Multivariate large deviations spectrum for the multiscale analysis of stock markets

We extend the classical roughness exponent (detrended fluctuation analysis) into multivariate signals, aiming at detecting the effectiveness and advantages of the multivariate multifractal detrended fluctuation analysis (MMDFA) based large deviations spectrum. Results show that large deviations spectrum is sensitive to non-concavities and contains more information than the Legendre spectrum. Further, we investigate the large deviations spectrum for stock markets with the closing prices and volumes. Volumes have a tendency of scale invariance. For global markets, we construct 9 univariate series and 3 multivariate time series separately for Asia, Europe and America and quantify the scale invariance and generating mechanism of multifractality for multivariate stock markets through comparison. It is shown that markets of the same region have a more similar evolution and the q ranges for slope in the fit process are different from each other for both univariate and multivariate situations. Besides, European markets have better scaling properties.