A copula test space model: How to avoid the wrong copula choice

We introduce and discuss the test space problem as a part of the whole copula fitting process. In particular, we explain how an efficient copula test space can be constructed by taking into account information about the existing dependence. Although our model is developed in a bivariate environment it can be used for higher dimensional copula fitting applications. This is shown on the 3 dimensional dependence structure of an illustrative porfolio containing the S&P 500 Composite Index, the JP Morgan Government Bond Index and the NAREIT All index.