A sequential test for the specification of predictive densities

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  • This article has been accepted for publication and undergone full peer review but has not been through the copyediting, typesetting, pagination and proofreading process, which may lead to differences between this version and the Version of Record. Please cite this article as doi: 10.1111/ectj.12085

Summary

We develop a specification test of predictive densities based on that the generalized residuals of correctly specified predictive density models are i.i.d. uniform. The proposed sequential test examines the hypotheses of serial independence and uniformity in two stages, wherein the first stage test of serial independence is robust against violation to uniformity. The approach of data driven smooth test is employed to construct the test statistics. The asymptotic independence between the two stages facilitates proper control of the overall type I error of the sequential test. We derive the asymptotic null distribution of the test, which is nuisance parameter free, and establish its consistency. Monte Carlo simulations demonstrate excellent finite sample performance of the test. We apply this test to evaluate some commonly used models of stock returns.

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