Please use this identifier to cite or link to this item: https://hdl.handle.net/10419/297065 
Authors: 
Year of Publication: 
2022
Series/Report no.: 
Bank of Canada Staff Discussion Paper No. 2022-19
Publisher: 
Bank of Canada, Ottawa
Abstract: 
Forecast combinations, also known as ensemble models, routinely require practitioners to select a model from a massive number of potential candidates. Ten explanatory variables can be grouped into 21078 forecast combinations, and the number of possibilities increases further to 21078+21078 if we allow for forecast combinations of forecast combinations. This paper derives a calculation for the effective degrees of freedom of a forecast combination under a set of general conditions for linear models. It also supports this calculation with simulations. The result allows users to perform several other computations, including the F-test and various information criteria. These computations are particularly useful when there are too many candidate models to evaluate out of sample. Furthermore, computing effective degrees of freedom shows that the complexity cost of a forecast combination is driven by the parameters in the weighting scheme and the weighted average of parameters in the auxiliary models as opposed to the number of auxiliary models. This identification of complexity cost contributions can help practitioners make informed choices about forecast combination design.
Subjects: 
Econometric and statistical methods
JEL: 
C
C01
C02
C1
C13
C5
C50
C51
C52
C53
Persistent Identifier of the first edition: 
Document Type: 
Working Paper

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