SSA for monitoring structural stability of time series

One of the important areas where SSA can be very efficient is change-point detection, or monitoring structural stability of time series. sin with change in frequency

Assume that the observations x1,x2, ... of the series arrive sequentially in time and we apply the Basic SSA to the observations at hand. Then we can monitor the distances from the sequence of the trajectory matrices to the r-dimensional subspaces we construct and also the distances between these r-dimensional subspaces. Significant changes in any of these distances may indicate on a change in the mechanism generating the time series. Note that this change in the mechanism does not have to be a change in mean.

For a detailed description of the methodology see the references below and the web-site Change-point detection in time series.

Selected publications

  1. Moskvina V.G., Zhigljavsky A.A. (2003) An algorithm based on singular spectrum analysis for change-point detection, Communic. Statist. - Simulation and Computation, v. 32, No. 2, 319-352.
  2. Golyandina N.E., Nekrutkin V.V., Zhigljavsky A.A. (2001) Analysis of Time Series Structure: SSA and related technique, Chapman & Hall / CRS, Boca Raton, Chapter 3.