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

Author Info

Listed author(s):
  • 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.

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File URL: http://www.economics.adelaide.edu.au/research/papers/doc/wp2010-28.pdf
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Paper provided by University of Adelaide, School of Economics in its series School of Economics Working Papers with number 2010-28.

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Length: 56 pages
Date of creation: Oct 2010
Handle: RePEc:adl:wpaper:2010-28
Contact details of provider: Postal:
Adelaide SA 5005

Phone: (618) 8303 5540
Web page: http://www.economics.adelaide.edu.au/

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

This paper has been announced in the following NEP Reports:

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