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Kernel Likelihood Inference for Time Series

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  • CARLO GRILLENZONI

Abstract

. This paper develops non‐parametric techniques for dynamic models whose data have unknown probability distributions. Point estimators are obtained from the maximization of a semiparametric likelihood function built on the kernel density of the disturbances. This approach can also provide Kullback–Leibler cross‐validation estimates of the bandwidth of the kernel densities. Confidence regions are derived from the dual‐empirical likelihood method based on non‐parametric estimates of the scores. Limit theorems for martingale difference sequences support the statistical theory; moreover, simulation experiments and a real case study show the validity of the methods.

Suggested Citation

  • Carlo Grillenzoni, 2009. "Kernel Likelihood Inference for Time Series," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 36(1), pages 127-140, March.
    • Handle: RePEc:bla:scjsta:v:36:y:2009:i:1:p:127-140
    DOI: 10.1111/j.1467-9469.2008.00617.x
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    References listed on IDEAS

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    1. Gonzalez-Rivera, G. & Drost, F.C., 1998. "Efficiency comparisons of maximum likelihood-based estimators in garch models," Other publications TiSEM d93a8be0-5dcd-4ae8-9eb1-b, Tilburg University, School of Economics and Management.
    2. Gonzalez-Rivera, Gloria & Drost, Feike C., 1999. "Efficiency comparisons of maximum-likelihood-based estimators in GARCH models," Journal of Econometrics, Elsevier, vol. 93(1), pages 93-111, November.
    3. White,Halbert, 1996. "Estimation, Inference and Specification Analysis," Cambridge Books, Cambridge University Press, number 9780521574464, November.
    4. Carlo Grillenzoni, 1991. "Iterative And Recursive Estimation Of Transfer Functions," Journal of Time Series Analysis, Wiley Blackwell, vol. 12(2), pages 105-127, March.
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    Cited by:

    1. Xibin Zhang & Maxwell L. King, 2011. "Bayesian semiparametric GARCH models," Monash Econometrics and Business Statistics Working Papers 24/11, Monash University, Department of Econometrics and Business Statistics.
    2. Xibin Zhang & Maxwell L. King, 2013. "Gaussian kernel GARCH models," Monash Econometrics and Business Statistics Working Papers 19/13, Monash University, Department of Econometrics and Business Statistics.

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