A Class of Antipersistent Processes

Abstract

Abstract. We introduce a class of stationary processes characterized by the behaviour of their infinite moving average parameters. We establish the asymptotic behaviour of the covariance function and the behaviour around zero of the spectral density of these processes, showing their antipersistent character. Then, we discuss the existence of an infinite autoregressive representation for this family of processes, and we present some consequences for fractional autoregressive moving average models.