Prediction methods for 1/f^β processes with application to the analysis of stride interval time series

摘要

The power law in the frequency spectrum S(f)=1/f^β allows for a good representation of the various time evolutions and complex interactions of many physiological processes. The spectral exponent β can be interpreted as the degree of fractal characteristic which in turn makes it some sort of biomarker that gives an idea of the relative health of an individual. This thesis presents a thorough investigation of prediction of the fractal nature of the process with specific consideration given to experimentally measured gait stride interval time series. The goal is to consider the accuracy of several time series prediction methods such as the neural networks, regression trees and bagged regression trees learning method. To test these methods we simulated stride intervals time series as 1/f^β processes. This investigation is to complement previous analyses on predicting the process with which this study compared. It was shown as result of the research that the greatest number of points one can accurately predict is between five and fifteen using the regression tree, the feedforward neural network and the AR model.