Do USD-EUR Parity Exhibit Chaotic Behavior?

Abstract

Knowing of the chaos theory by the economists has caused the understanding of the difficulties of the balance in economy. The applications of the chaos theory related to economy have aimed to overcome these difficulties. Chaotic deterministic models with sensitive dependence on initial conditions provide a powerful tool in understanding the apparently random movements in financial data. The dynamic systems are analyzed by using linear and/or nonlinear methods in the previous studies. Although the linear methods used for stable linear systems, generally fails at the nonlinear analysis, however, they give intuition about the problem. Due to a nonlinear variable in the difference equations describing the dynamic systems, unpredictable dynamics may occur. The chaos theory or nonlinear analysis methods are used to examine such dynamics systems. The chaos that expresses an irregular condition can be characterized by ?sensitive dependence on initial conditions?. We employ four tests, viz. the BDS test on raw data, the BDS test on pre-filtered data, Correlation Dimension test and the Brock?s Residual test. The financial markets considered are the stock market, the foreign exchange market. The results from these tests provide very weak evidence for the presence of chaos in USD-EUR Parity. In this study, the methods for the chaotic analysis of the time series, obtained based on the discrete or continuous measurements of a variable are investigated. The chaotic analysis methods have been applied on the time series of various systems.