A Model for Interevent Times with Long Tails and Multifractality in Human Communications: An Application to Financial Trading

25 Pages Posted: 22 Jul 2008

See all articles by Josep Perelló

Josep Perelló

University of Barcelona - Department of Physics

Jaume Masoliver

University of Barcelona - Department of Physics

Andrzej Kasprzak

University of Warsaw - Faculty of Physics

Ryszard Kutner

University of Warsaw - Faculty of Physics

Date Written: July, 18 2008

Abstract

Social, technological and economic time series are divided by events which are usually assumed to be random albeit with some hierarchical structure. It is well known that the interevent statistics observed in these contexts differs from the Poissonian profile by being long-tailed distributed with resting and active periods interwoven. Understanding mechanisms generating consistent statistics have therefore become a central issue. The approach we present is taken from the Continuous Time Random Walk formalism and represents an analytical alternative to models of non-trivial priority that have been recently proposed. Our analysis also goes one step further by looking at the multifractal structure of the interevent times of human decisions. We here analyze the inter-transaction time intervals of several financial markets. We observe that empirical data describes a subtle multifractal behavior. Our model explains this structure by taking the pausing-time density in the form of a superstatistics where the integral kernel quantifies the heterogeneous nature of the executed tasks. An stretched exponential kernel provides a multifractal profile valid for a certain limited range. A suggested heuristic analytical profile is capable of covering a broader region.

Keywords: intertransaction, high-frequency, model

JEL Classification: C00

Suggested Citation

Perello, Josep and Masoliver, Jaume and Kasprzak, Andrzej and Kutner, Ryszard, A Model for Interevent Times with Long Tails and Multifractality in Human Communications: An Application to Financial Trading (July, 18 2008). Available at SSRN: https://ssrn.com/abstract=1162706 or http://dx.doi.org/10.2139/ssrn.1162706

Josep Perello (Contact Author)

University of Barcelona - Department of Physics ( email )

Diagonal, 647
Barcelona, E-08028
Spain
+34 9 34021150 (Phone)
+34 34021149 (Fax)

Jaume Masoliver

University of Barcelona - Department of Physics ( email )

Barcelona, E-08028
Spain
00 34 3 402 11 59 (Phone)
00 34 3 402 11 49 (Fax)

Andrzej Kasprzak

University of Warsaw - Faculty of Physics ( email )

Hoza 69
Warsaw, PL-00681
Poland
+48 22 5533215 (Phone)
+48 22 8535979 (Fax)

Ryszard Kutner

University of Warsaw - Faculty of Physics ( email )

Hoza 69
Warsaw, PL-00681
Poland
+48 22 5533215 (Phone)
+48 22 8535979 (Fax)

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