IDEAS home Printed from https://ideas.repec.org/p/ems/eureir/7028.html
   My bibliography  Save this paper

A simple test for GARCH against a stochastic volatility

Author

Listed:
  • Franses, Ph.H.B.F.
  • van der Leij, M.J.
  • Paap, R.

Abstract

The GARCH model and the Stochastic Volatility [SV] model are competing but non-nested models to describe unobserved volatility in asset returns. We propose a GARCH model with an additional error term, which can capture SV model properties, and which can be used to test GARCH against SV. We discuss model representation, parameter estimation and a simple test for model selection. Furthermore, we derive the theoretical moments and the autocorrelation function of our new model. We illustrate its merits for 9 daily stock return series.

Suggested Citation

  • Franses, Ph.H.B.F. & van der Leij, M.J. & Paap, R., 2005. "A simple test for GARCH against a stochastic volatility," Econometric Institute Research Papers EI 2005-41, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    • Handle: RePEc:ems:eureir:7028
    as

    Download full text from publisher

    File URL: https://repub.eur.nl/pub/7028/ei2005-41.pdf
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Danielsson, Jon, 1994. "Stochastic volatility in asset prices estimation with simulated maximum likelihood," Journal of Econometrics, Elsevier, vol. 64(1-2), pages 375-400.
    2. Sangjoon Kim & Neil Shephard & Siddhartha Chib, 1998. "Stochastic Volatility: Likelihood Inference and Comparison with ARCH Models," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 65(3), pages 361-393.
    3. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
    4. Jeff Fleming & Chris Kirby, 2003. "A Closer Look at the Relation between GARCH and Stochastic Autoregressive Volatility," Journal of Financial Econometrics, Oxford University Press, vol. 1(3), pages 365-419.
    5. 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.
    6. Wolak, Frank A., 1989. "Local and Global Testing of Linear and Nonlinear Inequality Constraints in Nonlinear Econometric Models," Econometric Theory, Cambridge University Press, vol. 5(1), pages 1-35, April.
    7. Wolak, Frank A., 1989. "Testing inequality constraints in linear econometric models," Journal of Econometrics, Elsevier, vol. 41(2), pages 205-235, 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. Andersen, Torben G. & Bollerslev, Tim & Christoffersen, Peter F. & Diebold, Francis X., 2005. "Volatility forecasting," CFS Working Paper Series 2005/08, Center for Financial Studies (CFS).
    2. Jean Pierre Fernández Prada Saucedo & Gabriel Rodríguez, 2020. "Modeling the Volatility of Returns on Commodities: An Application and Empirical Comparison of GARCH and SV Models," Documentos de Trabajo / Working Papers 2020-484, Departamento de Economía - Pontificia Universidad Católica del Perú.
    3. Andersen, Torben G. & Bollerslev, Tim & Christoffersen, Peter F. & Diebold, Francis X., 2006. "Volatility and Correlation Forecasting," Handbook of Economic Forecasting, in: G. Elliott & C. Granger & A. Timmermann (ed.), Handbook of Economic Forecasting, edition 1, volume 1, chapter 15, pages 777-878, Elsevier.
    4. Pezzo, Rosanna & Uberti, Mariacristina, 2006. "Approaches to forecasting volatility: Models and their performances for emerging equity markets," Chaos, Solitons & Fractals, Elsevier, vol. 29(3), pages 556-565.
    5. Demos, Antonis & Sentana, Enrique, 1998. "Testing for GARCH effects: a one-sided approach," Journal of Econometrics, Elsevier, vol. 86(1), pages 97-127, June.
    6. Yu, Jun & Yang, Zhenlin & Zhang, Xibin, 2006. "A class of nonlinear stochastic volatility models and its implications for pricing currency options," Computational Statistics & Data Analysis, Elsevier, vol. 51(4), pages 2218-2231, December.
    7. Danielsson, Jon, 1998. "Multivariate stochastic volatility models: Estimation and a comparison with VGARCH models," Journal of Empirical Finance, Elsevier, vol. 5(2), pages 155-173, June.
    8. Massimiliano Caporin & Michael McAleer, 2010. "Model Selection and Testing of Conditional and Stochastic Volatility Models," KIER Working Papers 724, Kyoto University, Institute of Economic Research.
    9. BAUWENS, Luc & HAFNER, Christian & LAURENT, Sébastien, 2011. "Volatility models," LIDAM Discussion Papers CORE 2011058, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
      • Bauwens, L. & Hafner C. & Laurent, S., 2011. "Volatility Models," LIDAM Discussion Papers ISBA 2011044, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
      • Bauwens, L. & Hafner, C. & Laurent, S., 2012. "Volatility Models," LIDAM Reprints ISBA 2012028, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    10. M. Hakan Eratalay, 2016. "Estimation of Multivariate Stochastic Volatility Models: A Comparative Monte Carlo Study," International Econometric Review (IER), Econometric Research Association, vol. 8(2), pages 19-52, September.
    11. Fałdziński, Marcin & Fiszeder, Piotr & Molnár, Peter, 2024. "Improving volatility forecasts: Evidence from range-based models," The North American Journal of Economics and Finance, Elsevier, vol. 69(PB).
    12. M. Hakan Eratalay, 2016. "Estimation of Multivariate Stochastic Volatility Models: A Comparative Monte Carlo Study," International Econometric Review (IER), Econometric Research Association, vol. 8(2), pages 19-52, September.
    13. Dinghai Xu & Yuying Li, 2010. "Empirical Evidence of the Leverage Effect in a Stochastic Volatility Model: A Realized Volatility Approach," Working Papers 1002, University of Waterloo, Department of Economics, revised May 2010.
    14. Mehmet Balcilar & Zeynel Abidin Ozdemir, 2020. "A re-examination of growth and growth uncertainty relationship in a stochastic volatility in the mean model with time-varying parameters," Empirica, Springer;Austrian Institute for Economic Research;Austrian Economic Association, vol. 47(3), pages 611-641, August.
    15. Francq, Christian & Zakoïan, Jean-Michel, 2009. "Testing the Nullity of GARCH Coefficients: Correction of the Standard Tests and Relative Efficiency Comparisons," Journal of the American Statistical Association, American Statistical Association, vol. 104(485), pages 313-324.
    16. Font, Begoña, 1998. "Modelización de series temporales financieras. Una recopilación," DES - Documentos de Trabajo. Estadística y Econometría. DS 3664, Universidad Carlos III de Madrid. Departamento de Estadística.
    17. G. Dhaene, 2004. "Indirect Inference for Stochastic Volatility Models via the Log-Squared Observations," Review of Business and Economic Literature, KU Leuven, Faculty of Economics and Business (FEB), Review of Business and Economic Literature, vol. 0(3), pages 421-440.
    18. So, Mike K.P. & Choi, C.Y., 2008. "A multivariate threshold stochastic volatility model," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 79(3), pages 306-317.
    19. Masahito Kobayashi & Xiuhong Shi, 2005. "Testing for EGARCH Against Stochastic Volatility Models," Journal of Time Series Analysis, Wiley Blackwell, vol. 26(1), pages 135-150, January.
    20. Andersen, Torben G. & Chung, Hyung-Jin & Sorensen, Bent E., 1999. "Efficient method of moments estimation of a stochastic volatility model: A Monte Carlo study," Journal of Econometrics, Elsevier, vol. 91(1), pages 61-87, July.

    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:ems:eureir:7028. See general information about how to correct material in RePEc.

    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 bibliographic 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.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: RePub (email available below). General contact details of provider: https://edirc.repec.org/data/feeurnl.html .

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

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.