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

By Hajo Holzmann, Matthias Eulert. 2014

65 citations recorded by the source corpus.

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.

Subfields: Finance, Management Science and Operations Research

View Paper: https://www.semanticscholar.org/paper/a7dd955e703593557828fed99221bfb7a4f76aad

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Citations in the corpus

Regression diagnostics meets forecast evaluation: conditional calibration, reliability diagrams, and coefficient of determination (2021, background): “Consistent scoring functions serve as all-purpose performance measures that elicit fair and honest assessments and reward the utilization of broad information bases (Holzmann and Eulert, 2014).”
Comparing Possibly Misspecified Forecasts (2020, background): “Holzmann and Eulert (2014) showed that (correctly specified) forecasts based on larger information sets lead to lower expected loss.”
Expected Shortfall is jointly elicitable with Value at Risk - Implications for backtesting (2015, background): “tly consistent scoring function, so elicitability is crucial. In particular, proper scoring rules and consistent scoring functions are sensitive to increasing information utilized for prediction; see Holzmann and Eulert (2014). However, as consistent scoring functions are not unique, a question of p”
Elicitability and backtesting: Perspectives for banking regulation (2016, background): “} ∈N, {R∗t} are the optimal conditional forecasts with repect to their ﬁltrations as deﬁned at (2.8), then the internal procedure dominates the standard procedure, both, conditionally and on average [Holzmann and Eulert, 2014, Theorem 1]. The same is true if {Rt}t∈N is F∗-conditionally optimal and {”
Of quantiles and expectiles: consistent scoring functions, Choquet representations and forecast rankings (2015, background): “Holzmann and Eulert (2014) proved that, when forecasts make ideal use of nested information bases, the forecast with the broader information basis is preferable under any consistent scoring function.”