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

$X\left(t\right)$, the Hilbert transform is defined as

$Y\left(t\right)={\pi}^{-1}P\int X\left({t}^{\text{'}}\right){(t-{t}^{\text{'}})}^{-1}\phantom{\rule{0.166667em}{0ex}}dt$, 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.