  In this paper, we consider a bidimensional autoregressive model of order 1
with $\alpha-$stable noise. 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. Here, we investigate the asymptotic
relation between these two dependence measures applied to the description of
the cross-dependence of the bidimensional model. We demonstrate the case when
the dependence measures are asymptotically proportional with the coefficient of
proportionality equal to the parameter $\alpha$. The theoretical results are
supported by illustrating the asymptotic behavior of the dependence measures
for two exemplary bidimensional $\alpha-$stable AR(1) systems.
