Applications of Hilbert–Huang transform to non‐stationary financial time series analysis

Abstract

SUMMARYA 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 analysing nonlinear and non-stationary data. The method consists of two parts: (1) the empirical mode decomposition (EMD), and (2) 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 the local maxima, and minima respectively. The IMF also thus admits well-behaved Hilbert transforms. 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 non-linear and non-stationary processes. With the Hilbert transform, the IMF yield 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, which we designate as the Hilbert Spectrum. Comparisons with Wavelet and 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 volatility of the market. Published in

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