Generalized distance component method based on spatial amplitude and trend difference weighting operator for complex time series

Abstract

The generalized distance component (GDISCO) approach, which uses the property that the energy distance is rotationally invariant in high-dimensional space to measure the complexity of univariate or multivariate time series, was recently proposed. However, because this method disregards the time series’ spatial trend distribution and amplitude structure, this work offers a new spatial amplitude and trend difference weighting operator, abbreviated as WSATD. We present the weighted generalized distance component (WSATD-GDISCO) technique based on WSATD. Numerical simulations show that WSATD-GDISCO is effective for short and long time series, and it is robust to noise. Compared to the GDISCO method, the WSATD-GDISCO shows better performance to measure the dynamic characteristics of a system. Finally, the method is applied to investigate the relationship between EEG and alcoholics’ response to stimuli, as well as the long-term and short-term differences in stock market volatility in China and the United States.