Traditional forecasting methods often assume that there is a "true" model for the process under study. Under such an assumption, one can use maximum likelihood method to estimate the model and then use the estimated model for forecasting. In practice, however, there is no "true" model. Consequently, the traditional forecasting method may fare poorly in long-term forecasts. To overcome this difficulty, we proposed in this project an adaptive forecasting procedure that can produce accurate long-term forecasts. The proposed procedure selects a statistical model for each forecasting horizon. In other words, under the proposed procedure, different models are used to produce different multi-step ahead forecasts. Our preliminary results suggest that such an adaptive procedure outperforms substantially the traditional forecasting 1 methods. In this project, we plan to investigate properties of such an adaptive forecasting procedure, to provide theoretical justifications of the procedure, and to develop statistical criteria of model selection in adaptive forecasting. The second part of the proposed research is concerned with Bayesian time-series analysis. Its main objective is to develop new methodologies for Bayesian inference that (a) make use of the recent developments in repeated stochastic substitution such as the Gibbs sampler, (b) allow for various structural changes in a process, and (c) provide a flexible framework for estimating common features in a vector process. For instance, we consider a Markov switching framework for modeling macroeconomic time series and for discriminating non-nested non-linear time series models. We also augment a probit model to a random variance-shift model to relate the probability of a variance change to a set of chosen explanatory variables. These preliminary results are very encouraging as they successfully describe many features that cannot be captured by the traditional time-series analysis. The proposed research consists of two main projects. In the first project, we propose to develop new methods that can produce accurate long-term forecasts. The basic idea of the proposed research is that different models are selected to produce forecasts of different horizons. Under the proposed research, statistical models are used adaptively in long-term forecasts. Advantages of the proposed new forecasting methods include (a) they relate directly model selection to the objective of forecasts, (b) it relaxes many "unrealistic assumptions" commonly imposed by the traditional forecasting methods, and (c) they make use of the recent advances in statistical computing. Our preliminary experience on forecasting the U.S. monthly consumer price index for foods indicates that the proposed methods outperform substantially other forecasting methods available in the literature. The second project is concerned with time-series analysis. It emphasizes the recent developments in statistical algorithms and the advances in computing. The main objective is to develop new methodologies that can incorporate prior acknowledge on subject matters into data analysis in an efficient manner. It also widens the applicability of many statistical methods by enlarging the class of possible statistical distributions such as using scale mixture of traditional distributions.
