Fast generation of generalized autoregressive moving average processes

This paper presents a new fast algorithm for synthesizing sequences of generalized Autoregressive Moving Average (GARMA) processes. These can be used to model time series which exhibit both short-range and long- range dependencies, as well as periodic behavior. The proposed synthesis scheme is based upon parameterizing the Gegenbauer coefficients by ARMA models using well-established signal modeling techniques such as Padé, Prony, Shanks, or Steiglitz-Mcbride methods. The proposed method is computationally efficient, sufficiently accurate, and very simple to implement. The generated sequences can be used in simulation studies such as network traffic.