A Bayesian approach to state space multivariate time series modeling

Abstract

Time series modeling is mainly a model specification exercise. Recognizing this fact, a new Bayesian procedure is developed that takes full advantage of the subjective probability foundations of the Bayesian approach, allowing logical consistency in the face of an unknown model. The computational demands of this new procedure have been greatly reduced relative to earlier techniques through the application of linear systems theory. Linear systems theory substitutes a formal model approximation based on the rank of an autocovariance matrix of the time series for the more arbitrary model selection processes of some other procedures. This formalization ensures that the most important elements of the series' dynamics are included in the model. Model selection procedures and an approach to the construction of optimal composite forecasts are derived using Bayesian methodologies. Two empirical applications demonstrate the tractability and the accuracy of the new procedure. © 1992.