IDEAS home Printed from https://ideas.repec.org/p/pra/mprapa/49344.html
   My bibliography  Save this paper

Estimation and Inference in Univariate and Multivariate Log-GARCH-X Models When the Conditional Density is Unknown

Author

Listed:
  • Sucarrat, Genaro
  • Grønneberg, Steffen
  • Escribano, Alvaro

Abstract

Exponential models of Autoregressive Conditional Heteroscedasticity (ARCH) enable richer dynamics (e.g. contrarian or cyclical), provide greater robustness to jumps and outliers, and guarantee the positivity of volatility. The latter is not guaranteed in ordinary ARCH models, in particular when additional exogenous or predetermined variables ("X") are included in the volatility specification. Here, we propose estimation and inference methods for univariate and multivariate Generalised log-ARCH-X (i.e. log-GARCH-X) models when the conditional density is not known via (V)ARMA-X representations. The multivariate specification allows for volatility feedback across equations, and time-varying correlations can be fitted in a subsequent step. Finally, our empirical applications on electricity prices show that the model-class is particularly useful when the X-vector is high-dimensional.

Suggested Citation

  • Sucarrat, Genaro & Grønneberg, Steffen & Escribano, Alvaro, 2013. "Estimation and Inference in Univariate and Multivariate Log-GARCH-X Models When the Conditional Density is Unknown," MPRA Paper 49344, University Library of Munich, Germany.
  • Handle: RePEc:pra:mprapa:49344
    as

    Download full text from publisher

    File URL: https://mpra.ub.uni-muenchen.de/49344/1/loggarch.pdf
    File Function: original version
    Download Restriction: no

    File URL: https://mpra.ub.uni-muenchen.de/57237/1/loggarch.pdf
    File Function: revised version
    Download Restriction: no

    File URL: https://mpra.ub.uni-muenchen.de/57238/1/MPRA_paper_57238.pdf
    File Function: revised version
    Download Restriction: no

    File URL: https://mpra.ub.uni-muenchen.de/62352/1/MPRA_paper_62352.pdf
    File Function: revised version
    Download Restriction: no

    Other versions of this item:

