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


  • Lee, Sangyeol
  • Na, Seongryong


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.

Suggested Citation

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

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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. 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.
    3. Horváth, Lajos & Zitikis, Ricardas, 2004. "Asymptotics of the Lp-norms of density estimators in the first-order autoregressive models," Statistics & Probability Letters, Elsevier, vol. 66(2), pages 91-103, January.
    4. 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.


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