Spatio-Temporal Dependence Measures for Bivariate AR(1) Models with alpha-Stable Noise

Many real phenomena exhibit non-Gaussian behavior. The non-Gaussianity is manifested by impulsive behavior of the real data that can be found in both one-dimensional and multi-dimensional cases. Especially the multi-dimensional datasets with non-Gaussian behavior pose substantial analysis challenges to scientists and statisticians. In this article, we analyze the bidimensional vector autoregressive (VAR) model based on general bidimensional alpha-stable distribution. This time series can be applied in modeling bidimensional data with impulsive behavior. We focus on the description of the spatio-temporal dependence for analyzed bidimensional time series which in the considered case cannot be expressed in the language of the classical cross-covariance or cross-correlation function. We propose a new cross measure based on the alternative measure of dependence adequate for infinite variance processes, namely cross-covariation. This article is an extension of the authors' previous work where the cross-codifference was considered as the spatio-temporal measure of the components of VAR model based on sub-Gaussian distribution. In this article, we demonstrate that cross-codifference and cross-covariation can give different information about the relationships between components of bidimensional VAR models.