Compound Autoregressive Models.

We introduce a class of nonlinear dynamic processes, called compound au- toregressive (CAR), and characterized by the conditional log-Laplace trans- forms which are aÆne functions of the lagged values of the process. The CAR processes resemble the linear autoregressive processes in that their forecasting distributions at all horizons admit analytical expressions, and can be used to derive the ergodicity conditions, the stationary distribution, as well as the ltering formula.