Physica A 419 (2015) 122–127 Contents lists available at ScienceDirect Physica A journal homepage: www.elsevier.com/locate/physa An autocatalytic network model for stock markets Marco Antonio Leonel Caetano a,∗ , Takashi Yoneyama b a INSPER Instituto de Ensino e Pesquisa, São Paulo, Brazil b ITA - Instituto Tecnológico da Aeronáutica, São José dos Campos, Brazil highlights • We model the dynamics of Boolean network to apply in financial market. • The model is applied to the actual data for stock market. • The states of network are binary and represent financial return. • It is possible to note the pattern of stocks observing behavior of network. article info Article history: Received 15 April 2014 Received in revised form 2 July 2014 Available online 18 October 2014 Keywords: Forecasting Stock markets Autocatalytic network Boolean network abstract The stock prices of companies with businesses that are closely related within a specific sec- tor of economy might exhibit movement patterns and correlations in their dynamics. The idea in this work is to use the concept of autocatalytic network to model such correlations and patterns in the trends exhibited by the expected returns. The trends are expressed in terms of positive or negative returns within each fixed time interval. The time series de- rived from these trends is then used to represent the movement patterns by a probabilis- tic boolean network with transitions modeled as an autocatalytic network. The proposed method might be of value in short term forecasting and identification of dependencies. The method is illustrated with a case study based on four stocks of companies in the field of natural resource and technology. © 2014 Elsevier B.V. All rights reserved. 1. Introduction The network theory has found applications in a variety of fields. For instance, Robert May [1] deals with the problem of biological chains in the nature. Estrada et al. [2] concern complexity metrics for networks such as centrality of information, node vulnerability and others. Connections between the theory of networks and of dynamic systems are explored in Jain and Krischna [3]. In particular, the latter presents dynamic autocatalytic models, which have been of value in the study of free scale small-world type networks (Wang et al. [4], Deng et al. [5], Lü et al. [6]). Perturbations in networks have become a major issue as the complexity of networks has increased, for instance, if one considers the case of internet, leading to new detection techniques (Liu et al. [7], Crucitti et al. [8], Strogatz [9]). In this work, boolean networks are used to model the dynamics of a group of stocks, with a view on forecasting and identification of the dependencies among the involved companies. A boolean network consists of nodes associated with boolean variables {0, 1} and edges determining the connectivity (Lewis [10]). The ‘‘strength’’ of the connections may vary in time, according to some dynamics. Boolean networks were ∗ Corresponding author. E-mail addresses: marcoALC1@insper.edu.br, malcaetano@uol.com.br (M.A.L. Caetano), takashi@ita.br (T. Yoneyama). http://dx.doi.org/10.1016/j.physa.2014.10.052 0378-4371/© 2014 Elsevier B.V. All rights reserved.