Calculating effective degrees of freedom for forecast combinations and ensemble models
针对线性模型预测组合，推导了有效自由度的计算公式，并通过模拟验证。该结果支持F检验和信息准则等计算，帮助用户在候选模型过多时评估复杂度，识别复杂度成本来源。
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.