Reconstructing High Dimensional Dynamic Distributions from Distributions of Lower Dimension

We propose a new procedure for estimating a dynamic joint distribution of a group of assets in a sequential manner starting from univariate marginals, continuing with pairwise bivariate distributions, then with triplewise trivariate distributions, etc., until the joint distribution for the whole group is constructed. The procedure uses principles and ideas from the copula theory in how at each step to arrive at a higher dimensional distribution utilizing the results from previous steps. The proposed procedure trades the dimensionality of the parameter space for numerous simpler estimations: even though there are more optimization problems to solve, each is of much lower dimension than the joint density estimation problem; in addition, the parameterization tends to be much more flexible. The paper demonstrates how to apply the new sequential technique to model a dynamic distribution of five DJIA constituents