A bootstrap approach for generalized Autocontour testing Implications for VIX forecast densities Articles uri icon

publication date

  • May 2020

start page

  • 971

end page

  • 990


  • 10


  • 39

International Standard Serial Number (ISSN)

  • 0747-4938

Electronic International Standard Serial Number (EISSN)

  • 1532-4168


  • We propose an extension of the Generalized Autocontour tests fordynamic 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.


  • har model; model evaluation; multiplicative error model; pit