New procedures for analyzing economic time series are developed using Bayesian methods of time series analysis and semiparametric specification testing in cointegrated systems. Empirical applications of these methods include analysis of data on macroeconomic time series for the United States economy, macroeconomic data for Korea, Australia and New Zealand, and some long stock price and dividend series. Extensive simulation experiments are conducted to evaluate the performance of the new procedures. The new estimation methods developed by this project should improve the quality of empirical economic research on a wide range of problems. The work is especially timely because of the recent increase in interest in applying Bayesian methods, the framework used by this project, to empirical economic research. The main activity of the project is concerned with objective Bayesian methods of time series analysis. Specific attention is given to economic time series whose behavior indicates possible nonstationary characteristics. Issues of determining model-based reference priors that accommodate nonstationary will be considered in detail. The effects of data conditioning in Bayesian time series analysis is the major focus of attention. The conceptual framework developed in the previous grant is extended to Bayes model likelihood tests, posterior odds tests and model selection criteria. The model selection criteria provides a generalization of a widely used criterion. All of these features of Bayesian inference are explored in detail and an asymptotic theory is developed for a general class of time series problems. The work on semiparametric specification testing in cointegration relies on the Lagrange multiplier (LM) principle. The LM approach delivers a model specification test for the long-run elements of a structural system and tests against both underspecification (too few long-run relations) and overspecification (too many long-run relations). The two parts of the project will be related by developing a Bayes model specification test which, in the case of cointegrated systems, will be closely related to the LM test procedure.
