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Multifractality within the continuous-time random walk in financial markets

Andrzej Kasprzak 1Josep Perelló 2Jaume Masoliver 2Ryszard Kutner 1

1. Warsaw University, Faculty of Physics, Hoża 69, Warszawa 00-681, Poland
2. Universitat de Barcelona, Departament de Fisica Fonamental, Diagonal 647, Barcelona 08028, Spain


We considered the intertransaction time-intervals for some future contracts as well-suited characteristics of investors activity. We observed that the moments of arbitrary order of the empirical intertransaction time-intervals possess negligible small statistical errors. Therefore we were able to verify their multifractal behavior, which was well described within the continuous-time random walk formalism. We found that this multifractality has closed left side and open right one of the spectrum of singularities. The multifractality can be considered here as an intermediate phenomenon between two unifractals observed for very small and asymptoticaly large orders of the moments. We came to conclusion that transition between uni- and multifractals can be considered as the phase transition of the third order.


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Related papers

Presentation: Oral at 3 Ogólnopolskie Sympozjum "Fizyka w Ekonomii i Naukach Społecznych", by Andrzej Kasprzak
See On-line Journal of 3 Ogólnopolskie Sympozjum "Fizyka w Ekonomii i Naukach Społecznych"

Submitted: 2007-10-31 15:40
Revised:   2009-06-07 00:48