Extremes of bilinear time series models

The class of bilinear time series models is an obvious generalization of linear ARMA models and has found many applications in time series modeling. It is known that the sample paths of even the simplest bilinear process may have sudden bursts of large negative and positive values that vary in form and amplitude depending on the model parameters. Yet, little is known about the extremal properties of this class. In this paper, we look at the extremal properties of bilinear processes and explain how model parameters affect the extremal behavior.