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A note on adaptation in garch models

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  • Gloria Gonzalez-Rivera

Abstract

In the framework of the Engle-type (G)ARCH models, I demonstrate that there is a family of symmetric and asymmetric density functions for which the asymptotic efficiency of the semiparametric estimator is equal to the asymptotic efficiency of the maximum likelihood estimator. This family of densities is bimodal (except for the normal). I also chracterize the solution to the problem of minimizing the mean squared distance between the parametric score and the semiparametric score in order to search for unimodal densities for which the semiparametric estimator is likely to perform well. The LaPlace density function emerges as one of these cases.

Suggested Citation

  • Gloria Gonzalez-Rivera, 1997. "A note on adaptation in garch models," Econometric Reviews, Taylor & Francis Journals, vol. 16(1), pages 55-68.
    • Handle: RePEc:taf:emetrv:v:16:y:1997:i:1:p:55-68
    DOI: 10.1080/07474939708800372
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    Cited by:

    1. Gabriele Fiorentini & Enrique Sentana, 2007. "On the Efficiency and Consistency of Likelihood Estimation in Multivariate Conditionally Heteroskedastic Dynamic Regression Models," Working Papers wp2007_0713, CEMFI.
    2. Jushan Bai & Serena Ng, 1998. "A Test for Conditional Symmetry in Time Series Models," Boston College Working Papers in Economics 410, Boston College Department of Economics.
    3. HAFNER, Christian & ROMBOUTS, Jeroen, 2003. "Semiparametric multivariate GARCH models," LIDAM Discussion Papers CORE 2003003, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    4. repec:rim:rimwps:38-07 is not listed on IDEAS
    5. Hafner, Christian M. & Rombouts, Jeroen V.K., 2007. "Semiparametric Multivariate Volatility Models," Econometric Theory, Cambridge University Press, vol. 23(2), pages 251-280, April.

    More about this item

    Keywords

    Adaptation; Generalized Autoregressive Conditional Heteroscedasticity (GARCH); maximum likelihood; semiparametric estimator;
    All these keywords.

    JEL classification:

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

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