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:
[thumbnail of Quaderni_2015_4_CavaliereGeorgievTaylor_Sieve.pdf]
License: Creative Commons: Attribution-Noncommercial-No Derivative Works 3.0 (CC BY-NC-ND 3.0)

Download (493kB) | Preview


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.

Document type
Monograph (Working Paper)
Cavaliere, Giuseppe
Georgiev, Iliyan
Taylor, Robert
Bootstrap, Sieve autoregression, Infinite variance, Time Series
Deposit date
20 Nov 2015 10:08
Last modified
07 Jun 2017 08:04

Other metadata



Staff only: View the document