Singular Spectrum Analysis for Time Series

Singular spectrum analysis (SSA) is a technique of time series analysis and forecasting. It combines elements of classical time series analysis, multivariate statistics, multivariate geometry, dynamical systems and signal processing. SSA aims at decomposing the original series into a sum of a small number of interpretable components such as a slowly varying trend, oscillatory components and a ‘structureless’ noise. It is based on the singular-value decomposition of a specific matrix constructed upon time series. Neither a parametric model nor stationarity-type conditions have to be assumed for the time series; this makes SSA a model-free technique. The commencement of SSA is usually associated with publication of the papers [1,2] by Broomhead and King. Nowadays SSA is becoming more and more popular, especially in applications. There are several hundred papers published on methodological aspects and applications of SSA, see [3–7] and references therein. SSA has proved to be very successful, and has already become a standard tool in the analysis of climatic, meteorological and geophysical time series; see, for example, [4-6]. More recent areas of application of SSA include engineering, medicine, econometrics and many other fields. Most recent developments in the theory and methodology of SSA can be found in [7]. We start with ‘Basic SSA’, which is the most common version of SSA.