A Test For Comparing Multiple Misspecified Conditional Interval Models

This paper introduces a test for the comparison of multiple misspecified conditional interval models, for the case of dependent observations. Model accuracy is measured using a distributional analog of mean square error, in which the approximation error associated with a given model, say, model i, for a given interval, is measured by the expected squared difference between the conditional confidence interval under model i and the “true” one.When comparing more than two models, a “benchmark” model is specified, and the test is constructed along the lines of the “reality check” of White (2000, Econometrica 68, 1097–1126). Valid asymptotic critical values are obtained via a version of the block bootstrap that properly captures the effect of parameter estimation error. The results of a small Monte Carlo experiment indicate that the test does not have unreasonable finite sample properties, given small samples of 60 and 120 observations, although the results do suggest that larger samples should likely be used in empirical applications of the test.The authors express their gratitude to Don Andrews and an anonymous referee for providing numerous useful suggestions, all of which we feel have been instrumental in improving earlier drafts of this paper. The authors also thank Russell Davidson, Clive Granger, Lutz Kilian, Christelle Viaroux, and seminar participants at the 2002 UK Econometrics Group meeting in Bristol, the 2002 European Econometric Society meetings, the 2002 University of Pennsylvania NSF-NBER time series conference, the 2002 EC2 Conference in Bologna, Cornell University, the State University of New York at Stony Brook, and the University of California at Davis for many helpful comments and suggestions on previous versions of this paper.