This paper provides empirical results supporting the theoretical ones by the first author on backtesting long-horizon distributional forecasts. The problem is quite general but for us it is motivated by the regulatory requirement of backtesting evolution models used in the measurement of...

In this paper we address a challenging aspect that arises in the regulatory requirement of back-testing the accuracy of distributional forecasts. The latter are core to measurement and capitalization of counterparty risk for banks under the IMM (Internal Models Method). The problem is very...

Multivariate distributional forecasts have become widespread in recent years. To assess the quality of such forecasts, suitable evaluation methods are needed. In the univariate case, calibration tests based on the probability integral transform (PIT) are routinely used. However, multivariate...

We propose a new framework for evaluating predictive densities in an environment where the estimation error of the parameters used to construct the densities is preserved asymptotically under the null hypothesis. The tests offer a simple way to evaluate the correct specification of predictive...

In this paper we present a new asymptotically normal test for out-of-sample evaluation in nested models. Our approach is a simple modification of a traditional encompassing test that is commonly known as Clark and West test (CW). The key point of our strategy is to introduce an independent...