Complex systems are ubiquitous. Their components, agents, live in an environment perceiving its changes and reacting with appropriate actions; they also interact with each other causing changes in the environment itself. Modelling an environment that shows this feedback loop with agents is still a big issue because the model must take into account the emerging behaviour of the whole system. In this paper, following the S[B] paradigm, we exploit topological data analysis and the information power of persistent entropy for deriving a persistent entropy automaton to model a global emerging behaviour of the Dow Jones stock market index. We devise early warning states of the automaton that signal a possible evolution of the system towards a financial crisis.