Change-point detection for a transient change and high-dimensional covering

The Singular Spectrum Analysis (SSA) technique is a novel and powerful technique of time series analysis incorporating elements of classical time series analysis, multivariate statistics, multivariate geometry, dynamical systems and signal processing. The main purpose of SSA is to decompose an original series of observations (indexed by time) into a sum of series, so that each component in this sum can be identified as either a trend, periodic or quasi-periodic component (perhaps amplitude-modulated), or noise. This is followed by a reconstruction of the original series using selected components. SSA is a useful tool which can be used for solving the following problems: finding trends of different resolution; smoothing a noisy or complex time series; extracting seasonality components; simultaneously extracting cycles with small and large periods from a time series; extracting periodicities with varying amplitudes; simultaneously extracting complex trends and periodicities; finding structure in short time series; forecasting and detecting change-points in a time series (amongst others).