Backtesting Value-at-Risk using Forecasts for Multiple Horizons, a Comment on the Forecast Rationality Tests of A.J. Patton and A. Timmermann
Patton and Timmermann (2011, 'Forecast Rationality Tests Based on Multi-Horizon Bounds', Journal of Business & Economic Statistics, forthcoming) 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.
|Keywords||backtest, forecast rationality, optimal revision, value-at-risk|
|JEL||C12, Hypothesis Testing (jel), C52, Model Evaluation and Testing (jel), C53, Forecasting and Other Model Applications (jel), G32, Financing Policy; Capital and Ownership Structure (jel)|
Hoogerheide, L.F, Ravazzolo, F, & van Dijk, H.K. (2011). Backtesting Value-at-Risk using Forecasts for Multiple Horizons, a Comment on the Forecast Rationality Tests of A.J. Patton and A. Timmermann (No. TI 2011-131/4). Discussion paper / Tinbergen Institute (pp. 1–17). Tinbergen Institute. Retrieved from http://hdl.handle.net/1765/26505