Eur. Phys. J. B (2014) 87: 168
https://doi.org/10.1140/epjb/e2014-50108-3

Regular Article

Information-theoretic approach to lead-lag effect on financial markets

Cracow University of Economics, Rakowicka 27, 31-510 Kraków, Poland

^a e-mail: s801dok@wizard.uek.krakow.pl

Received: 16 February 2014
Received in final form: 28 April 2014
Published online: 1 August 2014

Abstract

Recently the interest of researchers has shifted from the analysis of synchronous relationships of financial instruments to the analysis of more meaningful asynchronous relationships. Both types of analysis are concentrated mostly on Pearson’s correlation coefficient and consequently intraday lead-lag relationships (where one of the variables in a pair is time-lagged) are also associated with them. Under the Efficient-Market Hypothesis such relationships are not possible as all information is embedded in the prices, but in real markets we find such dependencies. In this paper we analyse lead-lag relationships of financial instruments and extend known methodology by using mutual information instead of Pearson’s correlation coefficient. Mutual information is not only a more general measure, sensitive to non-linear dependencies, but also can lead to a simpler procedure of statistical validation of links between financial instruments. We analyse lagged relationships using New York Stock Exchange 100 data not only on an intraday level, but also for daily stock returns, which have usually been ignored.