Universal behavior of the interoccurrence times between losses in financial markets: Independence of the time resolution

Josef Ludescher and Armin Bunde
Phys. Rev. E 90, 062809 – Published 16 December 2014

Abstract

We consider representative financial records (stocks and indices) on time scales between one minute and one day, as well as historical monthly data sets, and show that the distribution PQ(r) of the interoccurrence times r between losses below a negative threshold Q, for fixed mean interoccurrence times RQ in multiples of the corresponding time resolutions, can be described on all time scales by the same q exponentials, PQ(r)1/{[1+(q1)βr]1/(q1)}. We propose that the asset- and time-scale-independent analytic form of PQ(r) can be regarded as an additional stylized fact of the financial markets and represents a nontrivial test for market models. We analyze the distribution PQ(r) as well as the autocorrelation CQ(s) of the interoccurrence times for three market models: (i) multiplicative random cascades, (ii) multifractal random walks, and (iii) the generalized autoregressive conditional heteroskedasticity [GARCH(1,1)] model. We find that only one of the considered models, the multifractal random walk model, approximately reproduces the q-exponential form of PQ(r) and the power-law decay of CQ(s).

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  • Received 31 January 2014

DOI:https://doi.org/10.1103/PhysRevE.90.062809

©2014 American Physical Society

Authors & Affiliations

Josef Ludescher and Armin Bunde

  • Institut für Theoretische Physik, Justus-Liebig-Universität Giessen, D-35392 Giessen, Germany

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Issue

Vol. 90, Iss. 6 — December 2014

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