On a Class of Z+-Valued Autoregressive Moving Average (ARMA) Processes

Abstract

A convolution semigroup of probability generating functions and its related operator ⊙F are used to construct a class of stationary Z+-valued autoregressive moving average (ARMA) processes. Several distributional and regression properties are obtained. A number of ARMA processes with specific innovation sequences are presented.

Keywords

• stationarity
• semigroup of probability generating functions
• Mittag–Leffler distribution
• Linnik distribution
• time-reversibility