Simulation of Gegenbauer processes using wavelet packets
AbstractIn 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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Bibliographic InfoPaper 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.
Date of creation: 15 Jun 2005
Date of revision:
Gegenbauer process; Wavelet packet transform; Best-basis; Autocovariance;
This paper has been announced in the following NEP Reports:
- NEP-ALL-2007-02-17 (All new papers)
- NEP-ECM-2007-02-17 (Econometrics)
- NEP-ETS-2007-02-17 (Econometric Time Series)
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Mark J. Jensen, 1997.
"Using Wavelets to Obtain a Consistent Ordinary Least Squares Estimator of the Long Memory Parameter,"
- 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.
- 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.
- Mark J. Jensen, 1997. "An Alternative Maximum Likelihood Estimator of Long-Memeory Processes Using Compactly Supported Wavelets," Econometrics 9709002, EconWPA.
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