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A nonparametric test for the stationary density

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  • Neumann, Michael H.
  • Paparoditis, Efstathios

Abstract

We propose a nonparametric test for checking parametric hypotheses about the stationary density of weakly dependent observations. The test statistic is based on the L2-distance between a nonparametric and a smoothed version of a parametric estimate of the stationary density. It can be shown that this statistic behaves asymptotically as in the case of independent observations. Accordingly, we propose an i.i.d.-type bootstrap to determine the critical value for the test.

Suggested Citation

  • Neumann, Michael H. & Paparoditis, Efstathios, 1998. "A nonparametric test for the stationary density," SFB 373 Discussion Papers 1998,58, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
    • Handle: RePEc:zbw:sfb373:199858
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    References listed on IDEAS

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    1. Enno Mammen, "undated". "Comparing nonparametric versus parametric regression fits," Statistic und Oekonometrie 9205, Humboldt Universitaet Berlin.
    2. P. M. Robinson, 1983. "Nonparametric Estimators For Time Series," Journal of Time Series Analysis, Wiley Blackwell, vol. 4(3), pages 185-207, May.
    3. Neumann, Michael H., 1997. "On robustness of model-based bootstrap schemes in nonparametric time series analysis," SFB 373 Discussion Papers 1997,88, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
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    1. Neumann, Michael H. & Paparoditis, Efstathios, 2000. "On bootstrapping L2-type statistics in density testing," Statistics & Probability Letters, Elsevier, vol. 50(2), pages 137-147, November.

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