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
, the Hilbert transform is defined as
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.