IDEAS home Printed from https://ideas.repec.org/a/taf/emetrv/v39y2020i10p971-990.html
   My bibliography  Save this article

A bootstrap approach for generalized Autocontour testing Implications for VIX forecast densities

Author

Listed:
  • João Henrique G. Mazzeu
  • Gloria González-Rivera
  • Esther Ruiz
  • Helena Veiga

Abstract

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.

Suggested Citation

  • João Henrique G. Mazzeu & Gloria González-Rivera & Esther Ruiz & Helena Veiga, 2020. "A bootstrap approach for generalized Autocontour testing Implications for VIX forecast densities," Econometric Reviews, Taylor & Francis Journals, vol. 39(10), pages 971-990, November.
  • Handle: RePEc:taf:emetrv:v:39:y:2020:i:10:p:971-990
    DOI: 10.1080/07474938.2020.1761150
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1080/07474938.2020.1761150
    Download Restriction: Access to full text is restricted to subscribers.

    As the access to this document is restricted, you may want to look for a different version below or search for a different version of it.

    Other versions of this item:

    References listed on IDEAS

    as
    1. 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.
    2. 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.
    3. Ian W. R. Martin & Christian Wagner, 2019. "What Is the Expected Return on a Stock?," Journal of Finance, American Finance Association, vol. 74(4), pages 1887-1929, August.
    4. Francis X. Diebold & Kamil Yilmaz, 2016. "Trans-Atlantic Equity Volatility Connectedness: U.S. and European Financial Institutions, 2004–2014," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 14(1), pages 81-127.
    5. Fulvio Corsi & Roberto Renò, 2012. "Discrete-Time Volatility Forecasting With Persistent Leverage Effect and the Link With Continuous-Time Volatility Modeling," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 30(3), pages 368-380, January.
    6. Todorova, Neda, 2015. "The course of realized volatility in the LME non-ferrous metal market," Economic Modelling, Elsevier, vol. 51(C), pages 1-12.
    7. Yongmiao Hong, 2005. "Nonparametric Specification Testing for Continuous-Time Models with Applications to Term Structure of Interest Rates," Review of Financial Studies, Society for Financial Studies, vol. 18(1), pages 37-84.
    8. Rossi, Barbara & Sekhposyan, Tatevik, 2013. "Conditional predictive density evaluation in the presence of instabilities," Journal of Econometrics, Elsevier, vol. 177(2), pages 199-212.
    9. Bai, Jushan & Chen, Zhihong, 2008. "Testing multivariate distributions in GARCH models," Journal of Econometrics, Elsevier, vol. 143(1), pages 19-36, March.
    10. 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.
    11. González-Rivera, Gloria & Sun, Yingying, 2015. "Generalized autocontours: Evaluation of multivariate density models," International Journal of Forecasting, Elsevier, vol. 31(3), pages 799-814.
    12. Konstantinidi, Eirini & Skiadopoulos, George, 2011. "Are VIX futures prices predictable? An empirical investigation," International Journal of Forecasting, Elsevier, vol. 27(2), pages 543-560.
    13. 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.
    14. 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.
    15. González-Rivera, Gloria & Yoldas, Emre, 2012. "Autocontour-based evaluation of multivariate predictive densities," International Journal of Forecasting, Elsevier, vol. 28(2), pages 328-342.
    16. Konstantinidi, Eirini & Skiadopoulos, George & Tzagkaraki, Emilia, 2008. "Can the evolution of implied volatility be forecasted? Evidence from European and US implied volatility indices," Journal of Banking & Finance, Elsevier, vol. 32(11), pages 2401-2411, November.
    17. Fulvio Corsi, 2009. "A Simple Approximate Long-Memory Model of Realized Volatility," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 7(2), pages 174-196, Spring.
    18. Atsushi Inoue & Lutz Kilian, 2005. "In-Sample or Out-of-Sample Tests of Predictability: Which One Should We Use?," Econometric Reviews, Taylor & Francis Journals, vol. 23(4), pages 371-402.
    19. Bollerslev, Tim & Kretschmer, Uta & Pigorsch, Christian & Tauchen, George, 2009. "A discrete-time model for daily S & P500 returns and realized variations: Jumps and leverage effects," Journal of Econometrics, Elsevier, vol. 150(2), pages 151-166, June.
