The Chaotic Analysis of Financial Time Series: Classification of Foreign Exchange Rates Series via Their Exponential Divergence Curves

In this work we evaluate the notable results of four interrelated successive works ([2–5]) dealing with the classification properties and temporal evolution of foreign exchange rates series (ForEX). The main idea in these works can be conceptualized through the behavior of the exponential divergence curves of financial time series that make a clear distinction for both spatial (between countries) and temporal (between different time segments of ForEX series) patterns. Despite being a well known concept, the use of exponential divergence curves for the classification of ForEX series is a relatively new concept. The classification procedure discussed here is based on the surrogate testing procedure where the statistics gathered from the original system is compared to the ones that are gathered from a completely randomized system. Our new researches on the data during the period of present economic recession (January 2008-October 2009) by calculating the largest Lyapunov exponent (LLE) has shown that the earlier classification of countries based on LLE’s holds true. By a similar approach, we have investigated the temporal evolution of the exponential divergence distance metrics where we have developed a computationally consistent procedure to obtain the metrics for various ForEX series. Finally we obtained strong indicators for the distinction of the temporal evolution of ForEX series for developed and developing countries. We discuss possible reasons for the existing separation of temporal structures.