A first-order AR model for non-Gaussian time series

A simple first-order autoregressive model for the generation of non-Gaussian time series is described. It is defined by X_n =ρX_n-1+W_n and has a hyperbolic secant marginal distribution. This hyperbolic secant model can be used to generate random non-Gaussian sequences which are free of the degeneracy that afflicts the sequences generated using the Laplace model. The generation formula and the bivariate distributions of this model are derived. It is shown that the mean-square (MS) backward prediction error is strictly less than the MS forward prediction error for all first-order autoregressive non-Gaussian models