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Simultaneous Testing of Mean and Variance Structures in Nonlinear Time Series Models

Author

Listed:
  • Song Xi Chen

    (Guanghua School of Management, Peking University)

  • Jiti Gao

    () (School of Economics, University of Adelaide)

Abstract

This paper proposes a nonparametric simultaneous test for parametric specification of the conditional mean and variance functions in a time series regression model. The test is based on an empirical likelihood (EL) statistic that measures the goodness of fit between the parametric estimates and the nonparametric kernel estimates of the mean and variance functions. A unique feature of the test is its ability to distribute natural weights automatically between the mean and the variance components of the goodness of fit. To reduce the dependence of the test on a single pair of smoothing bandwidths, we construct an adaptive test by maximizing a standardized version of the empirical likelihood test statistic over a set of smoothing bandwidths. The test procedure is based on a bootstrap calibration to the distribution of the empirical likelihood test statistic. We demonstrate that the empirical likelihood test is able to distinguish local alternatives which are different from the null hypothesis at an optimal rate.

Suggested Citation

  • Song Xi Chen & Jiti Gao, 2010. "Simultaneous Testing of Mean and Variance Structures in Nonlinear Time Series Models," School of Economics Working Papers 2010-28, University of Adelaide, School of Economics.
  • Handle: RePEc:adl:wpaper:2010-28
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    File URL: http://www.economics.adelaide.edu.au/research/papers/doc/wp2010-28.pdf
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    References listed on IDEAS

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    More about this item

    Keywords

    Bootstrap; empirical likelihood; goodness{of{ t test; kernel estimation; least squares empirical likelihood; rate-optimal test;

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