Simple Tests for the Correct Specification of Conditional Predictive Densities

We propose a simplified framework for evaluating conditional predictive densities based on the probability integral transform (PIT). The approach accommodates a wide range of estimation schemes, including expanding and rolling windows, and applies to both stationary and non-stationary processes. By treating the PIT as a primitive, our approach enables researchers to apply widely used tests in settings where their validity was previously uncertain. Monte Carlo simulations demonstrate favorable size and power properties of the tests. In an empirical application, we show that incorporating stochastic volatility into an unobserved components model is essential for generating correctly calibrated density forecasts of US industrial production growth at both monthly and quarterly frequencies.