Bayesian Predictive Synthesis: Forecast Calibration and Combination

The combination of forecast densities, whether they result from a set of models,

a group of consulted experts, or other sources, is becoming increasingly important

in the fields of economics, policy, and finance, among others. Requiring methodology

that goes beyond standard Bayesian model uncertainty and model mixing -

with its well-known limitations based on a clearly proscribed theoretical basis - multiple

`density combination' methods have been proposed. While some proposals have

demonstrated empirical success, most apparently lack a core philosophical and theoretical

foundation. Interesting recent examples generalize the common `linear opinion

pool' with

flexible mixing weights that depend on the forecast variable itself -

i.e., outcome-dependent mixing. This dissertation takes a foundational subjective

Bayesian perspective in order to show that such a density combination scheme is

in fact justified as one example of Bayesian agent opinion analysis, or `predictive

synthesis'. This logically coherent framework clearly delineates the underlying assumptions

as well as the theoretical constraints and limitations of many combination

`rules', defining a broad class of Bayesian models for the general problem. A number

of examples, including applications to sets of predictive densities for foreign exchange

and United States inflation time series data, provide illustrations.

Chapters 1-2 introduce and describe the ideas involved in Bayesian predictive

synthesis (BPS) as a method of subjective analysis. Chapters 3-4 describe different

possible formulations of outcome-dependent mixing. Chapter 5 places the analysis into a time series context and covers relevant inference techniques. Chapters 6 and 7

apply the time series analysis to euro currency forecasts and United States inflation

data. Chapter 8 concludes.