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Extended Glivenko-Cantelli Theorem in ARCH(p)-time series

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  • Cheng, Fuxia

Abstract

In this paper we consider the uniform strong consistency of nonparametric innovation distribution function estimation in ARCH(p)-time series. We obtain the extended Glivenko-Cantelli Theorem for the residual-based empirical distribution function.

Suggested Citation

  • Cheng, Fuxia, 2008. "Extended Glivenko-Cantelli Theorem in ARCH(p)-time series," Statistics & Probability Letters, Elsevier, vol. 78(12), pages 1434-1439, September.
    • Handle: RePEc:eee:stapro:v:78:y:2008:i:12:p:1434-1439
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    References listed on IDEAS

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    1. Winfried Stute, 2001. "Residual analysis for ARCH(p)-time series," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 10(2), pages 393-403, December.
    2. Engle, Robert F, 1982. "Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation," Econometrica, Econometric Society, vol. 50(4), pages 987-1007, July.
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    Cited by:

    1. Cheng, Fuxia & Wen, Miin-Jye, 2011. "The L1 strong consistency of ARCH innovation density estimator," Statistics & Probability Letters, Elsevier, vol. 81(5), pages 548-551, May.

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