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Wavelet-Based Estimation Procedures For Seasonal Long-Memory Models


  • Brandon Whitcher



The appearance of long-range dependence has been observed in a wide variety of real-word time series. So called long-memory models, which exhibit a slowly decaying autocovariance sequence and a pole at frequency zero in their spectral density function, have been used to characterize long-range dependence parsimoniously. A generalization of such models allows the pole in the spectral density function to be placed anywhere in the frequency interval causing a slowly decaying oscillating autocovariance sequence. This is known as the so called seasonal long-memory model. While an exact method for maximizing the likelihood exists and a semiparametric Whittle approximation has been proposed, we investigate two estimating procedures using the discrete wavelet packet transform: an approximate maximum likelihood method and an ordinary least squares method. We utilize the known decorrelating properties of the wavelet transform to allow us to assume a simplified variance-covariance structure for the seasonal long-memory model. We describe our computational procedures and explore the versatility gained by using the wavelet transform. As an example, we fit a seasonal long-memory model to an observed time series. The proposed wavelet-based techniques offer useful and computationally efficient alternatives to previous time and frequency domain methods.

Suggested Citation

  • Brandon Whitcher, 2000. "Wavelet-Based Estimation Procedures For Seasonal Long-Memory Models," Computing in Economics and Finance 2000 148, Society for Computational Economics.
  • Handle: RePEc:sce:scecf0:148

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    References listed on IDEAS

    1. Arteche, Josu & Robinson, Peter M., 1998. "Semiparametric inference in seasonal and cyclical long memory processes," LSE Research Online Documents on Economics 2203, London School of Economics and Political Science, LSE Library.
    2. Ooms, M., 1995. "Flexible Seasonal Long Memory and Economic Time Series," Econometric Institute Research Papers EI 9515-/A, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    3. Ignacio N. Lobato, 1997. "Semiparametric estimation of seasonal long memory models: theory and an application to the modeling of exchange rates," Investigaciones Economicas, FundaciĆ³n SEPI, vol. 21(2), pages 273-296, May.
    4. Jensen Mark J., 1999. "An Approximate Wavelet MLE of Short- and Long-Memory Parameters," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 3(4), pages 1-17, January.
    5. Arteche, Josu & Robinson, Peter M., 1998. "Seasonal and cyclical long memory," LSE Research Online Documents on Economics 2241, London School of Economics and Political Science, LSE Library.
    6. Mark J. Jensen, 1997. "Using Wavelets to Obtain a Consistent Ordinary Least Squares Estimator of the Long Memory Parameter," Econometrics 9710002, EconWPA.
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    Cited by:

    1. Mehmet Balcilar, 2003. "Multifractality of the Istanbul and Moscow Stock Market Returns," Emerging Markets Finance and Trade, M.E. Sharpe, Inc., vol. 39(2), pages 5-46, March.
    2. Ramsey James B., 2002. "Wavelets in Economics and Finance: Past and Future," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 6(3), pages 1-29, November.

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