Humbert Generalized Fractional Differenced ARMA Processes

Abstract: In this article, we use the generating functions of the Humbert polynomials to define two types of Humbert generalized fractional differenced ARMA processes. We present stationarity and invertibility conditions for the introduced models. The singularities for the spectral densities of the introduced models are obtained. In particular, Pincherle ARMA, Horadam ARMA and Horadam-Pethe ARMA processes are studied.