Current Development in Theory and Applications of Wavelets
Volume 1, Issue 2, Pages 143 - 164
(August 2007)
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WAVELET SMOOTHING FOR DATA WITH AUTOCORRELATED ERRORS
Rogério F. Porto (Brazil), João R. Sato (Brazil), Elisete C. Q. Aubin (Brazil) and Pedro A. Morettin (Brazil)
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Abstract:
This paper presents an alternative approach to wavelet smoothing procedure for a time series model of signal added to autocorrelated stationary errors. The aim is to estimate the signal globally with near minimum risk. The usual approach to this problem is to threshold the wavelet coefficients with different thresholds in each level. In this paper, the autocorrelation is taken account in a parametric way letting the wavelet methods for the function estimation only. Thus, an iterative semi-parametric method is proposed. This iterative method borrows some ideas from the Cochrane-Orcutt procedure. The simulation results show that the proposed method is at least as good as other benchmark wavelet methods independent of the type of autocorrelation present in the error term. |
| Keywords and phrases: autocorrelation, semi-parametric estimation, smoothing, wavelets. |
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