Detrended fluctuation analysis of multivariate time series

• We extend the detrended fluctuation analysis to the multivariate case, named MVDFA.
• The MVDFA exponent is identical with the average exponent of the individual series.
• The scaling exponent of correlated bivariate series is irrelevant to correlation levels.
• The number of series with large exponent in the system affects the MVDFA exponent.
• Multi-scale MVDFA reveals different properties between Chinese and US stock markets.

In this work, we generalize the detrended fluctuation analysis (DFA) to the multivariate case, named multivariate DFA (MVDFA). The validity of the proposed MVDFA is illustrated by numerical simulations on synthetic multivariate processes, where the cases that initial data are generated independently from the same system and from different systems as well as the correlated variate from one system are considered. Moreover, the proposed MVDFA works well when applied to the multi-scale analysis of the returns of stock indices in Chinese and US stock markets. Generally, connections between the multivariate system and the individual variate are uncovered, showing the solid performances of MVDFA and the multi-scale MVDFA.