Multiresolution transmission of the correlation modes between bivariate time series based on complex network theory

• There exist different types of correlation modes between bivariate time series.
• The transmission among correlation modes shows a multiscale phenomenon.
• We transform the transmission in multiscale time series into complex networks.
• There exists a strongly positive correlation over the duration of 32–64 days.
• The extent of persistence of correlation-fluctuation strengthens over long term.

This study introduces an approach to study the multiscale transmission characteristics of the correlation modes between bivariate time series. The correlation between the bivariate time series fluctuates over time. The transmission among the correlation modes exhibits a multiscale phenomenon, which provides richer information. To investigate the multiscale transmission of the correlation modes, this paper describes a hybrid model integrating wavelet analysis and complex network theory to decompose and reconstruct the original bivariate time series into sequences in a joint time–frequency domain and defined the correlation modes at each time–frequency domain. We chose the crude oil spot and futures prices as the sample data. The empirical results indicate that the main duration of volatility (32–64 days) for the strongly positive correlation between the crude oil spot price and the futures price provides more useful information for investors. Moreover, the weighted degree, weighted indegree and weighted outdegree of the correlation modes follow power-law distributions. The correlation fluctuation strengthens the extent of persistence over the long term, whereas persistence weakens over the short and medium term. The primary correlation modes dominating the transmission process and the major intermediary modes in the transmission process are clustered both in the short and long term.