论文标题
抽样变异性对分布预测的估计组合的影响
The Impact of Sampling Variability on Estimated Combinations of Distributional Forecasts
论文作者
论文摘要
我们研究了估计预测组合的性能和抽样变异性，特别注意预测分布的组合。根据适当的评分规则，根据标准函数优化了预测组合中的未知参数，以奖励对当前问题重要的预测准确性的形式，并使用所述评分规则的样本外的预期来测量预测性能。我们的结果为估计预测组合的行为提供了新的见解。首先，我们表明，渐近地，标准预测组合性能的采样可变性仅通过估计组成模型的估计来确定，并估算了在第一阶的组合权重造成任何采样可变性的组合权重。其次，我们表明，如果在计算上可行的，在单个步骤中产生的预测组合（共同估算的组成模型和组合函数参数）具有较高的预测精度和更低的采样可变性，而构成模型和组合函数参数在两个步骤中估算了构成模型和组合功能参数。这些理论见解在模拟设置和使用S＆P500回报的时间序列的广泛经验图中进行了数值证明。
We investigate the performance and sampling variability of estimated forecast combinations, with particular attention given to the combination of forecast distributions. Unknown parameters in the forecast combination are optimized according to criterion functions based on proper scoring rules, which are chosen to reward the form of forecast accuracy that matters for the problem at hand, and forecast performance is measured using the out-of-sample expectation of said scoring rule. Our results provide novel insights into the behavior of estimated forecast combinations. Firstly, we show that, asymptotically, the sampling variability in the performance of standard forecast combinations is determined solely by estimation of the constituent models, with estimation of the combination weights contributing no sampling variability whatsoever, at first order. Secondly, we show that, if computationally feasible, forecast combinations produced in a single step -- in which the constituent model and combination function parameters are estimated jointly -- have superior predictive accuracy and lower sampling variability than standard forecast combinations -- where constituent model and combination function parameters are estimated in two steps. These theoretical insights are demonstrated numerically, both in simulation settings and in an extensive empirical illustration using a time series of S&P500 returns.
