Blind Source Separation for Compositional Time Series

Abstract

This thesis shows how blind source separation methods for time-series can be applied to compositional time series. In many applications data sets are of compositional nature, meaning that the relative values of the variables are of interest instead of the absolute ones. Blind source separation (BSS) is a popular modelling approach for multivariate time-series, since it aims to decompose them into latent sources on which univariate modelling is possible. Compositional time-series are per definition multivariate. Moreover, in their isometric-log-ratio-coordinate representation, on which the BSS models are built, they are multivariate if the number of compositions is greater than two. Therefore blind source separation is very useful for compositional time-series. Our methodology is illustrated on a real world data set: Absorption data from a stream in Lower Austria. In the study of dissolved organic matter, ratios of absorption coefficients have been used to indicate the quality of dissolved organic matter in various environments, yielding compositional time series data, on which our new method can be applied.