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Wavelet estimation of the memory parameter for long range dependent random fields

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  • Lihong Wang
  • Jinde Wang

Abstract

In this paper we study the estimation of the spatial long memory parameter for stationary long range dependent random fields using wavelet methods. We first show the relation between the wavelet coefficients of the random fields and its long memory parameter. Based on this relation, we construct a log-regression wavelet estimator of the long memory parameter. Under some mild regularity assumptions, the asymptotic properties of the estimators are investigated. Finally, a small simulation study illustrates the method. Copyright Springer-Verlag Berlin Heidelberg 2014

Suggested Citation

  • Lihong Wang & Jinde Wang, 2014. "Wavelet estimation of the memory parameter for long range dependent random fields," Statistical Papers, Springer, vol. 55(4), pages 1145-1158, November.
    • Handle: RePEc:spr:stpapr:v:55:y:2014:i:4:p:1145-1158
    DOI: 10.1007/s00362-013-0558-2
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    References listed on IDEAS

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    1. 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, March.
    2. Jean‐Marc Bardet & Pierre R. Bertrand, 2010. "A Non‐Parametric Estimator of the Spectral Density of a Continuous‐Time Gaussian Process Observed at Random Times," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 37(3), pages 458-476, September.
    3. Mark J. Jensen, 1997. "Using Wavelets to Obtain a Consistent Ordinary Least Squares Estimator of the Long Memory Parameter," Econometrics 9710002, University Library of Munich, Germany.
    4. Guo, Hongwen & Lim, Chae Young & Meerschaert, Mark M., 2009. "Local Whittle estimator for anisotropic random fields," Journal of Multivariate Analysis, Elsevier, vol. 100(5), pages 993-1028, May.
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