Calculating Effective Degrees of Freedom for Forecast Combinations and Ensemble Models

James Younker

No 2022-19, Discussion Papers from Bank of Canada

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 2^1078 forecast combinations, and the number of possibilities increases further to 2^(1078+2^1078) 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.

Keywords: Econometric; and; statistical; methods (search for similar items in EconPapers)
JEL-codes: C01 C02 C1 C13 C5 C50 C51 C52 C53 (search for similar items in EconPapers)
Pages: 21 pages
Date: 2022-09
New Economics Papers: this item is included in nep-ecm and nep-for
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.bankofcanada.ca/2022/09/staff-discussion-paper-2022-19/ Abstract (text/html)
https://www.bankofcanada.ca/wp-content/uploads/2022/09/sdp2022-19.pdf Full text (application/pdf)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:bca:bocadp:22-19

Access Statistics for this paper

More papers in Discussion Papers from Bank of Canada 234 Wellington Street, Ottawa, Ontario, K1A 0G9, Canada. Contact information at EDIRC.
Bibliographic data for series maintained by ().