Banco de España proposes simplified tests for conditional predictive densities
A Banco de España working paper proposes a simplified framework for evaluating conditional predictive densities based on the probability integral transform (PIT). The approach enables researchers to apply widely used tests in settings where their validity was previously uncertain.
Bridging the gap in predictive density evaluation
Probabilistic forecasting is crucial in economics and finance, making correct specification essential.
Existing methods, like Rossi and Sekhposyan (2019), have limitations, especially for models estimated in expanding windows.
This paper addresses this by providing alternative assumptions for valid tests of conditional predictive densities.
By treating probability integral transforms (PITs) as primitives, the framework accommodates both rolling and expanding window estimation schemes, extending the applicability of widely used tests.
PIT as a primitive for robust testing
The framework directly studies probability integral transforms (PITs), defined as the conditional predictive CDF evaluated at the realization.
The null hypothesis states that all predictive distributions are well specified.
The framework relies on two key assumptions: continuity of the true conditional CDF and pairwise stationarity of the PITs.
Monte Carlo simulations show favorable size and power.
An empirical application forecasting US industrial production growth demonstrates that incorporating stochastic volatility in unobserved components models yields correctly calibrated density forecasts.