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Estimation and Testing of Stochastic Variance Models

Author

Listed:
  • Andrew C Harvey
  • N.G. Shephard

Abstract

A stochastic variance model may be estimated by quasi-maximum likelihood procedure by transforming to a linear state space form. The properties of observations corrected for heteroscedasticity can be derived. A model with explanatory variables can be handled by correcting the observations for heteroscedasticity after estimating a stochastic variance model from the OLS residuals and then constructing a feasible GLS estimator. A model with stochastic variance, or standard deviation, as an explanatory variable can also be formulated. The paper explores the properties of these procedures and shows how they may be used as part of a model specification strategy/ It is argued that the approach is relatively robust since distributions need not be specified for the disturbances.

Suggested Citation

  • Andrew C Harvey & N.G. Shephard, 1993. "Estimation and Testing of Stochastic Variance Models," STICERD - Econometrics Paper Series 268, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
    • Handle: RePEc:cep:stiecm:268
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    Citations

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    Cited by:

    1. Ghysels, E. & Harvey, A. & Renault, E., 1995. "Stochastic Volatility," Papers 95.400, Toulouse - GREMAQ.
    2. J. I. Pena & E. Ruiz, 1995. "Stock market regulations and international financial integration: the case of Spain," The European Journal of Finance, Taylor & Francis Journals, vol. 1(4), pages 367-382.
    3. Paolo Girardello & Orietta Nicolis & Giovanni Tondini, 2003. "Comparing Conditional Variance Models: Theory and Empirical Evidence," Multinational Finance Journal, Multinational Finance Journal, vol. 7(3-4), pages 177-206, September.
    4. Hwang, Soosung & Satchell, Stephen E., 2000. "Market risk and the concept of fundamental volatility: Measuring volatility across asset and derivative markets and testing for the impact of derivatives markets on financial markets," Journal of Banking & Finance, Elsevier, vol. 24(5), pages 759-785, May.
    5. Francis E. Warnock & Veronica C. Warnock, 2000. "The declining volatility of U.S. employment: was Arthur Burns right?," International Finance Discussion Papers 677, Board of Governors of the Federal Reserve System (U.S.).
    6. Tsyplakov, Alexander, 2010. "Revealing the arcane: an introduction to the art of stochastic volatility models," MPRA Paper 25511, University Library of Munich, Germany.
    7. Ramaprasad Bhar & Damien Lee, 2018. "Alternative characterization of volatility of short-term interest rate," International Journal of Financial Engineering (IJFE), World Scientific Publishing Co. Pte. Ltd., vol. 5(02), pages 1-15, June.
    8. Sandmann, Gleb & Koopman, Siem Jan, 1998. "Estimation of stochastic volatility models via Monte Carlo maximum likelihood," Journal of Econometrics, Elsevier, vol. 87(2), pages 271-301, September.
    9. Pedro L. Valls Pereira, 2004. "How Persistent is Volatility? An Answer with Stochastic Volatility Models with Markov Regime Switching State Equations," Finance Lab Working Papers flwp_59, Finance Lab, Insper Instituto de Ensino e Pesquisa.
    10. Alexander Tsyplakov, 2010. "Revealing the arcane: an introduction to the art of stochastic volatility models (in Russian)," Quantile, Quantile, issue 8, pages 69-122, July.
    11. Yueh-Neng Lin & Ken Hung, 2008. "Is Volatility Priced?," Annals of Economics and Finance, Society for AEF, vol. 9(1), pages 39-75, May.
    12. 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.
    13. Francis X. Diebold & Jose A. Lopez, 1995. "Measuring Volatility Dynamics," NBER Technical Working Papers 0173, National Bureau of Economic Research, Inc.
    14. P. Girardello & Orietta Nicolis & Giovanni Tondini, 2002. "Comparing conditional variance models: Theory and empirical evidence," Departmental Working Papers 2002-08, Department of Economics, Management and Quantitative Methods at Università degli Studi di Milano.
    15. Alin Sima, 2008. "Stylized Facts and Discrete Stochastic Volatility Models," Advances in Economic and Financial Research - DOFIN Working Paper Series 10, Bucharest University of Economics, Center for Advanced Research in Finance and Banking - CARFIB.
    16. Ramaprasad Bhar, 2010. "Stochastic Filtering with Applications in Finance," World Scientific Books, World Scientific Publishing Co. Pte. Ltd., number 7736, January.
    17. Bjorn Hansson & Peter Hordahl, 2005. "Forecasting variance using stochastic volatility and GARCH," The European Journal of Finance, Taylor & Francis Journals, vol. 11(1), pages 33-57.
    18. Alejandro Islas Camargo & Francisco Venegas Martínez, 2003. "Pricing Derivatives Securities with Prior Information on Long- Memory Volatility," Economía Mexicana NUEVA ÉPOCA, CIDE, División de Economía, vol. 0(1), pages 103-134, January-J.
    19. Grané, A. & Veiga, H., 2008. "Accurate minimum capital risk requirements: A comparison of several approaches," Journal of Banking & Finance, Elsevier, vol. 32(11), pages 2482-2492, November.
    20. Mike So & K. Lam & W. K. Li, 1999. "Forecasting exchange rate volatility using autoregressive random variance model," Applied Financial Economics, Taylor & Francis Journals, vol. 9(6), pages 583-591.
    21. G Sandmann & Siem Jan Koopman, 1996. "Maximum Likelihood Estimation of Stochastic Volatility Models," FMG Discussion Papers dp248, Financial Markets Group.
    22. Baillie, Richard T. & Bollerslev, Tim & Mikkelsen, Hans Ole, 1996. "Fractionally integrated generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 74(1), pages 3-30, September.
    23. Ronald Mahieu & Peter C. Schotman, 1994. "Stochastic volatility and the distribution of exchange rate news," Discussion Paper / Institute for Empirical Macroeconomics 96, Federal Reserve Bank of Minneapolis.
    24. Ester Ruiz & Fernando Lorenzo, 1998. "The relation between the level and uncertainty of inflation," Documentos de Trabajo (working papers) 0698, Department of Economics - dECON.

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