Title: Forecast calibration, backtests, and loss decompositions for Value-at-Risk forecasts
Authors: Marius Puke - University of Hohenheim (Germany) [presenting]
Timo Dimitriadis - Heidelberg University (Germany)
Abstract: The evaluation of Value-at-Risk (VaR) forecasts is an own strand of literature rooted in the importance of banking and insurance regulation. Usually, one distinguishes between absolute and relative forecast evaluation, where the former refers to backtesting procedures and the latter to the use of loss functions. We make use of recent contributions to forecast calibration assessment and illustrate that absolute and relative forecast evaluation are similar tasks. To establish the connection between absolute and relative forecast evaluation, we revisit a decomposition of loss functions into measures of miscalibration (MCB), discrimination (DSC), and uncertainty (UNC) and show empirically that common backtests entirely overlook the (DSC) component. This corresponds to ignoring the forecasting models ability to discriminate between low and higher-risk periods. As a consequence, that might lead to inconclusive backtest results. Instead, the loss decomposition reveals this additional, hitherto unexploited information, provoking more informative insights.