On the interplay between multiscaling and average cross-correlation. (arXiv:1802.01113v1 [q-fin.ST])

We find a nonlinear dependence between an indicator of the degree of multiscaling of log-returns time series of a stock and the average correlation of it with the other stocks traded in the same market. This result is a robust stylized fact holding for different financial markets. We investigate the relationship of this result with the stocks' capitalization and we show that a linear dependence from the logarithm of the capitalization does not explain the observed stylized fact.