Estimation risk taking into consideration the effect of forecasting scheme: robust inference about VaR

Abstract

The paper addresses the issue of estimation risk in VaR testing. The occurrence of estimation risk (also called parameter uncertainty) implies that the observed VaR violation process may not fulfil the standard requirements that underpin the testing framework. As a result, VaR tests may reject correct VaR models due to estimation errors committed when predicting the VaR. The paper examines the robustness of VaR tests to estimation risk. The research is based on an observation indicating that certain elements of a forecasting scheme have a significant influence on estimation risk. Thus, the article extends the previous studies to include several more realistic forecasting schemes than those based solely on a fixed window. The aim of the research is twofold: firstly, to find methods of mitigating the negative impact of estimation risk on VaR tests, and secondly, to provide a comprehensive comparison of VaR testing methods with reference to the issue of estimation risk. The conducted analyses demonstrate that a proper adjustment of the forecasting scheme yields better results in terms of the accuracy of the tests than correcting estimation errors by means of the subsampling technique.