Maximum likelihood and the bootstrap for nonlinear dynamic models (2004 21s).pdf

Journal of Econometrics 119 (2004) 199–219
ate/econbase
Maximum likelihood and the bootstrap for
nonlinear dynamic models
SÃ&lvia Gon(calvesa;∗, Halbert Whiteb;1
aCIRANO, CIREQ and Departementà de Sciences Economiques,à Universiteà de Montreal,Ã
. 6128, . Centre-Ville, Montreal,Ã Canada QC H3C 3J7
bUniversity of California, San Diego, 9500 Gilman Drive, La Jolla, CA 92093-0508, USA
Accepted 30 June 2003
Abstract
We provide a uniÿed framework for analyzing bootstrapped extremum estimators of nonlinear
dynamic models for heterogeneous dependent stochastic processes. We apply our results to the
moving blocks bootstrap of Kunsch( Stat. 17 (1989) 1217) and Liu and Singh(in: R.
Lepage, L. Billiard (Eds.), Exploring the Limits of the Bootstrap, Wiley, New York, 1992) and
prove the ÿrst-order asymptotic validity of the bootstrap approximation to the true distribution of
quasi-maximum likelihood estimators. We also consider bootstrap testing. In particular, we prove
the ÿrst-order asymptotic validity of the bootstrap distribution of suitable bootstrap analogs of
Wald and Lagrange Multiplier statistics for testing hypotheses.
Crown Copyright
c 2003 Published by Elsevier . All rights reserved.
JEL classiÿcation: C15; C22
Keywords: Block bootstrap; Quasi-maximum likelihood estimator; Nonlinear dynamic model; Near epoch
dependence; Wald test
1. Introduction
The bootstrap is a powerful and increasingly utilized method for obtaining conÿ-
dence intervals and performing statistical inference. Despite this, results validating the
bootstrap for the quasi-maximum likelihood estimator (QMLE) or generalized method
of moments (GMM) estimator have previously been available only under restrictive
∗ Corresponding author. Tel.: +1-514-343-6556. Gon(calves acknowledges ÿnancial support from Praxis
XXI and a Sloan Dissertation fellowship.
E-mail addresses: silvia.******@ (S. Gon(calves), ******@ (H. White).
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