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March 2014 The role of the information set for forecasting—with applications to risk management
Hajo Holzmann, Matthias Eulert
Ann. Appl. Stat. 8(1): 595-621 (March 2014). DOI: 10.1214/13-AOAS709

Abstract

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.

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Hajo Holzmann. Matthias Eulert. "The role of the information set for forecasting—with applications to risk management." Ann. Appl. Stat. 8 (1) 595 - 621, March 2014. https://doi.org/10.1214/13-AOAS709

Information

Published: March 2014
First available in Project Euclid: 8 April 2014

zbMATH: 06302249
MathSciNet: MR3192004
Digital Object Identifier: 10.1214/13-AOAS709

Keywords: forecast , information set , scoring function , scoring rule , value at risk

Rights: Copyright © 2014 Institute of Mathematical Statistics

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Vol.8 • No. 1 • March 2014
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