Time series analysis using fractal theory and online ensemble classifiers

Fractal analysis is proposed as a concept to establish the degree of persistence and self-similarity within the stock market data. This concept is carried out using the rescaled range analysis (R/S) method. The R/S analysis outcome is applied to an online incremental algorithm (Learn++) that is built to classify the direction of movement of the stock market. The use of fractal geometry in this study provides a way of determining quantitatively the extent to which time series data can be predicted. In an extensive test, it is demonstrated that the R/S analysis provides a very sensitive method to reveal hidden long run and short run memory trends within the sample data. The time series data that is measured to be persistent is used in training the neural network. The results from Learn++ algorithm show a very high level of confidence of the neural network in classifying sample data accurately.