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Modeling long-range dependent Gaussian processes with application in continuous-time financial models

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  • Gao, Jiti
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Abstract

This paper considers a class of nonstationary Gaussian processes with possible long-range dependence (LRD) and intermittency. The author proposes a new estimation method to simultaneously estimate both the LRD and intermittency parameter. An application of the proposed estimation method to a continuous-time financial model is discussed.

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File URL: http://mpra.ub.uni-muenchen.de/11973/
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Bibliographic Info

Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 11973.

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Date of creation: 27 May 2002
Date of revision: 18 Sep 2003
Publication status: Published in Journal of Applied probability 2.46(2004): pp. 467-482
Handle: RePEc:pra:mprapa:11973

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Keywords: continuous-time model; diffusion process; long-range dependent process; parameter estimation; stochastic volatility;

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  1. Eckhard Platen, 1999. "An Introduction to Numerical Methods for Stochastic Differential Equations," Research Paper Series, Quantitative Finance Research Centre, University of Technology, Sydney 6, Quantitative Finance Research Centre, University of Technology, Sydney.
  2. Comte, F. & Renault, E., 1996. "Long memory continuous time models," Journal of Econometrics, Elsevier, Elsevier, vol. 73(1), pages 101-149, July.
  3. Robert C. Merton, 1973. "Theory of Rational Option Pricing," Bell Journal of Economics, The RAND Corporation, The RAND Corporation, vol. 4(1), pages 141-183, Spring.
  4. Peter M Robinson, 2001. "The Memory of Stochastic Volatility Models," STICERD - Econometrics Paper Series, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE /2001/410, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
  5. Simon Hurst & Eckhard Platen & Svetlozar Rachev, 1997. "Subordinated Market Index Models: A Comparison," Asia-Pacific Financial Markets, Springer, Springer, vol. 4(2), pages 97-124, May.
  6. Benoit Mandelbrot & Adlai Fisher & Laurent Calvet, 1997. "A Multifractal Model of Asset Returns," Cowles Foundation Discussion Papers, Cowles Foundation for Research in Economics, Yale University 1164, Cowles Foundation for Research in Economics, Yale University.
  7. 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, Elsevier, vol. 1(1), pages 83-106, June.
  8. David Heath & Eckhard Platen, 2002. "A variance reduction technique based on integral representations," Quantitative Finance, Taylor & Francis Journals, Taylor & Francis Journals, vol. 2(5), pages 362-369.
  9. Gao, jiti & Anh, vo & Heyde, christopher, 1999. "Statistical estimation of nonstationaryGaussian processes with long-range dependence and intermittency," MPRA Paper 11972, University Library of Munich, Germany, revised 23 Oct 2001.
  10. Comte, F. & Renault, E., 1996. "Long Memory in Continuous Time Stochastic Volatility Models," Papers, Toulouse - GREMAQ 96.406, Toulouse - GREMAQ.
  11. Heyde, C. C. & Gay, R., 1993. "Smoothed periodogram asymptotics and estimation for processes and fields with possible long-range dependence," Stochastic Processes and their Applications, Elsevier, Elsevier, vol. 45(1), pages 169-182, March.
  12. Vasicek, Oldrich, 1977. "An equilibrium characterization of the term structure," Journal of Financial Economics, Elsevier, Elsevier, vol. 5(2), pages 177-188, November.
  13. Merton, Robert C, 1969. "Lifetime Portfolio Selection under Uncertainty: The Continuous-Time Case," The Review of Economics and Statistics, MIT Press, vol. 51(3), pages 247-57, August.
  14. Ding, Zhuanxin & Granger, Clive W. J., 1996. "Modeling volatility persistence of speculative returns: A new approach," Journal of Econometrics, Elsevier, Elsevier, vol. 73(1), pages 185-215, July.
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