# The fuzzy time series prediction system using chaos theory and fractal dimension

 Author: Kwong, Ng-fung Title: The fuzzy time series prediction system using chaos theory and fractal dimension Degree: M.Sc. Year: 2007 Subject: Hong Kong Polytechnic University -- Dissertations.Finance -- Mathematical models.Stock price forecasting.Time-series analysis.Prediction theory. Department: Dept. of Computing Pages: x, 87 leaves : ill. ; 30 cm. Language: English InnoPac Record: http://library.polyu.edu.hk/record=b2166849 URI: http://theses.lib.polyu.edu.hk/handle/200/2008 Abstract: In finance we are often left guessing at what series of events could have led to that bubble or crash. The economies behavior of stock prices, including apparent anomalies like market crashes, emerges as the result of a lot of complicated interactions. Interactions between companies, financial agents, governments and just chance. Emergence and complexity are words, often used synonymously, that describe a new concept of complex systems whose behavior cannot be understood in a simple manner. 'Complex systems' are systems with many interacting parts, in which simple rules (which specify how the system evolves) lead to complicated and unpredictable behavior. Thus complexity, like chaos theory and fractal dimension, it essentially describes the variation with a structure formed by a complex system or the degree to which such variation is present. Complexity is a more interesting kind of variation and one that is difficult to quantify. In addition, contemporary research takes the view financial time series prediction problems are highly complex and even chaotic and cannot be successfully modelled using classical non-linear models. However, there is an estimation of fractal dimension and numerical algorithm of chaos theory which are not completely accurate. For this reason, the new method of fuzzy estimation with fractal dimension that incorporates multi vector autoregressive process with chaotic signal has been proposed to solve the non-liner time series prediction problem. Chaos theory and fractal dimension are great achievement in the understanding of the mathematical principle at work in our universe. It shows us how under certain conditions, the complex system can behave predictably. The new approach was applied to the problem of Hong Kong Heng Sang Index (HSI) prediction involving the opening, closing, intraday-high, intraday-low prices and turnover. The experiment showed that the new approach is more accurate than the other contemporary non-linear time series models such as MLP, RBF, SVM and VAR. The solution is to implement fuzzy estimation with fractal dimension based on the paradigm of deterministic chaos and time series analysis to solve the nonlinear stock prediction problem.

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