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The L1 strong consistency of ARCH innovation density estimator

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  • Cheng, Fuxia
  • Wen, Miin-Jye

Abstract

In this paper we consider the global property for the innovation density estimator in ARCH time series. For the kernel innovation density estimator based on residuals, we obtain its strong consistency under L1-norm.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:stapro:v:81:y:2011:i:5:p:548-551
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    References listed on IDEAS

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    1. Cheng, Fuxia, 2008. "Extended Glivenko-Cantelli Theorem in ARCH(p)-time series," Statistics & Probability Letters, Elsevier, vol. 78(12), pages 1434-1439, September.
    2. 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.
    3. Weiss, Andrew A., 1986. "Asymptotic Theory for ARCH Models: Estimation and Testing," Econometric Theory, Cambridge University Press, vol. 2(1), pages 107-131, April.
    4. 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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