Empirical studies and market observations suggest that asset prices are driven by multiscale factors, ranging from long-term market regimes to rapid fluctuations. Embedded with different timescales, many financial time series often exhibit nonstationary behaviors with trends and time-varying volatilities. These characteristics can hardly be captured by linear models and call for an adaptive and nonlinear approach for analysis.
One approach for analyzing nonstationary time series is the Hilbert-Huang transform (HHT). The HHT method can decompose any time series into oscillating components with nonstationary amplitudes and frequencies using the empirical mode decomposition (EMD). This fully adaptive method provides a multiscale decomposition for the original time series, which gives richer information about the time series. The instantaneous frequency and instantaneous amplitude of each component are later extracted using the Hilbert transform. The decomposition onto different timescales also allows for reconstruction up to different resolutions, providing a smoothing and filtering tool that is ideal for noisy financial time series.
The method of HHT and its variations have been applied in numerous fields, from engineering to geophysics. Applications of HHT to finance date back to the work by Huang and co-authors on modeling mortgage rate data. The empirical mode decomposition (EMD) has been used for financial time series forecasting and for examining the correlation between financial time series.
In our recent paper, we present a novel method of applying adaptive complementary ensemble empirical mode decomposition (ACE-EMD) and Hilbert spectral analysis to study cryptocurrency price dynamics. As an emerging asset class, cryptocurrencies have a number of salient features compared to traditional equities, including significantly higher volatility and rapidly changing directional trends.