Automated mathematical modelling for financial time series prediction using fuzzy logic, dynamical systems and fractal theory

Abstract

We describe a new method for performing automated mathematical modelling for financial time series prediction using fuzzy logic techniques, dynamical systems and fractal theory. The main idea is that using fuzzy logic techniques we can simulate and automate the reasoning process of human experts in mathematical modelling for financial time series prediction. Our new method for automated modelling consists of three main parts: time series analysis, developing a set of admissible models, and selecting the best model. Our method for time series analysis consists of using the fractal dimension of a set of points as a measure of the geometrical complexity of the time series. Our method for developing a set of admissible dynamical systems models is based on the use of fuzzy logic techniques to simulate the decision process of the human experts in modelling financial problems. The selection of the best model for financial time series prediction (FTSP) is done using heuristics from the experts and statistical calculations. This new method can be implemented as a computer program and can be considered an intelligent system for automated mathematical modelling for FTSP.