Time series analysis using fractal theory and online ensemble classifiers with application to stock portfolio optimization
Lunga, Wadzanai Dalton
Neural Network method is a technique that is heavily researched and used in applications within the engineering field for various purposes ranging from process control to biomedical applications. The success of Neural Networks (NN) in engineering applications, e.g. object tracking and face recognition has motivated its application to the finance industry. In the financial industry, time series data is used to model economic variables. As a result, finance researchers, portfolio managers and stockbrokers have taken interest in applying NN to model non-linear problems they face in their practice. NN facilitates the approach of predicting stocks due to its ability to accurately and intuitively learn complex patterns and characterizes these patterns as simple equations. In this research, a methodology that uses fractal theory and NN framework to model the stock market behavior is proposed and developed. The time series analysis is carried out using the proposed approach with application to modelling the Dow Jones Average Index’s future directional movement. A methodology to establish self-similarity of time series and long memory effects that result in classifying the time series signal as persistent, random or non-persistent using the rescaled range analysis technique is developed. A linear regression technique is used for the estimation of the required parameters and an incremental online NN algorithm is implemented to predict the directional movement of the stock. An iterative fractal analysis technique is used to select the required signal intervals using the approximated parameters. The selected data is later combined to form a signal of interest and then pass it to the ensemble of classifiers. The classifiers are modelled using a neural network based algorithm. The performance of the final algorithm is measured based on accuracy of predicting the direction of movement and also on the algorithm’s confidence in its decision-making. The improvement within the final algorithm is easily assessed by comparing results from two different models in which the first model is implemented without fractal analysis and the second model is implemented with the aid of a strong fractal analysis technique. The results of the first NN model were published in the Lecture Notes in Computer Science 2006 by Springer. The second NN model incorporated a fractal theory technique. The results from this model shows a great deal of improvement when classifying the next day’s stock direction of movement. A summary of these results were submitted to the Australian Joint Conference on Artificial Intelligence 2006 for publishing. Limitations on the sample size, including problems encountered with the proposed approach are also outlined in the next sections. This document also outlines recommendations that can be implemented as further steps to advance and improve the proposed approach for future work.
Forecasting, MLP, WeakLearn