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Quasi‐maximum likelihood and the kernel block bootstrap for nonlinear dynamic models

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  • Paulo M. D. C. Parente
  • Richard J. Smith

Abstract

This article applies a novel bootstrap method, the kernel block bootstrap (KBB), to quasi‐maximum likelihood (QML) estimation of dynamic models with stationary strong mixing data. The method first kernel weights the components comprising the quasi‐log likelihood function in an appropriate way and then samples the resultant transformed components using the standard ‘m out of n’ bootstrap. We investigate the first‐order asymptotic properties of the KBB method for QML demonstrating, in particular, its consistency and the first‐order asymptotic validity of the bootstrap approximation to the distribution of the QML estimator. A set of simulation experiments for the mean regression model illustrates the efficacy of the kernel block bootstrap for QML estimation.

Suggested Citation

  • Paulo M. D. C. Parente & Richard J. Smith, 2021. "Quasi‐maximum likelihood and the kernel block bootstrap for nonlinear dynamic models," Journal of Time Series Analysis, Wiley Blackwell, vol. 42(4), pages 377-405, July.
    • Handle: RePEc:bla:jtsera:v:42:y:2021:i:4:p:377-405
    DOI: 10.1111/jtsa.12573
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    2. Paulo M.D.C. Parente & Richard J. Smith, 2018. "Generalised Empirical Likelihood Kernel Block Bootstrapping," Working Papers REM 2018/55, ISEG - Lisbon School of Economics and Management, REM, Universidade de Lisboa.

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    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes

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