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

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  • Kei Nanamiya

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.

Suggested Citation

  • Kei Nanamiya, 2011. "The Wavelet-based Estimation for Long Memory Signal Plus Noise Models," Global COE Hi-Stat Discussion Paper Series gd11-210, Institute of Economic Research, Hitotsubashi University.
    • Handle: RePEc:hst:ghsdps:gd11-210
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    File URL: http://gcoe.ier.hit-u.ac.jp/research/discussion/2008/pdf/gd11-210.pdf
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    References listed on IDEAS

    as
    1. Gilles Teyssière & Patrice Abry, 2007. "Wavelet Analysis of Nonlinear Long-Range Dependent Processes. Applications to Financial Time Series," Springer Books, in: Gilles Teyssière & Alan P. Kirman (ed.), Long Memory in Economics, pages 173-238, Springer.
    2. Harvey,Andrew & Koopman,Siem Jan & Shephard,Neil (ed.), 2004. "State Space and Unobserved Component Models," Cambridge Books, Cambridge University Press, number 9780521835954, January.
    3. 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.
    4. Gilles Teyssière & Alan P. Kirman (ed.), 2007. "Long Memory in Economics," Springer Books, Springer, number 978-3-540-34625-8, January.
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    Keywords

    Wavelet; Long Memory Process; Measurement Error Problem;
    All these keywords.

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