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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)=π -1 PX(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:
62P05Applications of statistics to actuarial sciences and financial mathematics
62M10Time series, auto-correlation, regression, etc. (statistics)
91B28Finance etc. (MSC2000)
65T60Wavelets (numerical methods)
91B84Economic time series analysis