Energy-Frequency Spectrum for Financial Time Series via Complementary Ensemble EMD

We discuss the method of complementary ensemble empirical mode decomposition (CEEMD) for analyzing nonstationary financial time series. This noise-assisted approach decomposes any time series into a number of intrinsic mode functions, along with the corresponding instantaneous amplitudes and instantaneous frequencies. Different combinations of modes allows us to reconstruct the time series based on different timescales. Using Hilbert spectral analysis, we compute the associated instantaneous energy-frequency spectrum to illustrate and interpret the properties of various timescales embedded in the original time series.