BOVESPA: Stochastic or Deterministic?

摘要

We aim to present an interdisciplinary way of showing the subject determinism versus stochasticity; and write the text in such a way that this subject can be treated from the point of view of physics teaching. We approach the technical part of this work intuitively and later we present this question in a more formal way. When the trajectory of a dynamical system in the phase space repeats itself after some time. We say that the system displays recurrence. Recurrence plots (RP) and recurrence quantification analysis (RQA) took place as tools to investigate this property. We employ the RP and the RQA the behavior of a long time series of the returns of the Bovespa index. We have carefully studied the obtention of the parameters for the phase space reconstruction of the supposed dynamical system which created the time series. After building the RPs for the time series of the returns, the values of the quantities from RQA were computed and then compared with values obtained for the randomized series. Our investigations suggest that the real financial market dynamics is a combination of deterministic chaos and stochastic behavior.