Examples of Regularly Varying Stationary Processes

In the previous chapter we provided the probabilistic background for general regularly varying strictly stationary processes \(\d ({\mathbf {X}}_t)_{t\in {\mathbb Z}}\) with generic element \(\mathbf {X}\) . In this chapter we consider various important classes of time series models which have the regular variation property. We focus on the derivation of the corresponding tail measures and the spectral tail process. In the presence of serial dependence the tail measures and spectral tail processes often have some interesting structure. They characterize the appearance of extremal dependence clusters and the propagation of an extreme event at a given time to future observations.