Diagnostic checking of Markov multiplicative error models

In a multiplicative error model (MEM), correct specification of the conditional mean function and that of the error distribution are of crucial importance. In this paper, we propose a test that can jointly check the two specifications in an MEM admitting a Markov structure. The proposed test is constructed by comparing the nonparametric kernel estimator with a parametric estimator of the marginal density function. Its asymptotic properties under the null and the alternative hypotheses are established. We propose a parametric bootstrap procedure to approximate the null distribution. A simulation study shows that the proposed test enjoys nice finite sample performance, while a real data example demonstrates its practical merit.