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The Wavelet-based Estimation for Long Memory Signal Plus Noise Models

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  • Kei Nanamiya
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    Abstract

    We propose new wavelet-based procedure to estimate the memory parameter of an unobserved process from an observed process affected by noise in order to improve the performance of the estimator by taking into account the dependency of the wavelet coefficients of long memory processes. In our procedure, using the AR (1) approximation for the wavelet transformed long memory processes which is introduced by Craigmile, Guttorp and Percival (2005), we apply the ARMA (1, 1) approximation to the wavelet coefficients of the observed process at each level. We also compare this procedure to the usual wavelet-based procedure by numerical simulations.

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    File URL: http://gcoe.ier.hit-u.ac.jp/research/discussion/2008/pdf/gd11-210.pdf
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    Bibliographic Info

    Paper provided by Institute of Economic Research, Hitotsubashi University in its series Global COE Hi-Stat Discussion Paper Series with number gd11-210.

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    Date of creation: Dec 2011
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    Handle: RePEc:hst:ghsdps:gd11-210

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    Keywords: Wavelet; Long Memory Process; Measurement Error Problem;

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    1. Breidt, F. Jay & Crato, Nuno & de Lima, Pedro, 1998. "The detection and estimation of long memory in stochastic volatility," Journal of Econometrics, Elsevier, vol. 83(1-2), pages 325-348.
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