Forecasting Multidimensional Tail Risk at Short and Long Horizons

Multidimensional Value at Risk (MVaR) generalises VaR in a natural way as the intersection of univariate VaRs. We reduce the dimensionality of MVaRs which allows for adapting the techniques and applications developed for VaR 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 multidimensional tail events 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