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Nontrivial mixture of long-range correlations and noise is one of the characteristic features of the dynamics of complex systems. Filtering of noise in such systems presents a difficult challenge. In the present paper this problem is studied by the example of volatility dynamics of wavelet-filtered stock price time series. Using the universal thresholding method of wavelet filtering and a principle of minimal linear autocorrelation of noise component we find that the quantitative characteristics of long-range memory in the volatility dynamics of denoised series are noticeably different from those of the raw data and the noise.
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Dremin et al. (2008) studied this question.
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