    20. Psaradellis, Ioannis & Sermpinis, Georgios, 2016. "Modelling and trading the U.S. implied volatility indices. Evidence from the VIX, VXN and VXD indices," International Journal of Forecasting, Elsevier, vol. 32(4), pages 1268-1283.
    21. 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.
    22. 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.
    23. Massimiliano Caporin & Eduardo Rossi & Paolo Santucci de Magistris, 2016. "Volatility Jumps and Their Economic Determinants," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 14(1), pages 29-80.
    24. Hall, Peter & Yao, Qiwei, 2003. "Inference in ARCH and GARCH models with heavy-tailed errors," LSE Research Online Documents on Economics 5875, London School of Economics and Political Science, LSE Library.
    25. 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.
    26. Ian Martin, 2017. "What is the Expected Return on the Market?," The Quarterly Journal of Economics, Oxford University Press, vol. 132(1), pages 367-433.
    27. Shimizu, Kenichi, 2014. "Bootstrapping the nonparametric ARCH regression model," Statistics & Probability Letters, Elsevier, vol. 87(C), pages 61-69.
    28. 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.
    29. Michael McAleer & Suhejla Hoti & Felix Chan, 2009. "Structure and Asymptotic Theory for Multivariate Asymmetric Conditional Volatility," Econometric Reviews, Taylor & Francis Journals, vol. 28(5), pages 422-440.
    30. Anthony Tay & Kenneth F. Wallis, 2000. "Density Forecasting: A Survey," Econometric Society World Congress 2000 Contributed Papers 0370, Econometric Society.
    31. Fresoli, Diego E. & Ruiz, Esther, 2016. "The uncertainty of conditional returns, volatilities and correlations in DCC models," Computational Statistics & Data Analysis, Elsevier, vol. 100(C), pages 170-185.
    32. Chen, Bin & Hong, Yongmiao, 2014. "A unified approach to validating univariate and multivariate conditional distribution models in time series," Journal of Econometrics, Elsevier, vol. 178(P1), pages 22-44.
    33. Reeves, Jonathan J., 2005. "Bootstrap prediction intervals for ARCH models," International Journal of Forecasting, Elsevier, vol. 21(2), pages 237-248.
    34. Donald W. K. Andrews & Moshe Buchinsky, 2000. "A Three-Step Method for Choosing the Number of Bootstrap Repetitions," Econometrica, Econometric Society, vol. 68(1), pages 23-52, January.
    35. Fresoli, Diego & Ruiz, Esther & Pascual, Lorenzo, 2015. "Bootstrap multi-step forecasts of non-Gaussian VAR models," International Journal of Forecasting, Elsevier, vol. 31(3), pages 834-848.
    36. Andrés Alonso & Daniel Peña & Juan Romo, 2006. "Introducing model uncertainty by moving blocks bootstrap," Statistical Papers, Springer, vol. 47(2), pages 167-179, March.
    37. 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.
    38. Huang, Zhuo & Liu, Hao & Wang, Tianyi, 2016. "Modeling long memory volatility using realized measures of volatility: A realized HAR GARCH model," Economic Modelling, Elsevier, vol. 52(PB), pages 812-821.
    39. 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.
    40. James Mitchell & Kenneth F. Wallis, 2011. "Evaluating density forecasts: forecast combinations, model mixtures, calibration and sharpness," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 26(6), pages 1023-1040, September.
    41. Manzan, Sebastiano & Zerom, Dawit, 2008. "A bootstrap-based non-parametric forecast density," International Journal of Forecasting, Elsevier, vol. 24(3), pages 535-550.
    42. Peter Hall & Qiwei Yao, 2003. "Inference in Arch and Garch Models with Heavy--Tailed Errors," Econometrica, Econometric Society, vol. 71(1), pages 285-317, January.
    43. Francis X. Diebold & Jinyong Hahn & Anthony S. Tay, 1999. "Multivariate Density Forecast Evaluation And Calibration In Financial Risk Management: High-Frequency Returns On Foreign Exchange," The Review of Economics and Statistics, MIT Press, vol. 81(4), pages 661-673, November.
    44. 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.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Veiga, Helena & Ruiz, Esther & González-Rivera, Gloria & Gonçalves Mazzeu, Joao Henrique, 2016. "A Bootstrap Approach for Generalized Autocontour Testing," DES - Working Papers. Statistics and Econometrics. WS 23457, Universidad Carlos III de Madrid. Departamento de Estadística.
