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Strong consistency of the distribution estimator in the nonlinear autoregressive time series

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  • Cheng, Fuxia

Abstract

This paper considers the uniform strong consistency of the error cumulative distribution function (CDF) estimator. Under appropriate assumptions, the classical Glivenko–Cantelli Theorem is obtained for the residual based empirical error CDF in the nonlinear autoregressive time series.

Suggested Citation

  • Cheng, Fuxia, 2015. "Strong consistency of the distribution estimator in the nonlinear autoregressive time series," Journal of Multivariate Analysis, Elsevier, vol. 142(C), pages 41-47.
    • Handle: RePEc:eee:jmvana:v:142:y:2015:i:c:p:41-47
    DOI: 10.1016/j.jmva.2015.07.014
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    References listed on IDEAS

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    1. Eckhard Liebscher, 1999. "Estimating the Density of the Residuals in Autoregressive Models," Statistical Inference for Stochastic Processes, Springer, vol. 2(2), pages 105-117, May.
    2. Fuxia Cheng, 2010. "Global property of error density estimation in nonlinear autoregressive time series models," Statistical Inference for Stochastic Processes, Springer, vol. 13(1), pages 43-53, April.
    3. Cheng, Fuxia & Sun, Shuxia, 2008. "A goodness-of-fit test of the errors in nonlinear autoregressive time series models," Statistics & Probability Letters, Elsevier, vol. 78(1), pages 50-59, January.
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    Cited by:

    1. Kaiyu Liang & Yong Zhang, 2024. "Almost Sure Central Limit Theorem for Error Variance Estimator in Pth-Order Nonlinear Autoregressive Processes," Mathematics, MDPI, vol. 12(10), pages 1-16, May.
    2. Gao, Min & Yang, Wenzhi & Wu, Shipeng & Yu, Wei, 2022. "Asymptotic normality of residual density estimator in stationary and explosive autoregressive models," Computational Statistics & Data Analysis, Elsevier, vol. 175(C).

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