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Semiparametric Analysis of Stationary Fractional Cointegration and the Implied-Realized Volatility Relation in High-Frequency Options Data

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  • Bent Jesper Christensen
  • Morten Ø. Nielsen

    ()
    (Department of Economics, University of Aarhus, Denmark)

Abstract

We consider semiparametric frequency domain analysis of cointegration between long memory processes, i.e. fractional cointegration. This concept allows derivation of useful long-run relations even among stationary long memory processes. The approach uses a degenerating part of the periodogram near the origin to form a frequency domain least squares (FDLS) estimator of the cointegrating relation. The resulting estimator is consistent for arbitrary short-run dynamics, whereas the latter would have to be specified correctly in any parametric approach. We derive the asymptotic distribution theory for the FDLS estimator of the cointegration vector in the stationary long memory case. The new theory requires a general theorem on the asymptotic order of the covariance between the cross-periodograms of stationary long memory processes, which we provide. The motivating example is the relation between the volatility realized in the stock market and the associated implicit volatility derived from option prices. An application to high-frequency U.S. stock index and option data is offered.

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Bibliographic Info

Paper provided by School of Economics and Management, University of Aarhus in its series Economics Working Papers with number 2001-4.

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Length: 35
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Handle: RePEc:aah:aarhec:2001-4

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Web page: http://www.econ.au.dk/afn/

Related research

Keywords: Long Memory; Stationary Fractional Cointegration; Semiparametric Inference; Realized Volatility; High-Frequency Options Data;

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References

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  1. Andersen, Torben G. & Bollerslev, Tim & Diebold, Francis X. & Ebens, Heiko, 2001. "The distribution of realized stock return volatility," Journal of Financial Economics, Elsevier, vol. 61(1), pages 43-76, July.
  2. Juan J. Dolado & Francisco Mármol, 1996. "Efficient Estimation of Cointegrating Relationships Among Higher Order and Fractionally Integrated Processes," Banco de Espa�a Working Papers 9617, Banco de Espa�a.
  3. Lobato, Ignacio N & Velasco, Carlos, 2000. "Long Memory in Stock-Market Trading Volume," Journal of Business & Economic Statistics, American Statistical Association, vol. 18(4), pages 410-27, October.
  4. Marinucci, D. & Robinson, P. M., 2001. "Semiparametric fractional cointegration analysis," Journal of Econometrics, Elsevier, vol. 105(1), pages 225-247, November.
  5. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-54, May-June.
  6. Engle, Robert F & Granger, Clive W J, 1987. "Co-integration and Error Correction: Representation, Estimation, and Testing," Econometrica, Econometric Society, vol. 55(2), pages 251-76, March.
  7. Carlos Velasco, 2003. "Gaussian Semi-parametric Estimation of Fractional Cointegration," Journal of Time Series Analysis, Wiley Blackwell, vol. 24(3), pages 345-378, 05.
  8. Cheung, Yin-Wong & Lai, Kon S, 1993. "A Fractional Cointegration Analysis of Purchasing Power Parity," Journal of Business & Economic Statistics, American Statistical Association, vol. 11(1), pages 103-12, January.
  9. 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.
  10. Juan J. Dolado & Francisco Mármol, 1996. "Efficient Estimation of Cointegrating Relationships Among Higher Order and Fractionally Integrated Processes," Banco de Espa�a Working Papers 9617, Banco de Espa�a.
  11. 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.
  12. Katsumi Shimotsu & Peter C.B. Phillips, 2002. "Exact Local Whittle Estimation of Fractional Integration," Economics Discussion Papers 535, University of Essex, Department of Economics.
  13. Christensen, B. J. & Prabhala, N. R., 1998. "The relation between implied and realized volatility," Journal of Financial Economics, Elsevier, vol. 50(2), pages 125-150, November.
  14. Granger, C. W. J., 1981. "Some properties of time series data and their use in econometric model specification," Journal of Econometrics, Elsevier, vol. 16(1), pages 121-130, May.
  15. Lobato, I. & Robinson, P. M., 1996. "Averaged periodogram estimation of long memory," Journal of Econometrics, Elsevier, vol. 73(1), pages 303-324, July.
  16. D Marinucci & Peter M. Robinson, 2001. "Semiparametric fractional cointegration analysis," LSE Research Online Documents on Economics 2269, London School of Economics and Political Science, LSE Library.
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Citations

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Cited by:
  1. Federico Carlini & Paolo Santucci de Magistris, 2013. "On the identification of fractionally cointegrated VAR models with the F(d) condition," CREATES Research Papers 2013-44, School of Economics and Management, University of Aarhus.
  2. Eduardo Rossi & Paolo Santucci de Magistris, 2009. "A No Arbitrage Fractional Cointegration Analysis Of The Range Based Volatility," CREATES Research Papers 2009-31, School of Economics and Management, University of Aarhus.
  3. Javier Hualde & Peter M Robinson, 2006. "Semiparametric Estimation of Fractional Cointegration," STICERD - Econometrics Paper Series /2006/502, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
  4. Hualde, J. & Robinson, P.M., 2007. "Root-n-consistent estimation of weak fractional cointegration," Journal of Econometrics, Elsevier, vol. 140(2), pages 450-484, October.
  5. Javier Hualde & Peter M. Robinson, 2006. "Semiparametric Estimation of Fractional Cointegration," LSE Research Online Documents on Economics 4537, London School of Economics and Political Science, LSE Library.

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