    2. Jonas Dovern & Hans Manner, 2020. "Order‐invariant tests for proper calibration of multivariate density forecasts," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 35(4), pages 440-456, June.
    3. Dovern, Jonas & Manner, Hans, 2016. "Robust Evaluation of Multivariate Density Forecasts," VfS Annual Conference 2016 (Augsburg): Demographic Change 145547, Verein für Socialpolitik / German Economic Association.
    4. Dovern, Jonas & Manner, Hans, 2016. "Order Invariant Evaluation of Multivariate Density Forecasts," Working Papers 0608, University of Heidelberg, Department of Economics.
    5. González-Rivera, Gloria & Yoldas, Emre, 2012. "Autocontour-based evaluation of multivariate predictive densities," International Journal of Forecasting, Elsevier, vol. 28(2), pages 328-342.
    6. Rossi, Barbara & Sekhposyan, Tatevik, 2019. "Alternative tests for correct specification of conditional predictive densities," Journal of Econometrics, Elsevier, vol. 208(2), pages 638-657.
    7. Igor L. Kheifets, 2015. "Specification tests for nonlinear dynamic models," Econometrics Journal, Royal Economic Society, vol. 18(1), pages 67-94, February.
    8. González-Rivera, Gloria & Sun, Yingying, 2017. "Density forecast evaluation in unstable environments," International Journal of Forecasting, Elsevier, vol. 33(2), pages 416-432.
    9. Corradi, Valentina & Swanson, Norman R., 2006. "Predictive density and conditional confidence interval accuracy tests," Journal of Econometrics, Elsevier, vol. 135(1-2), pages 187-228.
    10. Polanski, Arnold & Stoja, Evarist, 2012. "Efficient evaluation of multidimensional time-varying density forecasts, with applications to risk management," International Journal of Forecasting, Elsevier, vol. 28(2), pages 343-352.
    11. Polanski, Arnold & Stoja, Evarist & Zhang, Ren, 2013. "Multidimensional risk and risk dependence," Journal of Banking & Finance, Elsevier, vol. 37(8), pages 3286-3294.
    12. Ballestra, Luca Vincenzo & Guizzardi, Andrea & Palladini, Fabio, 2019. "Forecasting and trading on the VIX futures market: A neural network approach based on open to close returns and coincident indicators," International Journal of Forecasting, Elsevier, vol. 35(4), pages 1250-1262.
    13. Corradi, Valentina & Swanson, Norman R., 2006. "Bootstrap conditional distribution tests in the presence of dynamic misspecification," Journal of Econometrics, Elsevier, vol. 133(2), pages 779-806, August.
    14. De Gooijer, Jan G. & Hyndman, Rob J., 2006. "25 years of time series forecasting," International Journal of Forecasting, Elsevier, vol. 22(3), pages 443-473.
    15. Fresoli, Diego & Ruiz, Esther & Pascual, Lorenzo, 2015. "Bootstrap multi-step forecasts of non-Gaussian VAR models," International Journal of Forecasting, Elsevier, vol. 31(3), pages 834-848.
    16. Veiga, Helena & Ruiz, Esther & Gonçalves Mazzeu, Joao Henrique, 2015. "Model uncertainty and the forecast accuracy of ARMA models: A survey," DES - Working Papers. Statistics and Econometrics. WS ws1508, Universidad Carlos III de Madrid. Departamento de Estadística.
    17. Gloria Gonzalez‐Rivera & Yun Luo & Esther Ruiz, 2020. "Prediction regions for interval‐valued time series," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 35(4), pages 373-390, June.
    18. M. Jiménez Gamero, 2014. "On the empirical characteristic function process of the residuals in GARCH models and applications," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 23(2), pages 409-432, June.
    19. Harvey,Andrew C., 2013. "Dynamic Models for Volatility and Heavy Tails," Cambridge Books, Cambridge University Press, number 9781107034723, June.
    20. Cees Diks & Valentyn Panchenko & Dick van Dijk, 2008. "Partial Likelihood-Based Scoring Rules for Evaluating Density Forecasts in Tails," Tinbergen Institute Discussion Papers 08-050/4, Tinbergen Institute.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:taf:emetrv:v:39:y:2020:i:10:p:971-990. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (). General contact details of provider: http://www.tandfonline.com/LECR20 .

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.