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arXiv 1404.7653stat.APq-fin.RM
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信息集在预测中的作用--及其在风险管理中的应用

The role of the information set for forecasting - with applications to risk management

Hajo Holzmann, Matthias Eulert

摘要:

预测是根据某些信息作出的。如果正确地规定了预报机制,那么更多的可用信息应能带来更好的预报。对于点预测,我们展示了如何通过使用严格一致的评分函数来量化增加信息集的效果,从而获得较小的平均分数。此外,我们表明,经典的Diebold-Mariano测试,严格一致的评分函数和渐近理想的预测的基础上,是一个一致的测试增加的序列信息集上$h$ -步点预测的效果。对于风险价值(VaR),我们表明,平均分数,这对应于平均分位数风险,直接关系到预期的不足。因此,增加信息集将导致风险值预测,平均而言,这将导致较小的预期短缺。我们说明了我们的结果在模拟和应用程序的股票回报率无条件与有条件的风险管理,以及单变量建模的投资组合回报与多变量建模的个人风险因素。还讨论了通过使用严格适当的评分规则来评估概率预测的信息集的作用。

英文摘要:

Predictions are issued on the basis of certain information. If the forecasting mechanisms are correctly specified, a larger amount of available information should lead to better forecasts. For point forecasts, we show how the effect of increasing the information set can be quantified by using strictly consistent scoring functions, where it results in smaller average scores. Further, we show that the classical Diebold-Mariano test, based on strictly consistent scoring functions and asymptotically ideal forecasts, is a consistent test for the effect of an increase in a sequence of information sets on $h$-step point forecasts. For the value at risk (VaR), we show that the average score, which corresponds to the average quantile risk, directly relates to the expected shortfall. Thus, increasing the information set will result in VaR forecasts which lead on average to smaller expected shortfalls. We illustrate our results in simulations and applications to stock returns for unconditional versus conditional risk management as well as univariate modeling of portfolio returns versus multivariate modeling of individual risk factors. The role of the information set for evaluating probabilistic forecasts by using strictly proper scoring rules is also discussed.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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