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Robust maximum entropy test for GARCH models based on a minimum density power divergence estimator

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  • Kim, Byungsoo

Abstract

The maximum entropy test, as designed for examining goodness-of-fit with a non-robust estimator such as the maximum likelihood estimator, can suffer from severe size distortions when the data are contaminated by outliers. The objective of this study is to develop a robust maximum entropy test for the normality of GARCH models. We construct the test statistic based on the minimum density power divergence estimator and verify its limiting null distribution. A bootstrap method is also discussed, and its performance is evaluated through simulations. According to the simulation results, the proposed test can successfully achieve reasonable sizes in the presence of outliers.

Suggested Citation

  • Kim, Byungsoo, 2018. "Robust maximum entropy test for GARCH models based on a minimum density power divergence estimator," Economics Letters, Elsevier, vol. 162(C), pages 93-97.
    • Handle: RePEc:eee:ecolet:v:162:y:2018:i:c:p:93-97
    DOI: 10.1016/j.econlet.2017.11.003
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    References listed on IDEAS

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    1. Kim, Byungsoo & Lee, Sangyeol, 2013. "Robust estimation for the covariance matrix of multivariate time series based on normal mixtures," Computational Statistics & Data Analysis, Elsevier, vol. 57(1), pages 125-140.
    2. Sangyeol Lee & Junmo Song, 2009. "Minimum density power divergence estimator for GARCH models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 18(2), pages 316-341, August.
    3. Jushan Bai, 2003. "Testing Parametric Conditional Distributions of Dynamic Models," The Review of Economics and Statistics, MIT Press, vol. 85(3), pages 531-549, August.
    4. Winfried Stute & Wenceslao Manteiga & Manuel Quindimil, 1993. "Bootstrap based goodness-of-fit-tests," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 40(1), pages 243-256, December.
    5. Lee, Sangyeol & Vonta, Ilia & Karagrigoriou, Alex, 2011. "A maximum entropy type test of fit," Computational Statistics & Data Analysis, Elsevier, vol. 55(9), pages 2635-2643, September.
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    More about this item

    Keywords

    Entropy-based goodness-of-fit test; Normality test; GARCH models; Minimum density power divergence estimator; Parametric bootstrap method;
    All these keywords.

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: 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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