Sieve-based inference for infinite-variance linear processes

Giuseppe Cavaliere, Iliyan Georgiev () and Robert Taylor
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Iliyan Georgiev: Universidade Nova de Lisboa

No 4, Quaderni di Dipartimento from Department of Statistics, University of Bologna

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.

Keywords: Bootstrap; Sieve autoregression; Infinite variance; Time Series (search for similar items in EconPapers)
Pages: 59
Date: 2015
New Economics Papers: this item is included in nep-ecm and nep-ets
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Citations: View citations in EconPapers (4)

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