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Analysis of times between events by methods of statistical physics 
Mateusz Denys ^{1}, Tomasz Gubiec ^{1,2}, Ryszard Kutner ^{1}, Maciej Jagielski ^{1,2,3}, Eugene Stanley ^{2} 
1. Institute of Experimental Physics, Faculty of Physics, University of Warsaw (FUW), Pasteura 5, Warsaw 02093, Poland 
Abstract 
One of the most significant questions in the analysis of losses in financial market time series, closely related to an economic concept of value at risk (VaR), is description of times between subsequent losses of a particular magnitude (called interevent times). We provide such a description under two complementary approaches. First, we present a model of superstatistics founded on the continuoustime random walk (CTRW) model and the extreme value theory (EVT). The model provides a closed analytic formula for the universal distribution of interevent times valid for excessive losses and profits (irrespective of the asset type or the time resolution of data) as well as for some geophysical data of earthquakes [1]. Our description is an alternative to the approach involving qexponential functions [2]. Secondly, we propose an agentbased model of financial markets being a generalization of the Potts model from statistical mechanics [3]. A value of the spin variable in the model represents a short (–1), neutral (0), or long (+1) position taken by the investor on the market. The action, or decision, of the investor, i.e., buying or selling a stock is, in turn, defined as a change of the spin value (positive for buying and negative for selling). Thus, we identify the state of a spin with the actual market state of the investor (the position taken on the market), not the market action (buying or selling) as in the previous works. The model reproduces, inter alia, the empirical shapes of the autocorrelation function of both usual and absolute market returns, as well as the distribution of interevent times [4]. [1] M. Denys, T. Gubiec, R. Kutner, M. Jagielski, H.E. Stanley, Phys. Rev. E 94 (4), 042305 (2016). [2] J. Ludescher, C. Tsallis, and A. Bunde, Europhys. Lett. 95 (6) 68002 (2011). [3] M. Denys, T. Gubiec, R. Kutner, Acta Phys. Pol. A 123 (3) 513–517 (2013). [4] M. Denys, T. Gubiec, R. Kutner, arXiv:1411.1689 (2014). 
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