Wavelet Analysis of Time Series and its Application to Epidemiological Data

Abstract

<p>Wavelets offer many unique tools for data analysis. The first part of this thesis is an exposition of wavelet transforms and many of the associated tools for the analysis of time series. Specifically, wavelet denoising, wavelet power spectra and the detection of singularities are examined in detail. The second half of the thesis consists of a wavelet perspective on epidemiological time series. Focus is placed on analysing the incidence of infection of measles in Ontario, Canada. Other incidence data sets are also considered: chicken pox, rubella, and whooping cough. We show that wavelet analysis can be used to evaluate mathematical models in epidemiology by testing them against observed data, as well as to characterize the fine scale structure of the data. With some serendipity, it is also shown that distinct data sets for the same disease are characterized by a similar multifractal signature.</p>