# 11-131/4 (2011-09-20)

Lennart F. Hoogerheide, VU University Amsterdam; Francesco Ravazzolo, Norges Bank; Herman K. van Dijk, Erasmus University Rotterdam, VU University Amsterdam.
Value-at-Risk, backtest, optimal revision, forecast rationality
JEL codes:
C12, C52, C53, C58, G32

Patton and Timmermann (2011, “Forecast Rationality Tests Based on Multi-Horizon Bounds”, Journal of Business & Economic Statistics, 30(1), 1-17) propose a set of useful tests for forecast rationality or optimality under squared error loss, including an easily implemented test based on a regression that only involves (long-horizon and short-horizon) forecasts and no observations on the target variable. We propose an extension, a simulation-based procedure that takes into account the presence of errors in parameter estimates. This procedure can also be applied in the field of 'backtesting' models for Value-at-Risk. Applications to simple AR and ARCH time series models show that its power in detecting certain misspecifications is larger than the power of well-known tests for correct Unconditional Coverage and Conditional Coverage.