Application of the singular spectrum analysis for change-point detection in time series

Singular-spectrum analysis (SSA) is a powerful technique of time series analysis. SSA is based on a singular value decomposition of a ‘trajectory matrix’ obtained from the original time series with subsequent reconstruction of the series. A methodology of change-point detection in time series based on sequential application of the singular-spectrum analysis is proposed and studied. The underlying idea is that if at a certain time τ the mechanism generating the time series xt has changed, then an increase in the distance between the l-dimensional hyperplane spanned by the eigenvectors of the so-called lag-covariance matrix, and the M -lagged vectors (xτ+1, . . . , xτ+M ) is to be expected. Under certain conditions, the proposed algorithm can be considered as a proper statistical procedure with the moving sum of weighted squares of random variables being the detection statistic. The correlation structure of the moving sums is studied. Several asymptotic expressions for the significance level of the algorithm are compared.