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Testing Goodness Of Fit Based On Densities Of Garch Innovations

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  • Horváth, Lajos
  • Zitikis, Ričardas

Abstract

Testing goodness (or lack) of fit for distributions of observable and nonobservable random variables is one of the main topics in statistics. When they exist, the corresponding density functions and their shapes allow researchers to easily recognize the underlying distribution functions. The present paper is concerned with the densities of (unobservable) generalized autoregressive conditional heteroskedasticity (GARCH) innovations and also with developing goodness-of-fit tests for the densities. Specifically, we construct and investigate large-sample properties of a kernel-type density estimator for GARCH innovations based on (observable) residuals.The authors sincerely thank the Co-Editor Oliver Linton and three anonymous referees for constructive criticism and suggestions that helped us to prepare a much revised version of the original manuscript. The feedback by participants of the Conference on Statistical Models for Financial Data at the University of Graz in May 2004 is also greatly appreciated. The research of the first author was partially supported by NSF grant INT-0223262 and NATO grant PST.EAP.CLG 980599. The research of the second author was partially supported by a Discovery Research Grant from the Natural Sciences and Engineering Research Council (NSERC) of Canada.

Suggested Citation

  • Horváth, Lajos & Zitikis, Ričardas, 2006. "Testing Goodness Of Fit Based On Densities Of Garch Innovations," Econometric Theory, Cambridge University Press, vol. 22(3), pages 457-482, June.
    • Handle: RePEc:cup:etheor:v:22:y:2006:i:03:p:457-482_06
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    Cited by:

    1. Hira Koul & Nao Mimoto, 2012. "A goodness-of-fit test for GARCH innovation density," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 75(1), pages 127-149, January.
    2. Klar, B. & Lindner, F. & Meintanis, S.G., 2012. "Specification tests for the error distribution in GARCH models," Computational Statistics & Data Analysis, Elsevier, vol. 56(11), pages 3587-3598.
    3. Sangyeol Lee & Hiroki Masuda, 2010. "Jarque–Bera normality test for the driving Lévy process of a discretely observed univariate SDE," Statistical Inference for Stochastic Processes, Springer, vol. 13(2), pages 147-161, June.
    4. Zhu, Ke, 2015. "Hausman tests for the error distribution in conditionally heteroskedastic models," MPRA Paper 66991, University Library of Munich, Germany.
    5. Donghang Luo & Ke Zhu & Huan Gong & Dong Li, 2020. "Testing error distribution by kernelized Stein discrepancy in multivariate time series models," Papers 2008.00747, arXiv.org.
    6. Mimoto, Nao, 2008. "Convergence in distribution for the sup-norm of a kernel density estimator for GARCH innovations," Statistics & Probability Letters, Elsevier, vol. 78(7), pages 915-923, May.

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