    References listed on IDEAS

    as
    1. Koopman, Siem Jan & Ooms, Marius & Carnero, M. Angeles, 2007. "Periodic Seasonal Reg-ARFIMAGARCH Models for Daily Electricity Spot Prices," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 16-27, March.
    2. Ling, Shiqing & McAleer, Michael, 2003. "Asymptotic Theory For A Vector Arma-Garch Model," Econometric Theory, Cambridge University Press, vol. 19(02), pages 280-310, April.
    3. Engle, Robert F. & Kroner, Kenneth F., 1995. "Multivariate Simultaneous Generalized ARCH," Econometric Theory, Cambridge University Press, vol. 11(01), pages 122-150, February.
    4. Nelson, Daniel B, 1991. "Conditional Heteroskedasticity in Asset Returns: A New Approach," Econometrica, Econometric Society, vol. 59(2), pages 347-370, March.
    5. Hao Yu, 2007. "High Moment Partial Sum Processes of Residuals in ARMA Models and their Applications," Journal of Time Series Analysis, Wiley Blackwell, vol. 28(1), pages 72-91, January.
    6. Harvey,Andrew C., 2013. "Dynamic Models for Volatility and Heavy Tails," Cambridge Books, Cambridge University Press, number 9781107630024.
    7. Sébastien Laurent & Luc Bauwens & Jeroen V. K. Rombouts, 2006. "Multivariate GARCH models: a survey," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 21(1), pages 79-109.
    8. Hafner, Christian M. & Preminger, Arie, 2009. "Asymptotic Theory For A Factor Garch Model," Econometric Theory, Cambridge University Press, vol. 25(02), pages 336-363, April.
    9. Bauwens, Luc & Sucarrat, Genaro, 2010. "General-to-specific modelling of exchange rate volatility: A forecast evaluation," International Journal of Forecasting, Elsevier, vol. 26(4), pages 885-907, October.
    10. Jeantheau, Thierry, 1998. "Strong Consistency Of Estimators For Multivariate Arch Models," Econometric Theory, Cambridge University Press, vol. 14(01), pages 70-86, February.
    11. Olivier Wintenberger, 2013. "Continuous Invertibility and Stable QML Estimation of the EGARCH(1,1) Model," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 40(4), pages 846-867, December.
    12. Harvey, Andrew C & Shephard, Neil, 1996. "Estimation of an Asymmetric Stochastic Volatility Model for Asset Returns," Journal of Business & Economic Statistics, American Statistical Association, vol. 14(4), pages 429-434, October.
    13. Kawakatsu, Hiroyuki, 2006. "Matrix exponential GARCH," Journal of Econometrics, Elsevier, vol. 134(1), pages 95-128, September.
    14. Lee, Sangyeol, 1997. "A note on the residual empirical process in autoregressive models," Statistics & Probability Letters, Elsevier, vol. 32(4), pages 405-411, April.
    15. repec:imd:wpaper:wp2010-25 is not listed on IDEAS
    16. Luc Bauwens & Christian M. Hafner & Diane Pierret, 2013. "Multivariate Volatility Modeling Of Electricity Futures," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 28(5), pages 743-761, August.
    17. M. Angeles Carnero & Daniel Peña & Esther Ruiz, 2007. "Effects of outliers on the identification and estimation of GARCH models," Journal of Time Series Analysis, Wiley Blackwell, vol. 28(4), pages 471-497, July.
    18. Ibragimov, Rustam & Phillips, Peter C.B., 2008. "Regression Asymptotics Using Martingale Convergence Methods," Econometric Theory, Cambridge University Press, vol. 24(04), pages 888-947, August.
    19. Lumsdaine, Robin L, 1996. "Consistency and Asymptotic Normality of the Quasi-maximum Likelihood Estimator in IGARCH(1,1) and Covariance Stationary GARCH(1,1) Models," Econometrica, Econometric Society, vol. 64(3), pages 575-596, May.
    20. Kristensen Dennis & Rahbek Anders, 2009. "Asymptotics of the QMLE for Non-Linear ARCH Models," Journal of Time Series Econometrics, De Gruyter, vol. 1(1), pages 1-38, April.
    21. Sucarrat, Genaro & Escribano, Alvaro, 2013. "Unbiased QML Estimation of Log-GARCH Models in the Presence of Zero Returns," MPRA Paper 50699, University Library of Munich, Germany.
    22. Zacharias Psaradakis & Elias Tzavalis, 1999. "On regression-based tests for persistence in logarithmic volatility models," Econometric Reviews, Taylor & Francis Journals, vol. 18(4), pages 441-448.
    23. Christian Francq & Genaro Sucarrat, 2018. "An Exponential Chi-Squared QMLE for Log-GARCH Models Via the ARMA Representation," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 16(1), pages 129-154.
    24. Engle, Robert, 2002. "Dynamic Conditional Correlation: A Simple Class of Multivariate Generalized Autoregressive Conditional Heteroskedasticity Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(3), pages 339-350, July.
    25. Francq, Christian & Wintenberger, Olivier & Zakoïan, Jean-Michel, 2013. "GARCH models without positivity constraints: Exponential or log GARCH?," Journal of Econometrics, Elsevier, vol. 177(1), pages 34-46.
