## 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.

### 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
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