Generation and analysis of non-Gaussian Markov time series

Correlated non-Gaussian Markov sequences can be considered as filtered white noise (independent, identically distributed sequences of random variables), the filter being a nonlinear system in general. The authors discuss the applicability of linear models and nonlinear methods based on the diagonal series expansion of bivariate densities for analyzing this system. Non-Gaussian sequences exhibit different properties in the forward and backward directions of time. The authors explore the connection to system modeling of this temporal asymmetry and some of its consequences. As an example, they analyze a first-order linear autoregressive model with hyperbolic secant amplifier distribution at its output