Análise de evidências de dinâmica caótica e não linear aplicada ao mercado financeiro

Abstract

The present study contributes to the theory of asset pricing by analyzing evidence of non-linearity and chaos in the time series of daily returns from March 30, 2009 to December 31, 2013 provided by Bloomberg of the following countries and indices: India - CNX Finance, Germany - Dax All banks, United States - kbw bank, Brazil - IFNC, Australia - asx 200 financials, France - cac financials, Mexico - BMV, UK - nmx8350, Canada - TSX financials and Russia - Moscow Exchange Financials. As to the specific objectives of the study we have: 1) to analyze if the database in question can be classified in the light of efficient market theory, that is, if the returns of the assets follow a stochastic process, 2) use the BDS statistic to verify whether the series in question are linear or not, and 3) to verify the existence of Chaos in the database through the Liapunov Peak Expo. The Lyapunov maximum exponents were calculated by the mutual information method at the mean, and t = 1 was found for all series and the estimation of the immersion dimension was calculated by the method proposed in Cao (1997). From the obtained results, it was verified that the series in question are non-linear and also can not be considered chaotic, and these should be treated as stochastic and non-linear processes.