Simple Tests for the Correct Specification of Conditional Predictive Densities
A new working paper proposes a simplified framework for evaluating conditional predictive densities based on the probability integral transform (PIT). This approach accommodates various estimation schemes and applies to both stationary and non-stationary processes, enabling researchers to apply widely used tests in settings where their validity was previously uncertain.
Bridging gaps in predictive density evaluation
Probabilistic forecasting has become a central component in economics and finance, making the assessment of its correct specification essential.
While the probability integral transform (PIT) has been widely used for this purpose, existing tests often face limitations regarding parameter estimation uncertainty and specific estimation schemes, such as expanding windows.
This paper addresses these gaps by providing an alternative set of assumptions that validate existing tests.
By abstracting from parameter estimation uncertainty and specific estimation schemes, the framework accommodates both rolling and expanding window estimation, as well as stationary and non-stationary processes.
A novel aspect is the consideration of weighted test statistics, allowing researchers to focus on specific parts of the predictive distribution.
Empirical insights from US industrial production
The proposed framework directly studies the behavior of probability integral transforms (PITs), leveraging specific assumptions to achieve the same asymptotic distribution as prior work by Rossi and Sekhposyan (2019).
The null hypothesis posits that all predictive distributions are well specified, implying that forecasters could not have achieved more accurate densities with available information.
Monte Carlo simulations confirm that the new tests exhibit favorable size and power properties under the proposed assumptions.
In an empirical application forecasting US industrial production, the study demonstrates that incorporating stochastic volatility into an unobserved components model is crucial for generating correctly calibrated density forecasts at both monthly and quarterly frequencies.