Interval forecast for model averaging methods

摘要

This paper is aimed at the analysis and verification of the formula for computing the number of degrees of freedom for the combined model when averaging across a set of regression models, which was proposed by Moiseev (2017) but was not thoroughly analyzed. The key feature of this formula is that it is applicable to absolutely any averaging method what dramatically widens its scope of application. We notice that the exact number of degrees of freedom for the combined model can not be computed due to uncertainty of variance-covariance matrix of submodels’ errors. However, it is shown by conducted simulation study that even using unbiased estimator of this matrix yields reliable confidence intervals. Therefore, considered formula appears to be crucial when computing interval forecast by model averaging methods.