Journal of Business & Economic Statistics 2015, 33(1):128-143
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We present a family of smooth tests for the goodness of fit of semiparametric multivariate copula models.
The proposed tests are distribution free and can be easily implemented. They are diagnostic and constructive
in the sense that when a null distribution is rejected, the test provides useful pointers to alternative
copula distributions. We then propose a method of copula density construction, which can be viewed as
a multivariate extension of Efron and Tibshirani. We further generalize our methods to the semiparametric
copula-based multivariate dynamic models. We report extensive Monte Carlo simulations and three
empirical examples to illustrate the effectiveness and usefulness of our method.
Keywords: Copula; Dynamic models; Smooth test; Specification test