Continuous time ARIMA models with infinite memory
by
John Appleby
Dublin City University
Coauthors: Siobhan Devin

Autoregressive integrated moving average models (ARIMA) are one of the most popular dynamic time series models for non-stationary processes in discrete time. In this talk, we will introduce a class of stochastic processes which are solutions of stochastic Volterra equations with infinite memory and which have the property that the increments of the process are stationary or asymptotically stationary. Among the main results presented are necessary and sufficient conditions for the stationarity of the increments of the process. We also give conditions under which the process has long memory, in the sense that increments have a slowly decaying autocorrelation function. Applications to financial market modelling are also discussed.

Date received: March 30, 2007