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.