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Simulation of Gegenbauer processes using wavelet packets

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  • Collet J.J.
  • Fadili J.M.

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

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    Abstract

    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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    Bibliographic Info

    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

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    Keywords: Gegenbauer process; Wavelet packet transform; Best-basis; Autocovariance;

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    1. Mark J. Jensen, 1997. "Using Wavelets to Obtain a Consistent Ordinary Least Squares Estimator of the Long Memory Parameter," Econometrics 9710002, EconWPA.
    2. Mark J. Jensen, 1997. "An Alternative Maximum Likelihood Estimator of Long-Memeory Processes Using Compactly Supported Wavelets," Econometrics 9709002, EconWPA.
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