Abstract
Abstract 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.
Highlights
In a simplified way, the role of a scientist is to observe a system and explain it in order to translate such explanations into a mathematical form
The recurrence plots (RP) for a periodic time series consists of a series of parallel stripes at 45 degrees, with length decreasing from the length of the main diagonal line to the length of the shortest diagonal line at the lower-right corner of the RP
Motivated by the obtention of a simple function describing the distribution of recurrence times, we computed the probability p(l) of finding a diagonal line of length l from the RPs based on the intervals I1 and I2
Summary
The role of a scientist is to observe a system and explain it in order to translate such explanations into a mathematical form. The authors of the references [16] and [17] studied the question about the deterministic character in the stock market and considered the time series of such system in the context of recurrence plots (RP). Works like these have inspired us to conduct our research with the same tools. Regarding the Bovespa index, the following references present detailed studies of the time series based on the first Poincare return [18,19,20].
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