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Autocontour-based evaluation of multivariate predictive densities

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  • González-Rivera, Gloria
  • Yoldas, Emre

Abstract

We contribute to the rather sparse literature on multivariate density forecasting by introducing a new framework for the out-of-sample evaluation of multivariate density forecast models which builds on the concept of “autocontours” proposed by González-Rivera, Senyuz, and Yoldas (2011). This approach uniquely combines formal testing with graphical devices. We work with the one-step-ahead quantile residuals, which must be i.i.d. (univariate and multivariate) normal under the null hypothesis of a correct density model. Their corresponding autocontours are mathematically very tractable, and the tests based on them enjoy standard asymptotic properties. We show that parameter uncertainty is asymptotically irrelevant under certain conditions, and that, in general, a parametric bootstrap provides outstanding finite sample properties. We provide simulation evidence on the finite sample performances of the tests and compare their performances with that of an alternative testing procedure. We also illustrate this methodology by evaluating bivariate density forecasts of the returns on US value and growth portfolios.

Suggested Citation

  • González-Rivera, Gloria & Yoldas, Emre, 2012. "Autocontour-based evaluation of multivariate predictive densities," International Journal of Forecasting, Elsevier, vol. 28(2), pages 328-342.
  • Handle: RePEc:eee:intfor:v:28:y:2012:i:2:p:328-342
    DOI: 10.1016/j.ijforecast.2011.06.001
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    References listed on IDEAS

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    Citations

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    Cited by:

    1. Dovern, Jonas & Manner, Hans, 2016. "Robust Evaluation of Multivariate Density Forecasts," Annual Conference 2016 (Augsburg): Demographic Change 145547, Verein für Socialpolitik / German Economic Association.
    2. González-Rivera, Gloria & Sun, Yingying, 2017. "Density forecast evaluation in unstable environments," International Journal of Forecasting, Elsevier, vol. 33(2), pages 416-432.
    3. Gloria Gonzalez-Rivera & Joao Henrique Mazzeu & Esther Ruiz & Helena Veiga, 2017. "A Bootstrap Approach for Generalized Autocontour Testing. Implications for VIX Forecast Densities," Working Papers 201709, University of California at Riverside, Department of Economics.
    4. Covas, Francisco B. & Rump, Ben & Zakrajšek, Egon, 2014. "Stress-testing US bank holding companies: A dynamic panel quantile regression approach," International Journal of Forecasting, Elsevier, vol. 30(3), pages 691-713.
    5. Yves Dominicy & Hiroaki Ogata & David Veredas, 2013. "Inference for vast dimensional elliptical distributions," Computational Statistics, Springer, vol. 28(4), pages 1853-1880, August.
    6. Dovern, Jonas & Manner, Hans, 2016. "Order Invariant Evaluation of Multivariate Density Forecasts," Working Papers 0608, University of Heidelberg, Department of Economics.
    7. Gonçalves Mazzeu, Joao Henrique & González-Rivera, Gloria & Ruiz, Esther & Veiga, Helena, 2016. "A Bootstrap Approach for Generalized Autocontour Testing," DES - Working Papers. Statistics and Econometrics. WS 23457, Universidad Carlos III de Madrid. Departamento de Estadística.
    8. González-Rivera, Gloria & Sun, Yingying, 2015. "Generalized autocontours: Evaluation of multivariate density models," International Journal of Forecasting, Elsevier, vol. 31(3), pages 799-814.

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