IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v362y2006i2p450-464.html
   My bibliography  Save this article

A multivariate long memory stochastic volatility model

Author

Listed:
  • So, Mike K.P.
  • Kwok, Susanna W.Y.

Abstract

This paper develops a multivariate long-memory stochastic volatility model which allows the multi-asset long-range dependence in the volatility process. The motivation is from the fact that both autocorrelations and cross-correlations of some proxies of exchange rate volatility exhibit strong evidence of long-memory behavior. The statistical properties of the new stochastic volatility model provide theoretical explanation to the common findings that long memory volatility properties are more apparent if we use absolute return as a volatility proxy than squared return. Results of the real data application show that our model outperforms an existing multivariate stochastic volatility model.

Suggested Citation

  • So, Mike K.P. & Kwok, Susanna W.Y., 2006. "A multivariate long memory stochastic volatility model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 362(2), pages 450-464.
    • Handle: RePEc:eee:phsmap:v:362:y:2006:i:2:p:450-464
    DOI: 10.1016/j.physa.2005.08.078
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378437105010034
    Download Restriction: Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000
    File URL: https://libkey.io/10.1016/j.physa.2005.08.078?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

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

    References listed on IDEAS

    as
    1. Mike So, 2000. "Long-term memory in stock market volatility," Applied Financial Economics, Taylor & Francis Journals, vol. 10(5), pages 519-524.
    2. Ghysels, E. & Harvey, A. & Renault, E., 1995. "Stochastic Volatility," Papers 95.400, Toulouse - GREMAQ.
    3. Stephen J. Taylor, 1994. "Modeling Stochastic Volatility: A Review And Comparative Study," Mathematical Finance, Wiley Blackwell, vol. 4(2), pages 183-204, April.
    4. 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.
    5. 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.
    6. Cheung, Yin-Wong & Diebold, Francis X., 1994. "On maximum likelihood estimation of the differencing parameter of fractionally-integrated noise with unknown mean," Journal of Econometrics, Elsevier, vol. 62(2), pages 301-316, June.
    7. Mike K.P. So & K. Lam & W.K. Li, 1997. "An Empirical Study of Volatility in Seven Southeast Asian Stock Markets Using ARV Models," Journal of Business Finance & Accounting, Wiley Blackwell, vol. 24(2), pages 261-276.
    8. Ding, Zhuanxin & Granger, Clive W. J. & Engle, Robert F., 1993. "A long memory property of stock market returns and a new model," Journal of Empirical Finance, Elsevier, vol. 1(1), pages 83-106, June.
    9. Bollerslev, Tim & Ole Mikkelsen, Hans, 1996. "Modeling and pricing long memory in stock market volatility," Journal of Econometrics, Elsevier, vol. 73(1), pages 151-184, July.
    10. Andrew Harvey & Esther Ruiz & Neil Shephard, 1994. "Multivariate Stochastic Variance Models," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 61(2), pages 247-264.
    11. Mike K.P. So & K. Lam & W.K. Li, 1997. "An Empirical Study of Volatility in Seven Southeast Asian Stock Markets Using ARV Models," Journal of Business Finance & Accounting, Wiley Blackwell, vol. 24(2), pages 261-276, March.
    12. Mike K. P. So & W. K. Li & K. Lam, 1997. "Multivariate modelling of the autoregressive random variance process," Journal of Time Series Analysis, Wiley Blackwell, vol. 18(4), pages 429-446, July.
    13. 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.
    14. Breidt, F. Jay & Crato, Nuno & de Lima, Pedro, 1998. "The detection and estimation of long memory in stochastic volatility," Journal of Econometrics, Elsevier, vol. 83(1-2), pages 325-348.
    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. Viviana Fernandez & Brian M Lucey, 2006. "Portfolio management implications of volatility shifts: Evidence from simulated data," Documentos de Trabajo 219, Centro de Economía Aplicada, Universidad de Chile.
    2. G. Mesters & S. J. Koopman & M. Ooms, 2016. "Monte Carlo Maximum Likelihood Estimation for Generalized Long-Memory Time Series Models," Econometric Reviews, Taylor & Francis Journals, vol. 35(4), pages 659-687, April.
    3. Asai, Manabu & McAleer, Michael, 2015. "Forecasting co-volatilities via factor models with asymmetry and long memory in realized covariance," Journal of Econometrics, Elsevier, vol. 189(2), pages 251-262.
    4. Fernandez, Viviana & Lucey, Brian M., 2007. "Portfolio management under sudden changes in volatility and heterogeneous investment horizons," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 375(2), pages 612-624.
    5. Benjamin Poignard & Manabu Asai, 2023. "High‐dimensional sparse multivariate stochastic volatility models," Journal of Time Series Analysis, Wiley Blackwell, vol. 44(1), pages 4-22, January.
    6. Mike K. P. So & C. Y. Choi, 2009. "A threshold factor multivariate stochastic volatility model," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 28(8), pages 712-735.
    7. Dark, Jonathan, 2018. "Multivariate models with long memory dependence in conditional correlation and volatility," Journal of Empirical Finance, Elsevier, vol. 48(C), pages 162-180.
    8. Aida Karmous & Heni Boubaker & Lotfi Belkacem, 2021. "Forecasting Volatility for an Optimal Portfolio with Stylized Facts Using Copulas," Computational Economics, Springer;Society for Computational Economics, vol. 58(2), pages 461-482, August.
    9. 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.
    10. Manabu Asai & Michael McAleer & Jun Yu, 2006. "Multivariate Stochastic Volatility," Microeconomics Working Papers 22058, East Asian Bureau of Economic Research.
    11. Siddhartha Chib & Yasuhiro Omori & Manabu Asai, 2007. "Multivariate stochastic volatility (Revised in May 2007, Handbook of Financial Time Series (Published in "Handbook of Financial Time Series" (eds T.G. Andersen, R.A. Davis, Jens-Peter Kreiss," CARF F-Series CARF-F-094, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo.
    12. Wei, Yu, 2012. "Forecasting volatility of fuel oil futures in China: GARCH-type, SV or realized volatility models?," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(22), pages 5546-5556.
    13. Asai, Manabu & Chang, Chia-Lin & McAleer, Michael, 2022. "Realized matrix-exponential stochastic volatility with asymmetry, long memory and higher-moment spillovers," Journal of Econometrics, Elsevier, vol. 227(1), pages 285-304.

