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On the Bickel-Rosenblatt test for first-order autoregressive models


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  • Lee, Sangyeol
  • Na, Seongryong
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    In this paper we consider the goodness of fit test of the errors of autoregressive models using the kernel estimate of the marginal density function based on residuals. The test statistic is based on the integrated squared error of the nonparametric density estimate and a smoothed version of the parametric fit of the density. It is shown that the test statistic behaves asymptotically the same as the one based on true errors unless the autoregressive process is unstable.

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    Bibliographic Info

    Article provided by Elsevier in its journal Statistics & Probability Letters.

    Volume (Year): 56 (2002)
    Issue (Month): 1 (January)
    Pages: 23-35

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    Handle: RePEc:eee:stapro:v:56:y:2002:i:1:p:23-35

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    Keywords: AR(1) process Gaussian test Goodness of fit test Nonparametric density estimate Stationary process Explosive process Unstable process;


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    Cited by:
    1. 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.
    2. Nadine Hilgert & Bruno Portier, 2012. "Strong uniform consistency and asymptotic normality of a kernel based error density estimator in functional autoregressive models," Statistical Inference for Stochastic Processes, Springer, vol. 15(2), pages 105-125, July.
    3. 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.


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