Detecting nonlinear dynamics using BDS test and surrogate data in financial time series

Abstract

Physicists experimentalists use many observations of a phenomenon, which are the unknown equations that describe it, in order to understand the dynamics and obtain information on their future behavior. In this article we study the possibility of reproducing the dynamics of the phenomenon using only a measurement scale. The Whitney immersion theorem ideas are presented and generalization of Sauer for fractal sets to rebuild the asymptotic behavior of the phenomena and to investigate evidence of nonlinear dynamics in the reproduced dynamics using the Brock, Dechert, Scheinkman test (BDS). The applications are made in the financial market which are only known stock prices.