Bayesian System Averaging: A Theory Unifying Bayesian Forecasting System and Bayesian Model Averaging Methods
Liu, Jie, Systems Engineering - School of Engineering and Applied Science, University of Virginia
Krzysztofowicz, Roman, Department of Systems and Information Engineering, University of Virginia
There are two philosophically different approaches to address model uncertainty in forecasting practice. One is Bayesian Forecasting System (BFS) method. Another is forecast combination method. Bayesian Model Averaging (BMA) method is a typical kind of the latter. After reviewing these two approaches and comparing their respective theoretical advantages and disadvantages, this dissertation proposes a new theoretical framework and data analysis method called Bayesian System Averaging (BSA) that unifies BFS and BMA methods. Under the BSA theoretical framework, multiple forecasting systems constructed in the BFS manner are allowed, forecaster’s degrees of uncertainty about different systems’ validities are quantified, and all the alternative systems are combined in the BMA manner to form a coupled forecasting system. The properties of this coupled forecasting system are examined, and an example of the U.S. inflation forecast is developed to illustrate the BSA theoretical framework and operational models. In addition, this dissertation enriches BFS theory in two ways. First, it proposes four new parametric models for the families of posterior density functions with closed-form solutions. They are type-1 and type-2 uniform-triangular models, as well as type-1 and type-2 copula-triangular models. Second, it introduces parameter uncertainty into the theoretical framework of BFS and derives the closed-form solution for a uniform-triangular parametric model in this context.
PHD (Doctor of Philosophy)
Probabilistic Forecast, Bayesian Inference, Bayesian Forecasting System, Bayesian Model Averaging, Model Uncertainty