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.