We concentrate on constructing higher dimensional distributions using a fast growing graphical model called Vine/ pair-copula model which has been introduced and developed by Joe, Cooke, Bedford, Kurowica, Daneshkhah and others. Bedford et al. (2013) first construct a ndimensional copula density by stacking together n(n−1)/2 bivariate copula density, and they then approximate arbitrarily well these bivariate copulas and the corresponding multivariate distribution using a semi-parametric method. This constructive approach involves the use of minimum information copulas that can be specified to any required degree of precision based on the available data (or possibly based on the experts’ judgements). By using this method, one is able to use a fixed finite dimensional family of copulas to be employed in terms of a vine construction, with the promise of a uniform level of approximation. The basic idea behind this method is to use a two-dimensional ordinary polynomial series to approximate any log-density of a bivariate copula function by truncating the series at an appropriate point. We make this approximation method more accurate and computationally faster by using the orthonormal polynomial and Legendre multiwavelets series as the basis functions. We show the derived approximations are more precise and computationally faster with better properties than the one proposed by Bedford et al. (2013). We then apply our method to modelling a dataset of Norwegian financial data that was previously analysed in the series of papers, and finally compare our results by them. At the end, we present a method to simulate from the approximated models, and validate our approximation using the simulation results to recover the same dependency structure of the original data.
