Binomial autoregressive moving average models

Abstract

A family of models for a stationary sequence of dependent binomial random variables is introduced. The properties of the binomial distribution, along with the simplicity of the models, make them useful for modelling and simulation of dependent point processes. For the binomial AR(1) process we discuss the existence of a stationary distribution for the process. In addition to the AR(1) case we consider binomial MA(1), MA(q), ARMA(l,q), and multiple AR(1) processes. For each model, the autocorrelation function and joint distribution of consecutive observations are derived,and some properties such as regression and time reversibility are discussed.