Detection of correlation characteristics between financial time series based on multi-resolution analysis

Interactions between financial time series are complex and changeable in both time and frequency domains. To reveal the evolution characteristics of the time-varying relations between bivariate time series from a multi-resolution perspective, this study introduces an approach combining wavelet analysis and complex networks. In addition, to reduce the influence the phase lag between the time series has on the correlations, we propose dynamic time-warping (DTW) correlation coefficients to reflect the correlation degree between bivariate time series. Unlike previous studies that symbolized the time series only based on the correlation strength, the second-level symbol is set according to the correlation length during the coarse-graining process. This study presents a novel method to analyze bivariate time series and provides more information for investors and decision makers when investing in the stock market. We choose the closing prices of two stocks in China’s market as the sample and explore the evolutionary behavior of correlation modes from different resolutions. Furthermore, we perform experiments to discover the critical correlation modes between the bull market and the bear market on the high-resolution scale, the clustering effect during the financial crisis on the middle-resolution scale, and the potential pseudo period on the low-resolution scale. The experimental results exactly match reality, which provides powerful evidence to prove that our method is effective in financial time series analysis.