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Maximum Likelihood and the Bootstrap for Nonlinear Dynamic Models

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  • Goncalves, Silvia
  • White, Halbert

Abstract

The bootstrap is an increasingly popular method for performing statistical inference. This paper provides the theoretical foundation for using the bootstrap as a valid tool of inference for quasi-maximum likelihood estimators (QMLE). We provide a unified framework for analyzing bootstrapped extremum estimators of nonlinear dynamic models for heterogeneous dependent stochastic processes. We apply our results to two block bootstrap methods, the moving blocks bootstrap of Künsch (1989) and Liu and Singh (1992) and the stationary bootstrap of Politis and Romano (1994), and prove the first order asymptotic validity of the bootstrap approximation to the true distribution of QML estimators. Further, these block bootstrap methods are shown to provide heteroskedastic and autocorrelation consistent standard errors for the QMLE, thus extending the already large literature on robust inference and covariance matrix estimation. We also consider bootstrap testing. In particular, we prove the first order asymptotic validity of the bootstrap distribution of a suitable bootstrap analog of a Wald test statistic for testing hypotheses.

Suggested Citation

  • Goncalves, Silvia & White, Halbert, 2000. "Maximum Likelihood and the Bootstrap for Nonlinear Dynamic Models," University of California at San Diego, Economics Working Paper Series qt1bj657ff, Department of Economics, UC San Diego.
  • Handle: RePEc:cdl:ucsdec:qt1bj657ff
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    References listed on IDEAS

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    5. Gonçalves, Sílvia & White, Halbert, 2002. "The Bootstrap Of The Mean For Dependent Heterogeneous Arrays," Econometric Theory, Cambridge University Press, vol. 18(6), pages 1367-1384, December.
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    7. Valentina Corradi & Norman R. Swanson, 2003. "A Test for Comparing Multiple Misspecified Conditional Distributions," Departmental Working Papers 200314, Rutgers University, Department of Economics.
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    11. Goncalves, Silvia & White, Halbert, 2004. "Maximum likelihood and the bootstrap for nonlinear dynamic models," Journal of Econometrics, Elsevier, vol. 119(1), pages 199-219, March.
    12. Lahiri, Soumendra Nath, 1996. "On Edgeworth Expansion and Moving Block Bootstrap for StudentizedM-Estimators in Multiple Linear Regression Models," Journal of Multivariate Analysis, Elsevier, vol. 56(1), pages 42-59, January.
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    14. repec:cup:etheor:v:12:y:1996:i:1:p:187-97 is not listed on IDEAS
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