ON THE COMPARISON OF INTERVAL FORECASTS
ON THE COMPARISON OF INTERVAL FORECASTS
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DOI：
10.1111/jtsa.12426
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发表时间：
2018-11-01
影响因子：
0.9
通讯作者：
Shin, Minchul
中科院分区：
文献类型：
--
作者：
Askanazi, Ross;Diebold, Francis X.;Shin, Minchul
我们探讨区间预测比较时，名义上的置信水平是指定的，但基于区间的分位数没有指定。事实证明，这个问题是困难的，也许是无法解决的。我们首先考虑的情况下，区间满足克里斯托弗森条件（特别是，他们是正确的校准），在这种情况下，常见的处方，我们合理化和探索，是更喜欢最短的长度的间隔。然后，我们允许错误校准的间隔，在这种情况下，有一个校准长度权衡。我们提出了两个自然条件，区间预测损失函数应满足在这样的环境中，我们表明，各种流行的方法，区间预测比较失败。我们的负面结果加强了放弃区间预测而支持密度预测的理由：密度预测不仅提供更丰富的信息，而且可以使用已知的适当评分规则（如对数预测得分）进行比较，而区间预测则不能。
We explore interval forecast comparison when the nominal confidence level is specified, but the quantiles on which intervals are based are not specified. It turns out that the problem is difficult, and perhaps unsolvable. We first consider a situation where intervals meet the Christoffersen conditions (in particular, where they are correctly calibrated), in which case the common prescription, which we rationalize and explore, is to prefer the interval of shortest length. We then allow for mis-calibrated intervals, in which case there is a calibration-length tradeoff. We propose two natural conditions that interval forecast loss functions should meet in such environments, and we show that a variety of popular approaches to interval forecast comparison fail them. Our negative results strengthen the case for abandoning interval forecasts in favor of density forecasts: Density forecasts not only provide richer information, but also can be readily compared using known proper scoring rules like the log predictive score, whereas interval forecasts cannot.