Construction of Stationary Time Series via the Giggs Sampler with Application to Volatility Models.

In this paper, we provide a method for modeling stationary time series. We allow the family of marginal densities for the observations to be specified. Our approach is to construct the model with a specified marginal family and build the dependence structure around it. We show that the resulting time series is linear with a simple autocorrelation structure. In particular, we present an original application of the Gibbs sampler. We illustrate our approach by fitting a model to time series count data with a marginal Poisson-gamma density.