March 1st, 2012, 9:58 am
Hello,I have a high dimensional dataset...it is a 250 by 58 matrix of uniform observations. I have fitted various copula models to it including Student T, Gaussian, Archimedean, Vine copulas, etc. Now I would like to assess the fit. I have obtained the classical measures of fit such as Log-Likelihood, AIC and BIC...but these do not directly tell me whether to accept or reject the model. I am looking now to apply formal goodness of fit tests on the fitted models. I have tried implementing test statistics based on the distance between the empirical copula and the fitted copula. For example the Kolmogorov-Smirnov (KS), Cram´er-von Mises (CvM), Anderson-Darling (AD), etc. But these all rely on computing the CDF of the fitted copula. This has been a real problem for me since calculating the CDF of a T copula, for example, at a grid of points (100 by 58) is very time consuming. In fact, when I try to perform this within Matlab, I get the following error message Number of dimensions must be less than or equal to 25.So my question is...is there a more appropriate method (given my high dimensional dataset) of accepting or rejecting a copula model?Any help/recommendations will be greatly appreciated!