A new method, the Hilbert-Huang Transform (HHT), developed initially for natural and engineering sciences, has now been applied to financial data. The HHT method is specially developed for analyzing nonlinear and nonstationary data. The method consists of two parts: the Empirical Mode Decomposition (EMD), and the Hilbert Spectral Analysis. The key part of the method is the first step, the EMD, with which any complicated data set can be decomposed into a finite and often small number of intrinsic mode functions (IMF). An IMF is defined here as any function having the same number of zero-crossing and extrema, and also having symmetric envelopes defined by a local maxima and minima, respectively. The IMF also thus admits well-behaved Hilbert tranforms. This decomposition method is adaptive and therefore highly efficient. Since the decomposition is based on the local characteristic time scale of the data, it is applicable to nonlinear and nonstationary processes. With the Hilbert transform, the IMF yields instantaneous frequencies as functions of time that give sharp identifications of imbedded structures. The final presentation of the results is an energy-frequency-time distribution, designated as the Hilbert Spectrum. Comparisons with Wavelet Fourier analyses show the new method offers much better temporal and frequency resolutions. The EMD is also useful as a filter to extract variability of different scales. In the present application, HHT has been used to examine the changeability of the market as a measure of its volatility.
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