Finding structure in multivariate time series

Abstract

The scope of scientific data collection in modern projects such as the human genome project has made it effectively impossible for careful by-hand analyses of such data to be carried out. Simultaneously, the increase in computer power raises the possibility of replacing human scrutiny with computer systems that could effectively sort and filter copious data, presenting only the most salient features to researchers. This thesis details a method for combining a generalized version of the classical statistical method known as canonical correlation analysis, that possesses good computational properties, with the more recently developed multitaper spectral estimators. The developed method allows researchers to combine data from multiple experiments to generate more accurate spectral decompositions of the underlying processes involved while also giving researchers a sensitive method for finding the links between variables in the data sets. The only limitation is that the data to be analyzed must be homogeneous in certain specific ways (for example, it must contain no pronounced trends).