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Bootstrapping M-estimators in GARCH models

Research output: Contribution to journalJournal article

E-pub ahead of print
<mark>Journal publication date</mark>6/05/2020
<mark>Journal</mark>Biometrika
Number of pages8
Publication statusE-pub ahead of print
Early online date6/05/20
Original languageEnglish

Abstract

We consider the weighted bootstrap approximation of the distribution of a class of M-estimators of the GARCH (p, q) parameters. We prove that the bootstrap distribution, given the data, is a consistent estimate in probability of the distribution of the M-estimator which is asymptotically normal. We propose an algorithm for the computation of M-estimates which at the same time is software-friendly to compute the bootstrap replicates from the given data. Our simulation study indicates superior coverage rates for various weighted bootstrap schemes compared with the rates based on the normal approximation and the existing bootstrap methods in the literature such as percentile t-subsampling schemes for the GARCH model. Since some familiar bootstrap schemes are special cases of the weighted bootstrap, this paper thus provides a unified theory and algorithm for bootstrapping in GARCH models.

Bibliographic note

This is a pre-copy-editing, author-produced PDF of an article accepted for publication in Biometrika following peer review. The definitive publisher-authenticated version [citation] is available online at: