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Zbl 1063.62144
Huang, Norden E.; Wu, Man-Li; Qu, Wendong; Long, Steven R.; Shen, Samuel S.P.
Applications of Hilbert-Huang transform to non-stationary financial time series analysis. (English)
[J] Appl. Stoch. Models Bus. Ind. 19, No. 3, 245-268 (2003). ISSN 1524-1904; ISSN 1526-4025/e

The authors propose a new method, the method of Hilbert-Huang transform, for the analysis of nonlinear and non-stationary financial time series. The method consists of two parts: the empirical mode decomposition and Hilbert spectral analysis. For an arbitrary time series $X(t)$, the Hilbert transform is defined as $Y(t) = \pi^{-1} P \int X(t')(t -t')^{-1}\,dt$, where $P$ indicates the Cauchy principal value. The authors designate as the Hilbert spectrum an energy-frequency-time distribution. They use this method to examine the changeability of the market as a measure of the volatility of the market. They confirm that comparisons with wavelet and Fourier analysis show that the new method offers much better temporal and frequency resolutions.
[Yu. V. Kozachenko (Ky\"iv)]

MSC 2000:: *62P05 Appl. of statistics to actuarial sciences and financial mathematics
62M10 Time series, etc. (statistics)
91B28 Finance etc.
65T60 Wavelets
91B84 Economic time series analysis

Keywords: Hilbert-Huang transform (HHT); empirical mode decomposition (EMD); financial time series; data analysis; Hilbert spectral analysis; volatility; stock price analysis

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