Sieve-based inference for infinite-variance linear processes

Cavaliere, Giuseppe ; Georgiev, Iliyan ; Taylor, Robert (2015) Sieve-based inference for infinite-variance linear processes. Bologna, IT: Dipartimento di Scienze Statistiche "Paolo Fortunati", Alma Mater Studiorum Università di Bologna, p. 59. DOI 10.6092/unibo/amsacta/4404. In: Quaderni di Dipartimento. Serie Ricerche (4). ISSN 1973-9346.
Full text available as:
[img]
Preview
PDF
License: Creative Commons Attribution Non-commercial No Derivatives

Download (493kB) | 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.

Abstract
Document type
Monograph (Working Paper)
Creators
CreatorsAffiliationORCID
Cavaliere, Giuseppe
Georgiev, Iliyan
Taylor, Robert
Keywords
Bootstrap, Sieve autoregression, Infinite variance, Time Series
Subjects
ISSN
1973-9346
DOI
Deposit date
20 Nov 2015 10:08
Last modified
07 Jun 2017 08:04
URI

Other metadata

Downloads

Downloads

Staff only: View the document

^