Testing Density Forecasts, with Applications to Risk Management
by Jeremy Berkowitz of the University of California, Irvine
Abstract: The forecast evaluation literature has traditionally focused on methods of assessing point forecasts. However, in the context of many models of financial risk, interest centers on more than just a single point of the forecast distribution. For example, value-at-risk (VaR) models which are currently in extremely wide use form interval forecasts. Many other important financial calculations also involve estimates not summarized by a point forecast. Although some techniques are currently available for assessing interval and density forecasts, existing methods tend to display low power in sample sizes typically available. This paper suggests a new approach to evaluating such forecasts. It requires evaluation of the entire forecast distribution, rather than a scalar or interval. The information content of forecast distributions combined with ex post realizations is enough to construct a powerful test even with sample sizes as small as 100.
Keywords: Forecast, evaluation, risk, VaR.
Published in: Journal of Business and Economic Statistics, Vol. 19, No. 4, (October 2001), pp. 465-474.