This paper studies the theoretical predictive properties of classes of forecast combination methods. A novel strategy based on continuous time stochastic processesis 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.
We examine and compare the predictive properties of classes of ensemble methods, including the recently developed Bayesian predictive synthesis (BPS). We develop a novel strategy based on stochastic processes , where the predictive processes are expressed as stochastic differential equations, evaluated using It\^{o 's lemma. Using this strategy, we identify two main classes of ensemble methods: linear combination and non-linear synthesis, and show that a subclass of BPS is the latter. With regard to expected squared forecast error , we identify the conditions and mechanism for which non-linear synthesis improves over linear combinations; conditions that are commonly met in real world applications. We further show that a specific form of non-linear BPS (as in McAlinn and West, 2019) produces exact minimax predictive distributions for Kullback-Leibler risk and, under certain conditions, quadratic risk . A finite sample simulation study is presented to illustrate our results.
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This paper studies the theoretical
We examine and compare the
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forecast combination methods. A
ensemble methods, including the recently developed Bayesian predictive synthesis (BPS). We develop a
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continuous time stochastic processesis proposed and developed
stochastic processes
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combined predictive error
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We identify a class of forecast combination methods, which we categorize as
Using this strategy, we identify two main classes of ensemble methods: linear combination and
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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
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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
BPS is the latter. With regard to
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over any and all linear combination, averaging, and ensemble of forecasts, under mild
, we identify the conditions and mechanism for which non-linear synthesis improves over linear combinations;
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met in most real
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discuss the conditions for which
further show that a specific form of
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synthesis outperforms linear combinations, and its implications for developing further strategies
BPS (as in McAlinn and West, 2019) produces exact minimax predictive distributions for Kullback-Leibler risk and, under certain conditions, quadratic risk