On the interplay between multiscaling and stock dependence

Abstract

We find a nonlinear dependence between an indicator of the degree of multiscaling of log-price time series of a stock and the average correlation of the stock with respect to the other stocks traded in the same market. This result is a robust stylized fact holding for different financial markets. We investigate this result conditional on the stocks' capitalization and on the kurtosis of stocks' log-returns in order to search for possible confounding effects. We show that a linear dependence with the logarithm of the capitalization and the logarithm of kurtosis does not explain the observed stylized fact, which we interpret as being originated from a deeper relationship.

Keywords:

• Multiscaling
• Dependence
• Univariate properties
• Multivariate properties

JEL Classification:

• G19
• G10

Acknowledgments

Many thanks to the two anonymous reviewers for their important comments that have greatly improved the manuscript. T.D.M. wishes to thank the ESRC Network Plus project ‘Rebuilding macroeconomics’.

Disclosure statement

No potential conflict of interest was reported by the authors.

Notes

† In the text we refer to log as the natural logarithm.

† We carried out the analysis also using MFDFA (Jiang et al. 2018), and the results are qualitatively equivalent, suggesting the analysis is not method dependent.

† Filtering out both linear and nonlinear dependence via second degree polynomial regression, the dependence structure remains statistically significant in all markets apart the London Stock Exchange.

† We use the logarithm of the kurtosis since the range of the measure across each market covers many orders of magnitudes.

† Filtering out the nonlinear effect and both the linear and nonlinear effect does not change the results.