Fractal structure in the S&P500: A correlation-based threshold network approach

Abstract

This research aims to analyze the S&P500 network, one of the representatives of the global financial market, based on its network fractality. The research is conducted in the following steps. At first, we propose the concept of a correlation-based threshold network based on minimum spanning tree. Secondly, we investigate the fractal dimension of threshold networks and propose suitable fractal dimension measures. Lastly, we analyze the S&P500 network based on the proposed measures and utilize them in the market prediction. Based on the results, we discover the self-similarity characteristic of the S&P500 network, where a strong effective repulsion phenomenon is detected. Furthermore, we observe the different growth patterns of S&P500 network for different combinations of fractal conditions defined by the proposed measures. Then, we utilize the measures in the prediction of the cumulative log-return of S&P500 index via a simple artificial neural network and detect the improvement of prediction performance in the long-term development of the market.