an infeasible correction to be consistent, whereas the other two bootstrap schemes are shown to be consistent (the hybrid for symmetrically distributed innovations) under general conditions.

Item Type: Article
Subjects: H Social Sciences > HA Statistics
H Social Sciences > HG Finance
Divisions: Faculty of Social Sciences > Essex Business School
Faculty of Social Sciences > Essex Business School > Essex Finance Centre
Depositing User: Jim Jamieson
Date Deposited: 26 Nov 2015 15:45
Last Modified: 25 Sep 2018 15:15
URI: http://repository.essex.ac.uk/id/eprint/15539

Actions (login required)

View Item View Item