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



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.


Heavy Tail GARCH Model Occupation Time Conditional Moment Positive Lebesgue Measure 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.



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


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© Springer Science+Business Media New York 2013

Authors and Affiliations

  1. 1.Department of EconomicsUniversity of North CarolinaChapel HillUSA

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