Testing for Nonlinearity and Deterministic Chaos in Monthly Japanese Stock Market Data

It has been widely recognised that the randomness of a stock market may actually be an indicator of an underlying strange attractor which has a fractal structure and supports chaotic motion. The application of non-linear methods to such financial data may indicate the presence of nonlinearities and low-dimensional chaos. These methods include rescaled range (R/S) analysis, correlation dimension calculation and estimation of Lyapunov exponents. This study presents a preliminary analysis of these tests when applied to the monthly TOPIX data of the Tokyo Stock Exchange. Although there are a number of limitations for applied non-linear methods such as the presence of noise and limited data size, the results indicate the presence of nonlinearities and the long memory effect in the observed data set. In order to complement these methods, neural networks are used for non-linear modelling and the prediction of the TOPIX data. The results can serve as an additional evidence of a deterministic system by givig accuracy estimates for short-term prediction.