The modified Yule-Walker method for α-stable time series models

This paper discusses the problem of parameters estimation for stable periodic autoregressive (PAR) time series. Considered models generalize popular and widely accepted autoregressive (AR) time series. By examining measures of dependence for α-stable processes, first we introduce new empirical estimator of autocovariation for α-stable sequences. Based on this approach we generalize Yule-Walker method for estimation of parameter for PAR time series. Thus we fill a gap in estimation methods for non-Gaussian models. We test proposed procedure and show its consistency. Moreover, we use our approach to model real empirical data thus showing usefulness of heavy tailed models in statistical modelling.