Title: Asymptotic behaviour of auto- and cross-dependence measures for heavy-tailed time series
Authors: Aleksandra Grzesiek - Wroclaw Univeristy of Science and Technology (Poland) [presenting]
Agnieszka Wylomanska - Wroclaw University of Science and Technology (Poland)
Abstract: A bidimensional autoregressive model of order 1 with alpha-stable distributed noise is considered. Since in this case the classical measure of dependence known as the covariance function is not defined, the spatio-temporal dependence structure is described using the alternative measures, namely the codifference and the covariation functions. We investigate the asymptotic relation between these two dependence measures for the auto- and cross-dependence functions. We demonstrate the cases when the dependence measures are asymptotically proportional with the coefficient of proportionality equal to the stability parameter alpha. The theoretical results are supported by illustrating the asymptotic behavior of the dependence measures for an exemplary bidimensional alpha-stable AR(1) system.