Asymptotics for the residual-based bootstrap approximation in nearly nonstationary AR(1) models with possibly heavy-tailed innovations

Ke-Ang Fu, Yuechao Li and Andrew Cheuk-Yin Ng

Statistics & Probability Letters, 2013, vol. 83, issue 11, 2553-2562

Abstract: Consider a nearly nonstationary AR(1) model, Xt=θnXt−1+ut, where θn=1−γ/n, γ is a fixed constant, and the innovations are in the domain of attraction of the normal law with possibly infinite variance. As for the least squares estimator θˆn of θn, we propose to use a residual-based m-out-of-n bootstrap procedure to approximate the distribution of θˆn−θn, and its asymptotic validity is proved.

Keywords: Asymptotic distribution; Domain of attraction of the normal law; m-out-of-n bootstrap; Nearly nonstationary (search for similar items in EconPapers)
Date: 2013
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DOI: 10.1016/j.spl.2013.07.006

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