A Test for Comparing Multiple Misspecified Conditional Distributions - Valentina Corradi; Norman R. Swanson (Rutgers University, Department of Economics, 2003)
This paper introduces a conditional Kolmogorov test, in the spirit of Andrews (1997), that allows for comparison of multiple misspecifed conditional distribution models, for the case of dependent observations. A conditional confidence interval version of the test is also discussed. Model accuracy is measured using a distributional analog of mean square error, in which the squared (approximation) error associated with a given model, say model i; is measured in terms of the average over U of E((Fi(u|Zt,Theta-t-plus)-Fo(u|Zt,Theta-o)))^2; where U is a possibly unbounded set on the real line, Zt is the conditioning information set, Fi is the distribution function of a particular candidate model, and F0 is the true (unkown) distribution function. 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). Valid asymptotic critical values are obtained via a version of the block bootstrap which properly captures the effect of parameter estimation error. The results of a small Monte Carlo experiment indicate that the conditional confidence interval version of the test has reasonable finite sample properties even for samples with as few as 60 observations.
Keywords: C22; C52; 330; block bootstrap; conditional Kolmogorov test; data snooping; misspecified conditional distribution; Bootstrap-Verfahren; Statistische Verteilung; Theorie; conditional Kolmogorov test