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Wavelet Method for Locally Stationary Seasonal Long Memory Processes

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  • Dominique Guegan

    ()
    (CES - Centre d'économie de la Sorbonne - CNRS : UMR8174 - Université Paris I - Panthéon-Sorbonne, EEP-PSE - Ecole d'Économie de Paris - Paris School of Economics - Ecole d'Économie de Paris)

  • Zhiping Lu

    ()
    (CES - Centre d'économie de la Sorbonne - CNRS : UMR8174 - Université Paris I - Panthéon-Sorbonne, ECNU - East China Normal University [Shangaï])

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    Abstract

    Long memory processes have been extensively studied over the past decades. When dealing with the financial and economic data, seasonality and time-varying long-range dependence can often be observed and thus some kind of non-stationarity can exist inside financial data sets. To take into account this kind of phenomena, we propose a new class of stochastic process : the locally stationary k-factor Gegenbauer process. We describe a procedure of estimating consistently the time-varying parameters by applying the discrete wavelet packet transform (DWPT). The robustness of the algorithm is investigated through simulation study. An application based on the error correction term of fractional cointegration analysis of the Nikkei Stock Average 225 index is proposed.

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    Bibliographic Info

    Paper provided by HAL in its series Post-Print with number halshs-00375531.

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    Date of creation: Mar 2009
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    Handle: RePEc:hal:journl:halshs-00375531

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    Related research

    Keywords: Discrete wavelet packet transform ; Gegenbauer process ; Nikkei Stock Average 225 index ; non-stationarity ; ordinary least square estimation;

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    References

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    1. 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.
    2. Abdou Kâ Diongue & Dominique Guegan & Bertrand Vignal, 2009. "Forecasting electricity spot market prices with a k-factor GIGARCH process," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00307606, HAL.
    3. L. A. Gil-Alaña & Peter M. Robinson, 2001. "Testing of seasonal fractional integration in UK and Japanese consumption and income," LSE Research Online Documents on Economics 298, London School of Economics and Political Science, LSE Library.
    4. Gil-Alana, L. & Robinson, P.M., 1998. "Testing of Seasonal Fractional Integration in U.K. and Japanese Consumption and Income," Economics Working Papers eco98/20, European University Institute.
    5. Sowell, Fallaw, 1992. "Modeling long-run behavior with the fractional ARIMA model," Journal of Monetary Economics, Elsevier, vol. 29(2), pages 277-302, April.
    6. Francis X. Diebold & Glenn D. Rudebusch, 1988. "Long memory and persistence in aggregate output," Finance and Economics Discussion Series 7, Board of Governors of the Federal Reserve System (U.S.).
    7. Abdou Kâ Diongue & Dominique Guegan & Bertrand Vignal, 2009. "Forecasting electricity spot market prices with a k-factor GIGARCH process," Post-Print halshs-00307606, HAL.
    8. Abdou Kâ Diongue & Dominique Guegan, 2004. "Estimating parameters for a k-GIGARCH process," Post-Print halshs-00188531, HAL.
    9. Engle, Robert F & Granger, Clive W J, 1987. "Co-integration and Error Correction: Representation, Estimation, and Testing," Econometrica, Econometric Society, vol. 55(2), pages 251-76, March.
    10. Engle, Robert F. & Yoo, Byung Sam, 1987. "Forecasting and testing in co-integrated systems," Journal of Econometrics, Elsevier, vol. 35(1), pages 143-159, May.
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