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Efficient Evaluation of Multidimensional Time-Varying Density Forecasts with an Application to Risk Management


  • Evarist Stoja
  • Arnold Polanski



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 any continuous distribution 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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  • Evarist Stoja & Arnold Polanski, 2009. "Efficient Evaluation of Multidimensional Time-Varying Density Forecasts with an Application to Risk Management," Bristol Economics Discussion Papers 09/617, Department of Economics, University of Bristol, UK.
  • Handle: RePEc:bri:uobdis:09/617

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    More about this item


    Multivariate Density Forecast Evaluation; Probability Integral Transformation; Multidimensional Value at Risk; Monte Carlo Simulations;

    JEL classification:

    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection
    • C53 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Forecasting and Prediction Models; Simulation Methods

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