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Locally stationary long memory estimation

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  • Roueff, François
  • von Sachs, Rainer
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    Abstract

    There exists a wide literature on parametrically or semi-parametrically modelling strongly dependent time series using a long-memory parameter d, including more recent work on wavelet estimation. As a generalization of these latter approaches, in this work we allow the long-memory parameter d to be varying over time. We adopt a semi-parametric approach in order to avoid fitting a time-varying parametric model, such as tvARFIMA, to the observed data. We study the asymptotic behavior of a local log-regression wavelet estimator of the time-dependent d. Both simulations and a real data example complete our work on providing a fairly general approach.

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    Bibliographic Info

    Article provided by Elsevier in its journal Stochastic Processes and their Applications.

    Volume (Year): 121 (2011)
    Issue (Month): 4 (April)
    Pages: 813-844

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    Handle: RePEc:eee:spapps:v:121:y:2011:i:4:p:813-844

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    Related research

    Keywords: Locally stationary process Long memory Semi-parametric estimation Wavelets;

    References

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    1. Torben G. Andersen & Tim Bollerslev & Francis X. Diebold & Paul Labys, 2001. "Modeling and Forecasting Realized Volatility," Center for Financial Institutions Working Papers 01-01, Wharton School Center for Financial Institutions, University of Pennsylvania.
    2. Niels Haldrup & Morten O. Nielsen, 2004. "A Regime Switching Long Memory Model for Electricity Prices," Economics Working Papers 2004-2, School of Economics and Management, University of Aarhus.
    3. E. Moulines & F. Roueff & M. S. Taqqu, 2007. "On the Spectral Density of the Wavelet Coefficients of Long-Memory Time Series with Application to the Log-Regression Estimation of the Memory Parameter," Journal of Time Series Analysis, Wiley Blackwell, vol. 28(2), pages 155-187, 03.
    4. Ding, Zhuanxin & Granger, Clive W. J. & Engle, Robert F., 1993. "A long memory property of stock market returns and a new model," Journal of Empirical Finance, Elsevier, vol. 1(1), pages 83-106, June.
    5. F. Roueff & M. S. Taqqu, 2009. "Asymptotic normality of wavelet estimators of the memory parameter for linear processes," Journal of Time Series Analysis, Wiley Blackwell, vol. 30(5), pages 534-558, 09.
    6. Dahlhaus, Rainer & Neumann, Michael H., 2001. "Locally adaptive fitting of semiparametric models to nonstationary time series," Stochastic Processes and their Applications, Elsevier, vol. 91(2), pages 277-308, February.
    7. Thomas Mikosch & Catalin Starica, 2004. "Changes of structure in financial time series and the GARCH model," Econometrics 0412003, EconWPA.
    8. Dahlhaus, R., 1996. "On the Kullback-Leibler information divergence of locally stationary processes," Stochastic Processes and their Applications, Elsevier, vol. 62(1), pages 139-168, March.
    9. Granger, Clive W. J. & Ding, Zhuanxin, 1996. "Varieties of long memory models," Journal of Econometrics, Elsevier, vol. 73(1), pages 61-77, July.
    10. Faÿ, Gilles & Moulines, Eric & Roueff, François & Taqqu, Murad S., 2009. "Estimators of long-memory: Fourier versus wavelets," Journal of Econometrics, Elsevier, vol. 151(2), pages 159-177, August.
    11. Dahlhaus, Rainer, 2009. "Local inference for locally stationary time series based on the empirical spectral measure," Journal of Econometrics, Elsevier, vol. 151(2), pages 101-112, August.
    12. Roueff, F. & Taqqu, M.S., 2009. "Central limit theorems for arrays of decimated linear processes," Stochastic Processes and their Applications, Elsevier, vol. 119(9), pages 3006-3041, September.
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    Cited by:
    1. Lukas Vacha & Karel Janda & Ladislav Kristoufek & David Zilbermand, 2013. "Time-Frequency Dynamics of Biofuels-Fuels-Food System," CAMA Working Papers 2013-27, Centre for Applied Macroeconomic Analysis, Crawford School of Public Policy, The Australian National University.
    2. Heni Boubaker & Nadia Sghaier, 2014. "Wavelet based Estimation of Time- Varying Long Memory Model with Nonlinear Fractional Integration Parameter," Working Papers 2014-284, Department of Research, Ipag Business School.
    3. Tsangyao Chang & Xiao-lin Li & Stephen M. Miller & Mehmet Balcilar & Rangan Gupta, 2013. "The Co-Movement and Causality between the U.S. Real Estate and Stock Markets in the Time and Frequency Domains," Working Papers 201365, University of Pretoria, Department of Economics.
    4. Jozef Barunik & Evzen Kocenda & Lukas Vacha, 2013. "Gold, Oil, and Stocks," Papers 1308.0210, arXiv.org, revised Mar 2014.

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