    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. Ghysels, E. & Harvey, A. & Renault, E., 1995. "Stochastic Volatility," Papers 95.400, Toulouse - GREMAQ.
    2. Ana Pérez & Esther Ruiz, 2002. "Modelos de memoria larga para series económicas y financieras," Investigaciones Economicas, Fundación SEPI, vol. 26(3), pages 395-445, September.
    3. Perez, Ana & Ruiz, Esther, 2001. "Finite sample properties of a QML estimator of stochastic volatility models with long memory," Economics Letters, Elsevier, vol. 70(2), pages 157-164, February.
    4. Arteche, Josu, 2004. "Gaussian semiparametric estimation in long memory in stochastic volatility and signal plus noise models," Journal of Econometrics, Elsevier, vol. 119(1), pages 131-154, March.
    5. Carmen Broto & Esther Ruiz, 2004. "Estimation methods for stochastic volatility models: a survey," Journal of Economic Surveys, Wiley Blackwell, vol. 18(5), pages 613-649, December.
    6. Breidt, F. Jay & Crato, Nuno & de Lima, Pedro, 1998. "The detection and estimation of long memory in stochastic volatility," Journal of Econometrics, Elsevier, vol. 83(1-2), pages 325-348.
    7. Per Frederiksen & Morten Orregaard Nielsen, 2008. "Bias-Reduced Estimation of Long-Memory Stochastic Volatility," Journal of Financial Econometrics, Oxford University Press, vol. 6(4), pages 496-512, Fall.
    8. Bollerslev, Tim & Ole Mikkelsen, Hans, 1999. "Long-term equity anticipation securities and stock market volatility dynamics," Journal of Econometrics, Elsevier, vol. 92(1), pages 75-99, September.
    9. Thomas Mikosch, 2004. "Is it really long memory we see in financial returns?," Econometrics 0412002, University Library of Munich, Germany.
    10. Veiga, Helena, 2006. "A two factor long memory stochastic volatility model," DES - Working Papers. Statistics and Econometrics. WS ws061303, Universidad Carlos III de Madrid. Departamento de Estadística.
    11. Nigel Wilkins, 2004. "Indirect Estimation of Long Memory Volatility Models," Econometric Society 2004 Far Eastern Meetings 459, Econometric Society.
    12. Nuno Cassola & Claudio Morana, 2006. "Volatility of interest rates in the euro area: Evidence from high frequency data," The European Journal of Finance, Taylor & Francis Journals, vol. 12(6-7), pages 513-528.
    13. Ruiz, Esther & Veiga, Helena, 2008. "Modelling long-memory volatilities with leverage effect: A-LMSV versus FIEGARCH," Computational Statistics & Data Analysis, Elsevier, vol. 52(6), pages 2846-2862, February.
    14. Yuanhua Feng & Jan Beran & Sebastian Letmathe & Sucharita Ghosh, 2020. "Fractionally integrated Log-GARCH with application to value at risk and expected shortfall," Working Papers CIE 137, Paderborn University, CIE Center for International Economics.
    15. Brunetti, Celso & Gilbert, Christopher L., 2000. "Bivariate FIGARCH and fractional cointegration," Journal of Empirical Finance, Elsevier, vol. 7(5), pages 509-530, December.
    16. Liesenfeld, Roman, 2001. "A generalized bivariate mixture model for stock price volatility and trading volume," Journal of Econometrics, Elsevier, vol. 104(1), pages 141-178, August.
    17. Jonathan Wright, 2002. "Log-Periodogram Estimation Of Long Memory Volatility Dependencies With Conditionally Heavy Tailed Returns," Econometric Reviews, Taylor & Francis Journals, vol. 21(4), pages 397-417.
    18. Alexander Subbotin & Thierry Chauveau & Kateryna Shapovalova, 2009. "Volatility Models: from GARCH to Multi-Horizon Cascades," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00390636, HAL.
    19. Pedro J. F. de Lima & Michelle L. Barnes, 2000. "Modeling Financial Volatility: Extreme Observations, Nonlinearities and Nonstationarities," School of Economics and Public Policy Working Papers 2000-05, University of Adelaide, School of Economics and Public Policy.

    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:eee:phsmap:v:362:y:2006:i:2:p:450-464. 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: Catherine Liu (email available below). General contact details of provider: http://www.journals.elsevier.com/physica-a-statistical-mechpplications/ .

    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.