Smooth Tests for Correct Specification of Conditional Predictive Densities

We develop two specification tests of predictive densities based on that the generalized residuals of correctly specified predictive density models are i.i.d. uniform. The simultaneous test compares the joint density of generalized residuals with product of uniform densities; the sequential test examines the hypotheses of serial independence and uniformity sequentially based on the copula representation of a joint density. We propose data-driven smooth tests to construct the test statistics. We derive the asymptotic null distributions of the tests, which are nuisance parameter free, and establish their consistency. Monte Carlo simulations demonstrate excellent finite sample performance of the tests. We apply the proposed tests to evaluate some commonly used models of stock returns. JEL Classification Codes: C12; C52; C53