Asymptotic behavior of the covariation and the codifference for arma models with stable innovations

In this paper two measures of dependence – the covariation, CV, and the codifference, CD, – are considered. They extend the covariance function and are defined for ARMA processes with symmetric a-stable innovations. The asymptotic behavior of both measures is investigated for in order to determine the cases when the codifference and the covariation are asymptotically proportional with the coefficient of proportionality equal to α