Template-Type: ReDIF-Paper 1.0 Series: Tinbergen Institute Discussion Papers Creation-Date: 2011-09-20 Number: 11-131/4 Author-Name: Lennart F. Hoogerheide Author-Workplace-Name: VU University Amsterdam Author-Name: Francesco Ravazzolo Author-Workplace-Name: Norges Bank Author-Name: Herman K. van Dijk Author-Workplace-Name: Erasmus University Rotterdam, VU University Amsterdam. Title: Backtesting Value-at-Risk using Forecasts for Multiple Horizons, a Comment on the Forecast Rationality Tests of A.J. Patton and A. Timmermann Abstract: 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. Classification-JEL: C12, C52, C53, C58, G32 Keywords: Value-at-Risk, backtest, optimal revision, forecast rationality File-Url: https://papers.tinbergen.nl/11131.pdf File-Format: application/pdf File-Size: 154445 bytes Handle: RePEc:tin:wpaper:20110131