Bootstrap conditional distribution tests in the presence of dynamic misspecification

In this paper, we show the first order validity of the block bootstrap for Kolmogorov-type conditional distribution tests under dynamic misspecification and parameter estimation error. Our approach is unique because we construct statistics that allow for dynamic misspecification under both hypotheses. We consider two tests; the CK test of Andrews [1997. A conditional Kolmogorov test, Econometrica 65, 1097–1128], and a version of the DGT test of Diebold, Gunther and Tay [1998a. Evaluating density forecasts with applications to finance and management. International Economic Review 39, 863–883]. Test limiting distributions are Gaussian processes with covariance kernels that reflect dynamic misspecification and parameter estimation error. Critical values are based on an extension of the empirical process version of the block bootstrap to the case of nonvanishing parameter estimation error. Monte Carlo experiments are also carried out.