Infinite variance stable Gegenbaeur Arfisma models

Abstract

This paper develops the theory of the Gegenbauer AutoRegressive Fractionally Integrated Seasonal Moving Average (GARFISMA) process with α-stable innovations. We establish its conditions for causality and invertibility. This is a finite parameter process which exhibits high variability, long memory, cyclical, and seasonality in financial, hydrological data studies, and more. We perform some simulations to illustrate the behavior of our process.