New framework validates conditional predictive densities for diverse models
Researchers from Banco de España have proposed a simplified framework for evaluating conditional predictive densities. Published in September 2025, the new approach accommodates a wide range of estimation schemes and applies to both stationary and non-stationary processes.
Bridging theoretical gaps in forecast evaluation
Probabilistic forecasting has become a cornerstone in economics and finance, with increasing focus on the uncertainty surrounding predictions for variables like inflation and growth.
Assessing the correct specification of these forecasts is crucial.
Existing methodologies, such as those by Rossi and Sekhposyan (2019), often face limitations when applied to models estimated with expanding windows or dynamic latent variables, which exploit the entire history of a process.
This creates a gap between theoretical validity and common empirical practice.
The new framework addresses this by providing an alternative set of assumptions under which existing tests remain valid.
By abstracting from parameter estimation uncertainty and treating probability integral transforms (PITs) as primitives, the approach accommodates both rolling and expanding window estimation schemes, as well as stationary and non-stationary processes, thereby broadening the applicability of widely used tests.
Stochastic volatility refines US production forecasts
The proposed framework introduces weighted test statistics, allowing researchers to focus on specific parts of the predictive distribution, such as the left tail, without entirely disregarding calibration issues elsewhere.
Monte Carlo simulations demonstrate that the tests exhibit favorable size and power properties under the new assumptions.
In a practical application, the study forecasts US industrial production growth.
The empirical findings highlight that incorporating stochastic volatility into an unobserved components model is essential for generating correctly calibrated density forecasts.
This holds true for both monthly and quarterly frequencies, underscoring the practical implications of the refined evaluation framework for economic modeling and forecasting practices.