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.


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
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