A bootstrap approach for generalized Autocontour testing Implications for VIX forecast densities
提出一种基于Bootstrap的广义自轮廓检验，用于评估条件密度模型的设定正确性，无需假设误差分布，并应用于VIX指数的预测密度检验，发现参数假设存在显著问题。
We propose an extension of the Generalized Autocontour tests for dynamic specification (evaluation) of in-sample (out-of-sample) conditional densities. The new tests are based on probability integral transforms computed from bootstrap conditional densities that incorporate parameter uncertainty without relying on parametric assumptions of the error distribution. Their finite sample distributions are well approximated using standard asymptotic distributions while they are easy to implement and provide information about potential sources of misspecification. We apply the new tests to the Heterogeneous Autoregressive and the Multiplicative Error models of the VIX index and find strong evidence against the parametric assumptions of the conditional densities.