    26. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
    27. Harvey, A C, 1976. "Estimating Regression Models with Multiplicative Heteroscedasticity," Econometrica, Econometric Society, vol. 44(3), pages 461-465, May.
    28. Bénédicte Vidaillet & V. D'Estaintot & P. Abécassis, 2005. "Introduction," Post-Print hal-00287137, HAL.
    29. White, Halbert, 1980. "A Heteroskedasticity-Consistent Covariance Matrix Estimator and a Direct Test for Heteroskedasticity," Econometrica, Econometric Society, vol. 48(4), pages 817-838, May.
    30. Genaro Sucarrat & Alvaro Escribano, 2012. "Automated Model Selection in Finance: General-to-Specific Modelling of the Mean and Volatility Specifications," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 74(5), pages 716-735, October.
    31. Engle, Robert F. & Marcucci, Juri, 2006. "A long-run Pure Variance Common Features model for the common volatilities of the Dow Jones," Journal of Econometrics, Elsevier, vol. 132(1), pages 7-42, May.
    32. Comte, F. & Lieberman, O., 2003. "Asymptotic theory for multivariate GARCH processes," Journal of Multivariate Analysis, Elsevier, vol. 84(1), pages 61-84, January.
    33. Christian Francq & Jean-Michel Zakoïan, 2006. "Linear-representation Based Estimation of Stochastic Volatility Models," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 33(4), pages 785-806.
    34. Peter Reinhard Hansen & Zhuo Huang & Howard Howan Shek, 2012. "Realized GARCH: a joint model for returns and realized measures of volatility," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 27(6), pages 877-906, September.
    35. repec:dau:papers:123456789/10571 is not listed on IDEAS
    36. Sucarrat, Genaro & Escribano, Álvaro, 2010. "The power log-GARCH model," UC3M Working papers. Economics we1013, Universidad Carlos III de Madrid. Departamento de Economía.
    37. Francq, Christian & Zakoian, Jean-Michel, 2010. "QML estimation of a class of multivariate GARCH models without moment conditions on the observed process," MPRA Paper 20779, University Library of Munich, Germany.
    38. Weiss, Andrew A., 1986. "Asymptotic Theory for ARCH Models: Estimation and Testing," Econometric Theory, Cambridge University Press, vol. 2(01), pages 107-131, April.
    39. Alvaro Escribano & J. Ignacio Peña & Pablo Villaplana, 2011. "Modelling Electricity Prices: International Evidence," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 73(5), pages 622-650, October.
    40. Francq, Christian & Sucarrat, Genaro, 2015. "Equation-by-Equation Estimation of a Multivariate Log-GARCH-X Model of Financial Returns," MPRA Paper 67140, University Library of Munich, Germany.
    41. Engle, Robert F, 1982. "Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation," Econometrica, Econometric Society, vol. 50(4), pages 987-1007, July.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Christian Francq & Genaro Sucarrat, 2018. "An Exponential Chi-Squared QMLE for Log-GARCH Models Via the ARMA Representation," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 16(1), pages 129-154.
    2. Sucarrat, Genaro & Grønneberg, Steffen, 2016. "Models of Financial Return With Time-Varying Zero Probability," MPRA Paper 68931, University Library of Munich, Germany.
    3. Francq, Christian & Sucarrat, Genaro, 2017. "An equation-by-equation estimator of a multivariate log-GARCH-X model of financial returns," Journal of Multivariate Analysis, Elsevier, vol. 153(C), pages 16-32.
    4. Escribano, Alvaro & Sucarrat, Genaro, 2016. "Equation-by-Equation Estimation of Multivariate Periodic Electricity Price Volatility," MPRA Paper 72736, University Library of Munich, Germany.
    5. Sucarrat, Genaro & Escribano, Álvaro, 2013. "Unbiased QML Estimation of Log-GARCH Models in the Presence of Zero Returns," UC3M Working papers. Economics we1321, Universidad Carlos III de Madrid. Departamento de Economía.
    6. Francq, Christian & Sucarrat, Genaro, 2015. "Equation-by-Equation Estimation of a Multivariate Log-GARCH-X Model of Financial Returns," MPRA Paper 67140, University Library of Munich, Germany.

    More about this item

    Keywords

    ARCH; exponential GARCH; log-GARCH; ARMA-X; Multivariate GARCH;

    JEL classification:

    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models
    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection

    NEP fields

    This paper has been announced in the following NEP Reports:

    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:pra:mprapa:49344. 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: (Joachim Winter) or (Rebekah McClure). General contact details of provider: http://edirc.repec.org/data/vfmunde.html .

    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.