Which Pure Chaos Model Will Describe IDX Composite (Jakarta Composite Index (JCI) of Indonesia Stock Exchange (IDX)) Better?

Abstract

Is it possible to approach a time series by modeling it through a predicted model of a fully deterministic and pure chaotic model? IDX Composite (Jakarta Composite Index) time series will be examined whether it can be explained by one of renowned fully deterministic and pure chaotic models or their variants.Daily return data of Jakarta Composite Index (JCI) of Indonesia Stock Exchange from January 05, 1988 to June 30, 2009 are observed. “Compass rose” pattern of scatter diagram will be observed. Chosen renowned fully deterministic and pure chaotic models are Logistic map equation, Henon map and Mackey Glass delay differential equation which have low dimensionality. The initial value return of JCI is applied to three chaotic models to create the chaotic series that have the same initial conditions with JCI return. The length of data points of chaotic series is set to be the same length of JCI series.In addition to the scatter diagram comparisons other three tests are applied to all chosen chaos models and JCI series. BDS Statistic, R/S Analysis and Lyapunov Exponent of Wolf et al (1985) algorithm are the used test tools to investigating some characteristics of chaotic system: nonlinear, persistence (fractal) and sensitive dependence on initial condition. Performance results of chaos characteristic tests on chosen models will be explored to approach predicted chaotic model of JCI. The objective of this research result is to find - if any - the best approached and fitted chaos model to describe JCI better as an approximation model. Understanding of chaotic attributes - nonlinear, fractal and sensitive dependence on initial condition - will provide better analysis of non periodicity of crisis on Indonesia Stock Exchange as well as of phenomenon of crisis, order and disorder on Indonesia Stock Exchange.