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**Applications of Hilbert-Huang transform to non-stationary financial time series analysis.**
*(English)*
Zbl 1063.62144

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.

Reviewer: Yu. V. Kozachenko (Kyïv)

### MSC:

62P05 | Applications of statistics to actuarial sciences and financial mathematics |

62M10 | Time series, auto-correlation, regression, etc. in statistics (GARCH) |

91B28 | Finance etc. (MSC2000) |

65T60 | Numerical methods for 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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\textit{N. E. Huang} et al., Appl. Stoch. Models Bus. Ind. 19, No. 3, 245--268 (2003; Zbl 1063.62144)

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