Fractional lower order covariance-based estimator for bidimensional AR(1) model with stable distribution

Real data modeling often requires the use of non-Gaussian models. A natural extension of the Gaussian distribution is the alpha\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\alpha$$\end{document}-stable one. The dependence structure description of the alpha\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\alpha$$\end{document}-stable-based models poses a substantial challenge due to the infinite variance. The classical second moment-based measures cannot be applied in this case. To overcome this issue one can use the alternative dependence measures. The measures of dependence can be applied to estimate the parameters of the model. In this paper, we propose a new estimation method for the parameters of the bidimensional autoregressive model of order 1. The procedure is based on fractional lower order covariance. The use of this method is reasonable from the theoretical point of view. The practical aspect of the method is justified by showing the efficiency of the procedure on the simulated data. Moreover, the new technique is compared with the classical Yule-Walker method based on the covariance function.