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

  • Bent Jesper Christensen
  • Morten Ø. Nielsen

    ()

    (Department of Economics, University of Aarhus, Denmark)

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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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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Handle: RePEc:aah:aarhec:2001-4
Contact details of provider: Web page: http://www.econ.au.dk/afn/

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  8. Baillie, Richard T & Bollerslev, Tim, 1994. " Cointegration, Fractional Cointegration, and Exchange Rate Dynamics," Journal of Finance, American Finance Association, vol. 49(2), pages 737-45, June.
  9. D Marinucci & Peter Robinson, 2001. "Narrow-band analysis of nonstationary processes," LSE Research Online Documents on Economics 2015, London School of Economics and Political Science, LSE Library.
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  11. 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.
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  16. 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.
  17. 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.
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  22. Marinucci, D. & Robinson, P. M., 2001. "Semiparametric fractional cointegration analysis," Journal of Econometrics, Elsevier, vol. 105(1), pages 225-247, November.
  23. 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.
  24. Chen, Willa W. & Hurvich, Clifford M., 2003. "Semiparametric Estimation of Multivariate Fractional Cointegration," Journal of the American Statistical Association, American Statistical Association, vol. 98, pages 629-642, January.
  25. D. Marinucci & Peter M. Robinson, 2001. "Narrow-band analysis of nonstationary processes," LSE Research Online Documents on Economics 303, London School of Economics and Political Science, LSE Library.
  26. Andersen T. G & Bollerslev T. & Diebold F. X & Labys P., 2001. "The Distribution of Realized Exchange Rate Volatility," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 42-55, March.
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