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

TL;DR

This paper investigates how increasing the information set improves forecast accuracy for point forecasts and VaR, using scoring functions and tests, with applications in risk management and financial data.

Contribution

It introduces a framework linking information set size to forecast quality using strictly consistent scoring functions and tests, with practical applications in finance.

Findings

Larger information sets lead to better point forecasts with smaller scores.

The Diebold-Mariano test is consistent for evaluating information set effects.

Increasing information reduces expected shortfalls in VaR forecasts.

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.