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Bivariate FIGARCH and fractional cointegration

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  • Brunetti, Celso
  • Gilbert, Christopher L.

Abstract

We consider the modelling of volatility on closely related markets. Univariate fractional volatility (FIGARCH) models are now standard, as are multivariate GARCH models. In this paper we adopt a combination of the two methodologies. There is as yet little consensus on the methodology for testing for fractional cointegration. The contribution of this paper is to demonstrate the feasibility of estimating and testing cointegrated bivariate FIGARCH models. We apply these methods to volatility on the NYMEX and IPE crude oil markets. We find a common order of fractional integration for the two volatility processes and confirm that they are fractionally cointegrated. An estimated error correction FIGARCH model indicates that the preponderant adjustment is of the IPE towards NYMEX.
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  • Brunetti, Celso & Gilbert, Christopher L., 2000. "Bivariate FIGARCH and fractional cointegration," Journal of Empirical Finance, Elsevier, vol. 7(5), pages 509-530, December.
    • Handle: RePEc:eee:empfin:v:7:y:2000:i:5:p:509-530
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    1. Cheung, Yin-Wong & Ng, Lilian K., 1996. "A causality-in-variance test and its application to financial market prices," Journal of Econometrics, Elsevier, vol. 72(1-2), pages 33-48.
    2. Sowell, Fallaw, 1992. "Maximum likelihood estimation of stationary univariate fractionally integrated time series models," Journal of Econometrics, Elsevier, vol. 53(1-3), pages 165-188.
    3. Marco Corazza & A.G. Malliaris & Carla Nardelli, 1997. "Searching for fractal structure in agricultural futures markets," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 17(4), pages 433-473, June.
    4. Baillie, Richard T & Bollerslev, Tim, 1994. "The long memory of the forward premium," Journal of International Money and Finance, Elsevier, vol. 13(5), pages 565-571, October.
    5. Engle, Robert & Granger, Clive, 2015. "Co-integration and error correction: Representation, estimation, and testing," Applied Econometrics, Russian Presidential Academy of National Economy and Public Administration (RANEPA), vol. 39(3), pages 106-135.
    6. G. Teyssière, 1996. "Double Long-Memory Financial Time Series," Working Papers 348, Queen Mary University of London, School of Economics and Finance.
    7. Engle, Robert F. & Kroner, Kenneth F., 1995. "Multivariate Simultaneous Generalized ARCH," Econometric Theory, Cambridge University Press, vol. 11(1), pages 122-150, February.
    8. C. W. J. Granger & Zhuanxin Ding, 1995. "Some Properties of Absolute Return: An Alternative Measure of Risk," Annals of Economics and Statistics, GENES, issue 40, pages 67-91.
    9. 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.
    10. 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.
    11. 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.
    12. 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.
    13. Karim M. Abadir & A. M. Robert Taylor, 1999. "On the Definitions of (Co‐)integration," Journal of Time Series Analysis, Wiley Blackwell, vol. 20(2), pages 129-137, March.
    14. Michael Dueker & Richard Startz, 1998. "Maximum-Likelihood Estimation Of Fractional Cointegration With An Application To U.S. And Canadian Bond Rates," The Review of Economics and Statistics, MIT Press, vol. 80(3), pages 420-426, August.
    15. Marinucci, D & Robinson, Peter M., 1998. "Semiparametric frequency domain analysis of fractional cointegration," LSE Research Online Documents on Economics 2258, London School of Economics and Political Science, LSE Library.
    16. Andersen, Torben G & Bollerslev, Tim, 1997. "Heterogeneous Information Arrivals and Return Volatility Dynamics: Uncovering the Long-Run in High Frequency Returns," Journal of Finance, American Finance Association, vol. 52(3), pages 975-1005, July.
    17. Ding, Zhuanxin & Granger, Clive W. J., 1996. "Modeling volatility persistence of speculative returns: A new approach," Journal of Econometrics, Elsevier, vol. 73(1), pages 185-215, July.
    18. Lobato, Ignacio N., 1999. "A semiparametric two-step estimator in a multivariate long memory model," Journal of Econometrics, Elsevier, vol. 90(1), pages 129-153, May.
    19. Baillie, Richard T., 1996. "Long memory processes and fractional integration in econometrics," Journal of Econometrics, Elsevier, vol. 73(1), pages 5-59, July.
    20. Goodhart, Charles A. E. & O'Hara, Maureen, 1997. "High frequency data in financial markets: Issues and applications," Journal of Empirical Finance, Elsevier, vol. 4(2-3), pages 73-114, June.
    21. Baillie, Richard T & Bollerslev, Tim, 1994. "Cointegration, Fractional Cointegration, and Exchange Rate Dynamics," Journal of Finance, American Finance Association, vol. 49(2), pages 737-745, June.
    22. Anning Wei & Raymond M. Leuthold, 1998. "Long Agricultural Futures Prices: ARCH, Long Memory, or Chaos Processes?," Finance 9805001, University Library of Munich, Germany.
    23. Lamoureux, Christopher G & Lastrapes, William D, 1990. "Persistence in Variance, Structural Change, and the GARCH Model," Journal of Business & Economic Statistics, American Statistical Association, vol. 8(2), pages 225-234, April.
    24. 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.
    25. C. Brunetti & C.L. Gilbert, 1998. "A Bivariate FIGARCH Model of Crude Oil Price Volatility," Working Papers 390, Queen Mary University of London, School of Economics and Finance.
    26. Granger, Clive W J, 1986. "Developments in the Study of Cointegrated Economic Variables," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 48(3), pages 213-228, August.
    27. repec:adr:anecst:y:1995:i:40:p:04 is not listed on IDEAS
    28. Bollerslev, Tim, 1990. "Modelling the Coherence in Short-run Nominal Exchange Rates: A Multivariate Generalized ARCH Model," The Review of Economics and Statistics, MIT Press, vol. 72(3), pages 498-505, August.
    29. Johansen, Soren, 1988. "Statistical analysis of cointegration vectors," Journal of Economic Dynamics and Control, Elsevier, vol. 12(2-3), pages 231-254.
    30. C. W. J. Granger & Roselyne Joyeux, 1980. "An Introduction To Long‐Memory Time Series Models And Fractional Differencing," Journal of Time Series Analysis, Wiley Blackwell, vol. 1(1), pages 15-29, January.
    31. Wright, Jonathan H., 1999. "A new estimator of the fractionally integrated stochastic volatility model," Economics Letters, Elsevier, vol. 63(3), pages 295-303, June.
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    More about this item

    JEL classification:

    • G0 - Financial Economics - - General
    • C2 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables
    • C3 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables

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