Some properties and generalizations of non-negative Bayesian time series models

We study the most basic Bayesian forecasting model for exponential family time series, the power steady model (PSM) of Smith, in terms of observable properties of one-step forecast distributions and sample paths. The PSM implies a constraint between location and spread of the forecast distribution. Including a scale parameter in the models does not always give an exact solution free of this problem, but it does suggest how to define related models free of the …