A Comparison of Two SSA Approaches

Jean Qian Wang
M.S., 2009
Advisor: Jan de Leeuw
Singular Spectrum Analysis (SSA) is still a relatively new method in statistics though numerous studies have employed this technique in a variety of appli- cations. It is similar to the extensively used method of Principal Component Analysis (PCA) in which the variables are being analyzed as lagged versions of a single time series. SSA is a nonparametric technique and it can isolate trends, seasonality and also noises. The idea was originally proposed by Broomhead and King [2] to extract qualitative dynamics from experimental time series during the 1980s. Ghil and associates realized that SSA can be used as a time-and-frequency domain method for time series analysis and they further investigated the properties and applications of SSA. A software called kSpectra Toolkit is developed based on Ghil and associates’ approach and it is used to illustrate examples. Another approach commonly known as the Caterpillar SSA method gained at- tention through the publication of Analysis of Time Series Structure: SSA and Related Structure by Golyandina, Nekrutkin and Zhigljavksy (2001). It has a corresponding software program called CaterpillarSSA which is used to illustrate examples. This paper provides an overview of the SSA methodology and aims to demonstrate the two approaches through real-life data.
2009