Banco de España develops simplified tests for conditional predictive densities

Probabilistic forecasting has become a central component in economics and finance, with researchers and policymakers increasingly focusing on forecast uncertainty.

Assessing the correct specification of these forecasts is crucial.

Existing methods, such as those by Rossi and Sekhposyan (2019), often have limitations, particularly regarding expanding window estimation schemes and dynamic latent variable models.

This paper addresses these gaps by providing an alternative set of assumptions under which existing tests remain valid.

By treating probability integral transforms (PITs) as primitives, the framework accommodates both rolling and expanding window estimation, as well as stationary and non-stationary processes, abstracting from parameter estimation uncertainty.

The authors also introduce weighted test statistics, allowing for focused analysis on specific parts of the predictive distribution.

The proposed tests demonstrate favorable size and power properties through extensive Monte Carlo simulations under the new alternative assumptions.

This provides strong theoretical support for their application in diverse settings.

In an empirical application, the paper forecasts US industrial production, revealing a significant finding: incorporating stochastic volatility into an unobserved components model is essential.

This integration leads to correctly calibrated density forecasts for US industrial production growth at both monthly and quarterly frequencies.

The findings highlight the practical importance of the framework for evaluating forecasts, rather than models, and contribute to the literature on absolute density forecast evaluation.