Forecasting multidimensional tail risk at short and long horizons

We define Multidimensional Value at Risk (MVaR) as a natural generalization of VaR. This generalization makes possible a number of important applications. For example, many techniques developed for VaR can be applied directly to MVaR. As an illustration, we employ VaR forecasting and evaluation techniques. One of our forecasting models builds on the progress made in the volatility literature and decomposes MVaR into long-term trend and short-term cycle components. We compute short- and long-term MVaR forecasts for several multidimensional time series and discuss their (un)conditional accuracy.