Statistics and Its Interface

Volume 8 (2015)

Number 1

Special Issue on Extreme Theory and Application (Part II)

Guest Editors: Yazhen Wang and Zhengjun Zhang

Marked point process adjusted tail dependence analysis for high-frequency financial data

Pages: 109 – 122



Alexander Malinowski (Institute for Mathematics, University of Mannheim, Germany)

Martin Schlather (Institute for Mathematics, University of Mannheim, Germany)

Zhengjun Zhang (Department of Statistics, University of Wisconsin, Madison, Wisc., U.S.A.)


Although the extremes of high-frequency financial transaction data have a huge economic impact, basic characteristics of the data have not been addressed up to now. To capture dependence between the tail behavior of intertransaction returns and the pattern of transaction times, this paper combines marked point process (MPP) theory with extreme value analysis. Suitable measures of interaction are provided, based on second-order moments of MPPs. Applying these measures to financial transaction data, it is verified that the extreme value index of the return distribution is indeed locally increased, i.e., on the scale of minutes, by the existence of surrounding transactions. A simulation study underpins the observed effects and enables assessing the finite sample properties of the respective estimators. Further, asymptotic results on the estimators are given.


tail index, mark-location dependence, moment measure, transaction data

2010 Mathematics Subject Classification

Primary 60G55. Secondary 60G70.

Published 13 February 2015