NON-GAUSSIAN ELLIPTICALLY CONTOURED ARMA MODELS

Non-Gaussian elliptically contoured autoregressive moving average (EC- ARMA) processes are defined as ARMA models with non-Gaussian noise. Th e driving noise series is uncorrelated but generally dependent, and fo llows elliptically contoured distributions. Moments, characteristic fu nctions, parametric representations, and other probabilistic character istics are given for elliptically contoured vectors and EC-ARMA proces ses. These characteristics are used to outline methods for generating samples of EC-ARMA processes. The analysis includes classical and dege nerated elliptically contoured driving noises. The Cauchy noise is an example of a degenerated noise, in the sense that it does not have mom ents. It is shown that EC-ARMA models with finite first two moments be come Gaussian as time increases. However, degenerate EC-ARMA models re main non-Gaussian at any time. Several numerical examples are used to demonstrate features of EC-ARMA processes and methods to generate real izations of these processes.