Análise do índice Bovespa pelo método dos gráficos de recorrência

Abstract

Recurrence analysis has been extensively used in approaching problems that deal with transitions between regular and chaotic behaviors, identi¯cation of structure of dynamic systems, such as frequencies and correlations hard to detect by linear methods, for example. Among the main tools of this analysis are the Recurrence Plots (RP) and the Quantitative Recurrence Analysis (RQA), which are constantly used in the analysis of time series supposedly proceeding from non-linear and even non-stationary dynamical systems. These tools have been applied in a wide range of phenomena, since the study of cardiac arrhythmia until the greater phenomena of nature, such as sunspots. Recently, many economic and ¯financial séries are being investigated under this perspective, as exchange rates, the financial crashes" and the behavior of some stock index. In this work we employ the RP and RQA for the study of a long time series of the returns of the Bovespa Index (Ibovespa), where we carefully studied the obtention of the parameters for the phase space reconstruction of the supposed system which created the time series, we analyze the patterns formed in RP as well as the values of the quantities of RQA, comparing the results obtained with the original and randomized series. We search, from these results,to establish whether there is some sort of deterministic component in the studied system, and what its intensity. Our investigations suggest that the real financial market dynamics is a combination of deterministic chaos and stochastic behavior.