Scaling analysis of price by multi-scale Shannon entropy

Multi-scale behaviors emerge in financial markets as complex systems. In this study, we intended to employ multi-scale Shannon entropy to trace the information transition of these phenomena, at different levels of Tehran stock market index (TEDPIX). The obtained results show that, in various magnitude scales and time scales, entropy Granger-causes TEDPIX index in terms of linear and nonlinear aspects. The results revealed that Granger causalities exist between entropy and TEDPIX. The causalities were linear in monthly (noise), quarterly (noise), semi-yearly (noise) and yearly (useful information) time spans; on the other hand, in quarterly (useful information) time span, the causalities were nonlinear. In this regard, one can conclude that entropy would be able to predict the market's behavior.