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Wavelet-Based Estimation Procedures For Seasonal Long-Memory Models

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  • Brandon Whitcher

    (EURANDOM)

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    Abstract

    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.

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    Bibliographic Info

    Paper provided by Society for Computational Economics in its series Computing in Economics and Finance 2000 with number 148.

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    Date of creation: 05 Jul 2000
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    Handle: RePEc:sce:scecf0:148

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    Postal: CEF 2000, Departament d'Economia i Empresa, Universitat Pompeu Fabra, Ramon Trias Fargas, 25,27, 08005, Barcelona, Spain
    Fax: +34 93 542 17 46
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    Web page: http://enginy.upf.es/SCE/
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    1. Mark J. Jensen, 1999. "An Approximate Wavelet MLE of Short- and Long-Memory Parameters," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 3(4), pages 5.
    2. repec:fth:erroem:9515/a is not listed on IDEAS
    3. Mark J. Jensen, 1997. "Using Wavelets to Obtain a Consistent Ordinary Least Squares Estimator of the Long Memory Parameter," Econometrics 9710002, EconWPA.
    4. Ooms, M., 1995. "Flexible Seasonal Long Memory and Economic Time Series," Econometric Institute Report EI 9515-/A, Erasmus University Rotterdam, Econometric Institute.
    5. Ignacio N. Lobato, 1997. "Semiparametric estimation of seasonal long memory models: theory and an application to the modeling of exchange rates," Investigaciones Economicas, Fundación SEPI, vol. 21(2), pages 273-296, May.
    6. Josu Artech & Peter M Robinson, 1998. "Semiparametric Inference in Seasonal and Cyclical Long Memory Processes - (Now published in Journal of Time Series Analysis, 21 (2000), pp.1-25.)," STICERD - Econometrics Paper Series /1998/359, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
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