Comparison of Value-at-Risk models using the MCS approach

This paper compares the Value-at-Risk (VaR) forecasts delivered by alternative model specifications using the Model Confidence Set (MCS) procedure recently developed by Hansen et al. (Econometrica 79(2):453-497, 2011). The direct VaR estimate provided by the Conditional Autoregressive Value-at-Risk (CAViaR) models of Engle and Manganelli (J Bus Econ Stat 22(4):367-381, 2004) are compared to those obtained by the popular Autoregressive Conditional Heteroskedasticity (ARCH) models of Engle (Econometrica 50(4):987-1007, 1982) and to the Generalised Autoregressive Score (GAS) models recently introduced by Creal et al. (J Appl Econom 28(5):777-795, 2013) and Harvey (Dynamic models for volatility and heavy tails: with applications to financial and economic time series. Cambridge University Press, Cambridge, 2013). The MCS procedure consists in a sequence of tests which permits to construct a set of superior models, where the null hypothesis of Equal Predictive Ability (EPA) is not rejected at a certain confidence level. Our empirical results, suggest that, during the European Sovereign Debt crisis of 2009-2010, highly non-linear volatility models deliver better VaR forecasts for the European countries as opposed to other regional indexes. Model comparisons have been performed using the package MCS developed by the authors and freely available at the CRAN website.