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Convergence in distribution for the sup-norm of a kernel density estimator for GARCH innovations

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  • Mimoto, Nao

Abstract

The estimation and identification of the GARCH innovation density is an important task, leading to efficient parameter estimation. In this paper we derive the asymptotic distribution for the sup-norm of a kernel density estimator, and presents a goodness-of-fit test for the innovation density.

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  • 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.
    • Handle: RePEc:eee:stapro:v:78:y:2008:i:7:p:915-923
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    References listed on IDEAS

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    1. Drost, Feike C. & Klaassen, Chris A. J., 1997. "Efficient estimation in semiparametric GARCH models," Journal of Econometrics, Elsevier, vol. 81(1), pages 193-221, November.
    2. Bachmann, Dirk & Dette, Holger, 2005. "A note on the Bickel-Rosenblatt test in autoregressive time series," Statistics & Probability Letters, Elsevier, vol. 74(3), pages 221-234, October.
    3. Linton, Oliver, 1993. "Adaptive Estimation in ARCH Models," Econometric Theory, Cambridge University Press, vol. 9(4), pages 539-569, August.
    4. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
    5. Lee, Sang-Won & Hansen, Bruce E., 1994. "Asymptotic Theory for the Garch(1,1) Quasi-Maximum Likelihood Estimator," Econometric Theory, Cambridge University Press, vol. 10(1), pages 29-52, March.
    6. Lumsdaine, Robin L, 1996. "Consistency and Asymptotic Normality of the Quasi-maximum Likelihood Estimator in IGARCH(1,1) and Covariance Stationary GARCH(1,1) Models," Econometrica, Econometric Society, vol. 64(3), pages 575-596, May.
    7. Bougerol, Philippe & Picard, Nico, 1992. "Stationarity of Garch processes and of some nonnegative time series," Journal of Econometrics, Elsevier, vol. 52(1-2), pages 115-127.
    8. 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.
    9. Nelson, Daniel B., 1990. "Stationarity and Persistence in the GARCH(1,1) Model," Econometric Theory, Cambridge University Press, vol. 6(3), pages 318-334, September.
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    Cited by:

    1. M. Jiménez Gamero, 2014. "On the empirical characteristic function process of the residuals in GARCH models and applications," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 23(2), pages 409-432, June.
    2. 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.
    3. Delaigle, Aurore & Meister, Alexander & Rombouts, Jeroen, 2016. "Root-T consistent density estimation in GARCH models," Journal of Econometrics, Elsevier, vol. 192(1), pages 55-63.

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