Specification Tests for the Error--Law in Vector Multiplicative Errors Models

We suggest specification tests for the error distribution in vector multiplicative error models (vMEM). The test statistic is formulated as a weighted integrated distance between the parametric estimator of the Laplace transform of the null distribution and its empirical counterpart computed from the residuals. Asymptotic results are obtained under both the null and alternative hypotheses. If the Laplace transform of the null distribution is not available in closed form, we propose a test statistic that uses independent artificial samples generated from the distribution under test, possibly with estimated parameters. The test statistic compares the empirical Laplace transforms of the residuals and the artificial errors using a similar weighted integrated distance. Bootstrap resampling is used to approximate the critical values of the test. The finite-sample performance of the two testing procedures is compared in a Monte Carlo simulation study.