A Bootstrap Approach for Generalized Autocontour Testing. Implications for VIX Forecast Densities
Gloria Gonzalez-Rivera (),
Joao Henrique Mazzeu (),
Esther Ruiz and
Helena Veiga ()
Additional contact information
Joao Henrique Mazzeu: UC3M
No 201709, Working Papers from University of California at Riverside, Department of Economics
We propose an extension of the Generalized Autocontour (G-ACR) tests for dynamic specification of in-sample conditional densities and for evaluation of out-of-sample forecast densities. The new tests are based on probability integral transforms (PITs) computed from bootstrap conditional densities that incorporate parameter uncertainty. Then, the parametric specification of the conditional moments can be tested without relying on any parametric error distribution yet exploiting distributional properties of the variable of interest. We show that the finite sample distribution of the bootstrapped G-ACR (BG-ACR) tests are well approximated using standard asymptotic distributions. Furthermore, the proposed tests are easy to implement and are accompanied by graphical tools that provide information about the potential sources of misspecification. We apply the BG-ACR tests to the Heterogeneous Autoregressive (HAR) model and the Multiplicative Error Model (MEM) of the U.S. volatility index VIX. We find strong evidence against the parametric assumptions of the conditional densities, i.e. normality in the HAR model and semi non-parametric Gamma (GSNP) in the MEM. In both cases, the true conditional density seems to be more skewed to the right and more peaked than either normal or GSNP densities, with location, variance and skewness changing over time. The preferred specification is the heteroscedastic HAR model with bootstrap conditional densities of the log-VIX.
Keywords: Distribution Uncertainty; Model Evaluation; Parameter Uncertainty; PIT; VIX; HAR model; Multiplicative Error Model (search for similar items in EconPapers)
New Economics Papers: this item is included in nep-ecm, nep-ets and nep-for
References: View references in EconPapers View complete reference list from CitEc
Citations: Track citations by RSS feed
Downloads: (external link)
https://economics.ucr.edu/repec/ucr/wpaper/201709.pdf First version, 2017 (application/pdf)
This item may be available elsewhere in EconPapers: Search for items with the same title.
Export reference: BibTeX
RIS (EndNote, ProCite, RefMan)
Persistent link: https://EconPapers.repec.org/RePEc:ucr:wpaper:201709
Access Statistics for this paper
More papers in Working Papers from University of California at Riverside, Department of Economics Contact information at EDIRC.
Bibliographic data for series maintained by Kelvin Mac ().