A Bootstrap Approach for Generalized Autocontour Testing

We propose an extension of the Generalized Autocontour (G-ACR) tests (Gonzàlez-Rivera and Sun, 2015) for dynamic specifications of conditional densities (in-sample) and of forecast densities (out-of-sample). The new tests are based on probability integral transforms (PITs) computed from bootstrap conditional densities so that no assumption on the functional form of the density is needed. The proposed bootstrap procedure generates predictive densities that incorporate parameter uncertainty. In addition, the bootstrapped G-ACR tests enjoy standard asymptotic distributions. This approach is particularly useful to evaluate multi-step predictive densities whose functional form is unknown or difficult to obtain even in cases where the conditional density of the model is known