SOME PROPERTIES AND GENERALIZATIONS OF NONNEGATIVE BAYESIAN TIME-SERIES MODELS

We study the most basic Bayesian forecasting model for exponential fam ily time series, the power steady model (PSM) of Smith, in terms of ob servable properties of one-step forecast distributions and sample path s. The PSM implies a constraint between location and spread of the for ecast distribution. Including a scale parameter in the models does not always give an exact solution free of this problem, but it does sugge st how to define related models free of the constraint. We define such a class of models which contains the PSM. We concentrate on the case where observations are non-negative. Probability theory and simulation show that under very mild conditions almost all sample paths of these models converge to some constant, making them unsuitable for modellin g in many situations. The results apply more generally to non-negative models defined in terms of exponentially weighted moving averages. We use these and related results to motivate, define and apply very simp le models based on directly specifying the forecast distributions.