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Title: Predictive properties of forecast combination, ensemble methods, and Bayesian synthesis Authors:  Kenichiro McAlinn - Temple University (United States) [presenting]
Kosaku Takanashi - Keio University (Japan)
Abstract: The aim is to study the theoretical predictive properties of multiple classes of forecast (model) combination strategies, motivated by a recent development in a foundational Bayesian framework called Bayesian predictive synthesis. A novel strategy based on continuous time stochastic processes is developed, where the predictive error processes are expressed as stochastic differential equations that are evaluated using Itos lemma. As a result, we show that a class of Bayesian predictive synthesis functions, which we categorize as non-linear synthesis, entails an extra term in the stochastic process that is interpreted as a shrinkage term on the error process, effectively improving forecasts. Theoretical properties are examined and shown that this subclass improves expected squared forecast error over any and all linear combination, averaging, and ensemble of forecasts. A finite sample simulation study is presented to illustrate our results. The results imply directions for further research and inquiry, which are discussed.