Heavy-Tail and Plug-In Robust Consistent Conditional Moment Tests of Functional Form
Jonathan B. Hill
University of North Carolina (UNC) at Chapel Hill – Department of Economics
May 17, 2012
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-root(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.
Number of Pages in PDF File: 36
Keywords: conditional moment test, tail trimming, heavy tails
JEL Classification: C13, C20, C22working papers series
Date posted: August 22, 2011 ; Last revised: May 18, 2012
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