Heavy-Tail and Plug-In Robust Consistent Conditional Moment Tests of Functional Form

Chapter

Abstract

We present asymptotic power-one tests of regression model functional form for heavy-tailed time series. Under the null hypothesis of correct specification the model errors must have a finite mean, and otherwise only need to have a fractional moment. If the errors have an infinite variance then in principle any consistent plug-in is allowed, depending on the model, including those with non-Gaussian limits and/or a sub-\(\sqrt{n}\)-convergence rate. One test statistic exploits an orthogonalized test equation that promotes plug-in robustness irrespective of tails. We derive chi-squared weak limits of the statistics, we characterize an empirical process method for smoothing over a trimming parameter, and we study the finite sample properties of the test statistics.

Keywords

Covariance Radon Volatility BILIN 

Notes

Acknowledgments

The author thanks an anonymous referee and Co-Editor Xiaohong Chen for constructive remarks.

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Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  1. 1.Department of EconomicsUniversity of North CarolinaChapel HillUSA

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