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.

研究了信息数量增加对预测机制的影响，证明了预测机制的正确规范可以提高预测准确性；通过严格一致的评分函数展示了增加信息集的效应，并且探究了信息集序列中值在风险管理和预测方面的实际应用。