Efficient Evaluation of Multidimensional Time-Varying Density Forecasts with an Application to Risk Management
Posted: 9 Oct 2010 Last revised: 22 Aug 2012
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Efficient Evaluation of Multidimensional Time-Varying Density Forecasts with an Application to Risk Management
Date Written: October 7, 2010
Abstract
We propose two simple evaluation methods for time-varying density forecasts of continuous higher-dimensional random variables. Both methods are based on the probability integral transformation for unidimensional forecasts. The first method tests multinormal densities and relies on the rotation of the coordinate system. The advantage of the second method is not only its applicability to arbitrary continuous distributions but also the evaluation of the forecast accuracy in specific regions of its domain as defined by the user’s interest. We show that the latter property is particularly useful for evaluating a multidimensional generalization of the Value at Risk. In simulations and in an empirical study, we examine the performance of both tests.
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