Chaotic analysis of BIST 100 return time series and short-term predictability with ANFIS

Abstract

The BIST 100 index is used to evaluate the success of the highest 100 shares in terms of criteria such as free float rate, transaction volume and market value. In this paper, it is aimed to determine whether the BIST 100 returns have a chaotic structure and short term predictability. First of all, using BIST 100 price index data between 02.01.2008 and 02.01.2018, BIST 100 returns were obtained. Using the optimal delay time and embedding dimension, the phase space required for chaos analysis was reconstructed. Then, the correlation dimension of the chaotic attractor in the new phase space obtained for this return series was calculated. BDS (Brock, Dechert and Scheinkman) test was used to determine whether the BIST 100 structure was linear. However, the Hurst exponential coefficient was determined by the transformed width method to determine whether the series had long term memory. As a result of positive Lyapunov exponent of return series, it was determined whether this series showed chaotic behavior. Following the chaos analysis, BIST 100 index was estimated by ANN and ANFIS model. The outputs of the model with the lowest error value are transformed into return series, and the estimated values of the BIST 100 returns are obtained.