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A goodness-of-fit test of the errors in nonlinear autoregressive time series models

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  • Cheng, Fuxia
  • Sun, Shuxia

Abstract

This paper considers the problem of fitting an error density to the goodness-of-fit test of the errors in a nonlinear autoregressive stationary time series regression model. The test statistic is based on the integrated squared error of the nonparametric error density estimate and the null error density. Without knowing the nonlinear autoregressive function, we can show that the test statistic behaves asymptotically the same as the one based on the true errors.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:stapro:v:78:y:2008:i:1:p:50-59
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    References listed on IDEAS

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    1. Lee, Sangyeol & Na, Seongryong, 2002. "On the Bickel-Rosenblatt test for first-order autoregressive models," Statistics & Probability Letters, Elsevier, vol. 56(1), pages 23-35, January.
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    Cited by:

    1. 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).
    2. 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.
    3. Benjamin Colling & Cédric Heuchenne & Rawane Samb & Ingrid Van Keilegom, 2015. "Estimation of the error density in a semiparametric transformation model," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 67(1), pages 1-18, February.
    4. Shang, Han Lin, 2013. "Bayesian bandwidth estimation for a nonparametric functional regression model with unknown error density," Computational Statistics & Data Analysis, Elsevier, vol. 67(C), pages 185-198.
    5. 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.
    6. Fuxia Cheng & Hira L. Koul, 2023. "An analog of Bickel–Rosenblatt test for fitting an error density in the two phase linear regression model," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 86(1), pages 27-56, January.
    7. Xibin Zhang & Maxwell L. King & Han Lin Shang, 2016. "Bayesian Bandwidth Selection for a Nonparametric Regression Model with Mixed Types of Regressors," Econometrics, MDPI, vol. 4(2), pages 1-27, April.
    8. 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.

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