Characterizing Complexity and Self-Similarity Based on Fractal and Entropy Analyses for Stock Market Forecast Modelling

Abstract

Complex systems constitute components that interact with one another and involve phenomena which are not always easy to understand in terms of their components and interactions. Alternative mathematical models have been developed so that the users’ tasks can be facilitated and an actual assistance can be provided for decision-making processes in case of every encountered incident which requires critical decision-making. Within this framework, financial systems can be regarded as complex systems with their volatile and vulnerable nature along with various parameters and interactions involved. Forecasting shifts in stock indices is crucial to validate the potential strategies of monetary mechanisms. Therefore, forecasting is an essential step in financial decision-making to manage data selection and attain robust prediction. Our purpose is to optimize the stock indices’ forecasting model in the stock indices dataset, constructed from the daily values. The following steps were applied to demonstrate the critical significance of Hurst exponent (HE) computed by Rescaled Range (R/S) fractal analysis when used as indicator in conjunction with Shannon entropy (SE) and Renyi entropy (RE) for the future forecasting ability of the stock indices. With this aim, the following stages were performed with indicators obtained from the applications and added into the dataset in the respective order. The first stage consists of: i) HE indicator, ii) Entropy based SE and RE indicators, iii) HE, SE and RE indicators. As the second stage, stock indices day-to-day valuation was evaluated using Multi Layer Regression (MLR), Support Vector Regression (SVR) and Feed Forward Back Propagation (FFBP) algorithms, applied for each indicator for comparative analysis. When compared with earlier works, no relevant work exists in the literature in which the algorithms and above-mentioned indicators have been used in conjunction with one another. This paper, through the multistage methodology and proposed model, demonstrates that HE is obviously a significant and critical determining indicator compared to RE and SE indicators for forecasting purposes. Consequently, experimental results demonstrate the accuracy and applicability of the proposed method. Thus, this study attempts to illustrate a new frontier in domains concerning critical decision-making processes in non-linear, dynamic, and volatile environments.