This paper studies the theoretical predictive properties of classes of forecast combination methods. The study is motivated by the recently developed Bayesian framework for synthesizing predictive densities: Bayesian predictive synthesis. A novel strategy based on continuous time stochastic processes is proposed and developed, where the combined predictive error processes are expressed as stochastic differential equations, evaluated using Ito's lemma. We show that a subclass of synthesis functions under Bayesian predictive synthesis , which we categorize as non-linear synthesis,  entails an extra term  that "corrects" the bias from misspecification and dependence in the predictive error process , effectively improving forecasts.  Theoretical properties are examined and shown that this subclass improves the expected squared forecast error over any and all linear combination, averaging, and ensemble of forecasts, under mild conditions  . We discuss the conditions for which this subclass outperforms others , and its implications for developing forecast combination methods . A finite sample simulation study is presented to illustrate our results.
This paper studies the theoretical predictive properties of classes of forecast combination methods. A novel strategy based on continuous time stochastic processes is proposed and developed, where the combined predictive error processes are expressed as stochastic differential equations, evaluated using Ito's lemma. We identify a class of forecast combination methods , which we categorize as non-linear synthesis, and find that it entails an extra term in the predictive error process that "corrects" the bias from misspecification and dependence amongst forecasts , effectively improving forecasts. We show that a subclass of the recently developed framework of Bayesian predictive synthesis fits within this class. Theoretical properties are examined and we show that non-linear synthesis improves the expected squared forecast error over any and all linear combination, averaging, and ensemble of forecasts, under mild conditions that are met in most real applications . We discuss the conditions for which non-linear synthesis outperforms linear combinations , and its implications for developing further strategies . A finite sample simulation study is presented to illustrate our results.
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The study is motivated by the recently developed Bayesian framework for synthesizing predictive densities: Bayesian predictive synthesis.
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show that a subclass of synthesis functions under Bayesian predictive synthesis
identify a class of forecast combination methods
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and find that it
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in the predictive error process
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in the predictive error process
amongst forecasts
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We show that a subclass of the recently developed framework of Bayesian predictive synthesis fits within this class.
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shown that this subclass
we show that non-linear synthesis
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that are met in most real applications
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this subclass outperforms others
non-linear synthesis outperforms linear combinations
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forecast combination methods
further strategies