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Simulation of Gegenbauer processes using wavelet packets

  • Collet J.J.
  • Fadili J.M.

    (School of Economics and Finance, Queensland University of Technology)

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    In this paper, we propose to study the synthesis of Gegenbauer processes using the wavelet packets transform. In order to simulate 1-factor Gegenbauer process, we introduce an original algorithm, inspired by the one proposed by Coifman and Wickerhauser [CW92], to adaptively search for the best-ortho-basis in the wavelet packet library where the covariance matrix of the transformed process is nearly diagonal. Our method clearly outperforms the one recently proposed by [Whi01], is very fast, does not depend on the wavelet choice, and is not very sensitive to the length of the time series. From these first results we propose an algorithm to build bases to simulate k-factor Gegenbauer processes. Given the simplicity of programming and running, we feel the general practitioner will be attracted to our simulator. Finally we evaluate the approximation due to the fact that we consider the wavelet packet coeficients as uncorrelated. An empirical study is carried out which supports our results.

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    File URL: http://external-apps.qut.edu.au/business/documents/discussionPapers/2005/No%20190%20-%20Collet%20Document%20Only.pdf
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    Paper provided by School of Economics and Finance, Queensland University of Technology in its series School of Economics and Finance Discussion Papers and Working Papers Series with number 190.

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    Date of creation: 15 Jun 2005
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    Handle: RePEc:qut:dpaper:190
    Contact details of provider: Postal: GPO Box 2434, BRISBANE QLD 4001
    Web page: http://www.bus.qut.edu.au/faculty/economics/
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    1. Jensen, Mark J., 2000. "An alternative maximum likelihood estimator of long-memory processes using compactly supported wavelets," Journal of Economic Dynamics and Control, Elsevier, vol. 24(3), pages 361-387, March.
    2. Jensen, Mark J, 1999. "Using wavelets to obtain a consistent ordinary least squares estimator of the long-memory parameter," MPRA Paper 39152, University Library of Munich, Germany.
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