Multiscaled Cross-Correlation Dynamics in Financial Time-Series

The cross-correlation matrix between equities comprises multiple interactions between traders with varying strategies and time horizons. In this paper, we use the Maximum Overlap Discrete Wavelet Transform (MODWT) to calculate correlation matrices over different time scales and then explore the eigenvalue spectrum over sliding time windows. The dynamics of the eigenvalue spectrum at different scales provides insight into the interactions between the numerous constituents involved. A study of the eigenvalue spectrum in its entirety provides further insight. On partitioning the eigenvalue time series, we show that negative index returns, (drawdowns), are associated with periods where the largest eigenvalue is greatest, while positive index returns, (drawups), are associated with periods where the largest eigenvalue is smallest. Furthermore, through the study of the small eigenvalues of the correlation matrix, we show that information about the correlation dynamics is visible at both ends of the eigenspectrum across all scales.