Statistics and Its Interface

Volume 10 (2017)

Number 1

On perturbation stability of SSA and MSSA forecasts and the supportiveness of time series

Pages: 33 – 46



Maria Vronskaya-Robl (School of Mathematics, Cardiff University, Cardiff, Wales, United Kingdom)

Karl Michael Schmidt (School of Mathematics, Cardiff University, Cardiff, Wales, United Kingdom)


Studying the stability of Singular Spectrum Analysis (SSA) and Multivariate Singular Spectrum Analysis (MSSA) forecasts under random perturbations of the input time series, we make the empirical observation that the reconstruction kernel of SSA as a convolution filter and the forecast recurrence vector are remarkably stable both under generated Gaussian and natural non-Gaussian noise. Assuming that these elements of the forecast procedure are noise-independent, we derive concise formulae for the variance under perturbations of SSA and MSSA forecasts. We suggest a criterion of supportiveness based on the behaviour of these proxy variances under scaling of the support series. Finally, we remark on a problem of lacking scaling invariance of MSSA.


multivariate time series analysis, stability analysis, perturbation theory, forecasting

2010 Mathematics Subject Classification

Primary 15B52, 62M10. Secondary 60G25, 62M15.

Published 27 September 2016