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Spatio‐Temporal Dependence Measures for Bivariate AR(1) Models with α‐Stable Noise

Aleksandra Grzesiek,G. Sikora,M. Teuerle,A. Wyłomańska

Published 2020 in Journal of Time Series Analysis

ABSTRACT

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 α‐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.

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