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PARAMETRIC SPECIFICATION TEST FOR NONLINEAR AUTOREGRESSIVE MODELS

Published online by Cambridge University Press:  02 October 2014

Kun Ho Kim ,
Ting Zhang  and
Wei Biao Wu
Kun Ho Kim*
Affiliation:
Hanyang University
Ting Zhang
Affiliation:
Boston University
Wei Biao Wu
Affiliation:
University of Chicago
*
*Address correspondence to Kun Ho Kim, Department of Economics and Finance, 222 Wangsimni-ro, Seongdong-gu Seoul 133-791, South Korea; e-mail: kunhokim8@gmail.com.
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Abstract

The paper considers testing parametric assumptions on the conditional mean and variance functions for nonlinear autoregressive models. To this end, we compare the kernel density estimate of the marginal density of the process with a convolution-type density estimate. It is shown that, interestingly, the latter estimate has a parametric $\left( {\sqrt n } \right)$ rate of convergence, thus substantially improving the classical kernel density estimates whose rates of convergence are much inferior. Our results are confirmed by a simulation study for threshold autoregressive processes and autoregressive conditional heteroskedastic processes.

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ARTICLES
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Econometric Theory , Volume 31 , Issue 5 , October 2015 , pp. 1078 - 1101
Copyright
Copyright © Cambridge University Press 2014 

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