BAYESIAN FORECASTING OF ECONOMIC TIME-SERIES

A model is suggested to forecast economic time series. This model inco rporates some innovative ideas of Harrison and Stevens [20] for buildi ng into the forecasting process important external shocks to the syste ms. Thus the occurrence of possibly significant real-world events may cause a fundamental change in the time series in question. The Jeffrey s-Savage (JS) Bayesian theory of hypothesis testing is used to test th e hypothesis that a particular event has been such as to free the seri es from its immediate past behavior. When the event frees the series i n this way, then we model the sequence of observations following such an event (until the next such event) as an exchangeable sequence. In t he simplest case of 0-1 valued data, such as in recording, the ups and downs of the value of a particular commodity or stock, our alternativ e hypothesis is a Polya process, and the null hypothesis is a simple r andom walk (unit roots model) with p = .50. Any exchangeable sequence is strictly stationary, and the observations in the Polya process are positively correlated, which can give rise to ''explosive'' behavior o f the series at isolated time points. We then use the JS theory to pre dict future observations by taking a weighted average of the optimal p redictions for each model, with weights given by the posterior probabi lities of the hypotheses. Results of simulation studies are presented which compare the predictive performance of the fully Bayesian method based upon the JS theory with those based upon the ''p-value'' or pre- test method. The de Finetti method for scoring predictions is used to assess their empirical performance. A theoretical methodology, which e xtends the ''evaluation game'' of Hill [28,37], is developed for compa ring predictors.