Asymmetrical correlation test for constructing super Bayesian influence networks for financial intermarket influence analysis

This paper presents a computational procedure for asymmetrical correlation test as the first step for constructing super Bayesian influence networks with an application in financial intermarket influence analysis. We start with a data set of multivariate time series without any prior knowledge about possible influences in the problem domain. With the belief on the existence of influence patterns, asymmetrical correlation test is developed to detect all possible asymmetries among all the pairs of random variables. We then use paired t-test to check the statistical significance for each detected asymmetric correlation. Furthermore, we check the possible existence of ever-changing cycles in nonlinear dynamical systems such as financial markets. This procedure results in a dynamic directed acyclic graph of the random variables, which provides a graphical basis for a super Bayesian influence network. Note that asymmetrical correlation test can quickly become complicated when the scale space of time and the expanding set of conditioning variables for each asymmetrical correlation are introduced. On the other hand, symmetrical or undirected correlations should not be ignored completely, as they may bear additional information for augmenting super Bayesian influence networks to general super influence networks.