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A Bootstrap Approach for Generalized Autocontour Testing

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  • Gonçalves Mazzeu, Joao Henrique
  • González-Rivera, Gloria
  • Ruiz Ortega, Esther
  • Veiga, Helena

Abstract

We propose an extension of the Generalized Autocontour (G-ACR) tests (González-Rivera and Sun, 2015) for one-step-ahead 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 that incorporate the parameter uncertainty without assuming any particular forecast error distribution. Consequently, the parametric specification of the conditional moments can be tested without relying on any particular error distribution. We show that the asymptotic distributions 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 which provide suggestions about the potential misspecification. The results are illustrated by testing the dynamic specification of the Heterogenous autoregressive (HAR) model when fitted to the popular U.S. volatility index VIX.

Suggested Citation

  • Gonçalves Mazzeu, Joao Henrique & González-Rivera, Gloria & Ruiz Ortega, 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.
    • Handle: RePEc:cte:wsrepe:23457
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    1. Engle, Robert F. & Gallo, Giampiero M., 2006. "A multiple indicators model for volatility using intra-daily data," Journal of Econometrics, Elsevier, vol. 131(1-2), pages 3-27.
    2. Fernandes, Marcelo & Medeiros, Marcelo C. & Scharth, Marcel, 2014. "Modeling and predicting the CBOE market volatility index," Journal of Banking & Finance, Elsevier, vol. 40(C), pages 1-10.
    3. Massimiliano Caporin & Eduardo Rossi & Paolo Santucci de Magistris, 2016. "Volatility Jumps and Their Economic Determinants," Journal of Financial Econometrics, Oxford University Press, vol. 14(1), pages 29-80.
    4. González-Rivera, Gloria & Senyuz, Zeynep & Yoldas, Emre, 2011. "Autocontours: Dynamic Specification Testing," Journal of Business & Economic Statistics, American Statistical Association, vol. 29(1), pages 186-200.
    5. Park, Yang-Ho, 2016. "The effects of asymmetric volatility and jumps on the pricing of VIX derivatives," Journal of Econometrics, Elsevier, vol. 192(1), pages 313-328.
    6. Federico M. Bandi & Benoit Perron, 2006. "Long Memory and the Relation Between Implied and Realized Volatility," Journal of Financial Econometrics, Oxford University Press, vol. 4(4), pages 636-670.
    7. Shimizu, Kenichi, 2014. "Bootstrapping the nonparametric ARCH regression model," Statistics & Probability Letters, Elsevier, vol. 87(C), pages 61-69.
    8. Berkowitz, Jeremy, 2001. "Testing Density Forecasts, with Applications to Risk Management," Journal of Business & Economic Statistics, American Statistical Association, vol. 19(4), pages 465-474, October.
    9. Lorenzo Pascual & Juan Romo & Esther Ruiz, 2004. "Bootstrap predictive inference for ARIMA processes," Journal of Time Series Analysis, Wiley Blackwell, vol. 25(4), pages 449-465, July.
    10. Goncalves, Silvia & White, Halbert, 2004. "Maximum likelihood and the bootstrap for nonlinear dynamic models," Journal of Econometrics, Elsevier, vol. 119(1), pages 199-219, March.
    11. Francis X. Diebold & Kamil Yilmaz, 2016. "Trans-Atlantic Equity Volatility Connectedness: U.S. and European Financial Institutions, 2004–2014," Journal of Financial Econometrics, Oxford University Press, vol. 14(1), pages 81-127.
    12. Shimotsu, Katsumi, 2012. "Exact local Whittle estimation of fractionally cointegrated systems," Journal of Econometrics, Elsevier, vol. 169(2), pages 266-278.
    13. Uwe Hassler & Paulo M.M. Rodrigues & Antonio Rubia, 2016. "Quantile Regression for Long Memory Testing: A Case of Realized Volatility," Journal of Financial Econometrics, Oxford University Press, vol. 14(4), pages 693-724.
    14. Yongmiao Hong, 2005. "Nonparametric Specification Testing for Continuous-Time Models with Applications to Term Structure of Interest Rates," The Review of Financial Studies, Society for Financial Studies, vol. 18(1), pages 37-84.
    15. Reeves, Jonathan J., 2005. "Bootstrap prediction intervals for ARCH models," International Journal of Forecasting, Elsevier, vol. 21(2), pages 237-248.
    16. Choi,In, 2015. "Almost All about Unit Roots," Cambridge Books, Cambridge University Press, number 9781107482500.
    17. González-Rivera, Gloria & Sun, Yingying, 2015. "Generalized autocontours: Evaluation of multivariate density models," International Journal of Forecasting, Elsevier, vol. 31(3), pages 799-814.
    18. Diebold, Francis X & Gunther, Todd A & Tay, Anthony S, 1998. "Evaluating Density Forecasts with Applications to Financial Risk Management," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 39(4), pages 863-883, November.
    19. Pascual, Lorenzo & Romo, Juan & Ruiz, Esther, 2006. "Bootstrap prediction for returns and volatilities in GARCH models," Computational Statistics & Data Analysis, Elsevier, vol. 50(9), pages 2293-2312, May.
    20. González-Rivera, Gloria & Yoldas, Emre, 2012. "Autocontour-based evaluation of multivariate predictive densities," International Journal of Forecasting, Elsevier, vol. 28(2), pages 328-342.
    21. Massimiliano Caporin & Eduardo Rossi & Paolo Santucci de Magistris, 2015. "Volatility Jumps and Their Economic Determinants," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 14(1), pages 29-80.
    22. Song, Zhaogang & Xiu, Dacheng, 2016. "A tale of two option markets: Pricing kernels and volatility risk," Journal of Econometrics, Elsevier, vol. 190(1), pages 176-196.
    23. Giraitis, Liudas & Kokoszka, Piotr & Leipus, Remigijus, 2000. "Stationary Arch Models: Dependence Structure And Central Limit Theorem," Econometric Theory, Cambridge University Press, vol. 16(1), pages 3-22, February.
    24. Fulvio Corsi, 2009. "A Simple Approximate Long-Memory Model of Realized Volatility," Journal of Financial Econometrics, Oxford University Press, vol. 7(2), pages 174-196, Spring.
    25. Valentina Corradi & Norman Swanson, 2006. "Predictive Density Evaluation. Revised," Departmental Working Papers 200621, Rutgers University, Department of Economics.
    26. Jushan Bai, 2003. "Testing Parametric Conditional Distributions of Dynamic Models," The Review of Economics and Statistics, MIT Press, vol. 85(3), pages 531-549, August.
    27. Corradi, Valentina & Swanson, Norman R., 2006. "Predictive Density Evaluation," Handbook of Economic Forecasting, in: G. Elliott & C. Granger & A. Timmermann (ed.), Handbook of Economic Forecasting, edition 1, volume 1, chapter 5, pages 197-284, Elsevier.
    28. Hidalgo, Javier & Zaffaroni, Paolo, 2007. "A goodness-of-fit test for ARCH([infinity]) models," Journal of Econometrics, Elsevier, vol. 141(2), pages 973-1013, December.
    29. Corradi, Valentina & Iglesias, Emma M., 2008. "Bootstrap refinements for QML estimators of the GARCH(1,1) parameters," Journal of Econometrics, Elsevier, vol. 144(2), pages 500-510, June.
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