Sensitive Dependence on Initial Condition (SDIC) on the Three South East Asian Countries Capital Markets: A Comparison to Fully Deterministic and Pure Chaotic Models

Abstract

This research paper tries to detect the chaos structure on the three South East Asian Countries Capital Markets by investigating one of chaos attributes – Sensitive Dependence on Initial Condition (SDIC) - which can describe phenomenon of crisis, order and disorder. Knowledge of sensitivity to any changes or perturbation is important for understanding instability of Asia Capital Market due to the impact of future implementation of ASEAN Charter through multilateral agreement ASEAN blueprint on AFAS (ASIAN Free Trade Agreement on Services) of Financial Services. SDIC is tested through performing positive largest (maximum) Lyapunov Exponent. This research paper also compares the three South East Asian Countries Capital Markets to chosen renowned fully deterministic and pure chaos models - Logistic Equation and Henon Map. Comparing to chosen renowned pure and fully deterministic chaos models - Logistic Equation and Henon Map- will provide broad view of analysis of SDIC on STI, PSEi & JCI indices series. The capital markets of three South East Asian Countries - Indonesia, Philippine, and Singapore - are chosen. Daily return data of Capital Markets composite indices from January 01, 1991 to December 31, 2007 with 4435 points of each series are observed: Straits Times Index (STI) of Singapore Exchange, Pilipino Stock Exchange Index (PSEi) of Philippines Stock Exchange and Jakarta Composite Index (JCI) of Indonesia Stock Exchange. Since there are some different algorithms and due to limitations of each algorithm for calculating Lyapunov exponent this research paper also tries to investigate some different algorithms and their results to convince of SDIC finding. Through using different algorithms of Lyapunov Exponent testing will assure of proofing SDIC. Two different Lyapunov Exponent algorithms of Wolf et al. (1985) algorithm and of Rosenstein et al. (1993) and Kantz (1994) algorithm as our tools for testing one of chaos attributes – SDIC - are applied. The evidence of chaotic process – SDIC - is confirmed through positive largest Lyapunov Exponent in all pure chaotic models by using two different algorithms of SDIC testing. The evidence of chaotic process SDIC is confirmed in all three capital markets through Wolf algorithm. SDIC are found through Rosenstein et al. and Kantz algorithm in JCI and STI series only. Testing results of SDIC through Rosenstein et al. and Kantz algorithm for all capital market return series suggests existence of noise in capital market data series to be filtered out. Other types of algorithms for comparison are also needed for further research.