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SIMULTANEOUS SPECIFICATION TESTING OF MEANAND VARIANCE STRUCTURES IN NONLINEAR TIME SERIESREGRESSION

Published online by Cambridge University Press:  03 March 2011

Song Xi Chen  and
Jiti Gao
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Abstract

This paper proposes a nonparametric simultaneous testfor parametric specification of the conditional meanand variance functions in a time series regressionmodel. The test is based on an empirical likelihood(EL) statistic that measures the goodness of fitbetween the parametric estimates and thenonparametric kernel estimates of the mean andvariance functions. A unique feature of the test isits ability to distribute natural weightsautomatically between the mean and the variancecomponents of the goodness-of-fit measure. To reducethe dependence of the test on a single pair ofsmoothing bandwidths, we construct an adaptive testby maximizing a standardized version of theempirical likelihood test statistic over a set ofsmoothing bandwidths. The test procedure is based ona bootstrap calibration to the distribution of theempirical likelihood test statistic. We demonstratethat the empirical likelihood test is able todistinguish local alternatives that are differentfrom the null hypothesis at an optimal rate.

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Type
Research Article
Information
Econometric Theory , Volume 27 , Issue 4 , August 2011 , pp. 792 - 843
Copyright
Copyright © Cambridge University Press 2011

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Footnotes

We thank Peter C.B. Phillips, the editor, YuichiKitamura, the associate editor, and two refereesfor their constructive and insightful comments andsuggestions, which have improved the presentationof the paper. We also thank Ming Li and IsabelCasas Villalba for their valuable computationalassistance. Chen acknowledges the financialsupport from National Science Foundation grantsSES-0518904 and DMS-0604533, and Gao acknowledgesthe financial support by Australian ResearchCouncil Discovery Grants under grant numbersDP0558602 and DP0879088.

References

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