Singular Spectrum Analysis of Categorical Time Series Data

Charles Ronen Blum
M.S., 2010
Advisor: Jan de Leeuw
Singular Spectrum Analysis (SSA) is a non parametric method of identifying and describing key properties in time series data. The results of time series analysis allow for the understanding and prediction of a system’s variability. The motivation for SSA began in the analysis of dynamical systems for geophysical applications and out of the Karhunen Loeve (KL) transform. SSA has subsequently evolved as a powerful tool for the analysis of time series data. In this paper SSA is applied to categorical data. Multiple correspondence analysis (MCA) is an analog to principle component analysis (PCA) where the data set is categorical. Hence, at the decomposition stage of SSA, MCA is the method used as PCA would be for numerical variables. Non linear transformations such as those which are used in MCA are necessary to allow for numerical interpretation and geometric representation of non metric elements. In this paper a variation of multiple correspondence analysis using Jacobi plane rotations (jMCA) is used in comparison with the eigen() routine in R as a method of analysis. The examples used in this paper are from synthetic and real life data to provide a construct with which to test the methodology. The results may offer a new framework for visualizing categorical time series data.
2010