REAL-TIME MULTIVARIATE DENSITY FORECAST EVALUATION AND CALIBRATION: MONITORlNG THE RISK OF HIGH-FREQUENCY RETURNS ON FOREIGN EXCHANGE

Abstract

We provide a framework for evaluating and improving multivariate density forecasts. Among other things, the multivariate framework lets us evaluate the adequacy of density forecasts involving cross-variable interactions, such as time-varying conditional correlations. We also provide conditions under which a technique of density forecast "calibration" can be used to improve deficient density forecasts. Finally, motivated by recent advances in financial risk management, we provide a detailed application to multivariate high-frequency exchange rate density forecasts.