Monte Carlo SSA: detecting irregular oscillations in the presence of colored noise

Abstract

Monte Carlo singular spectrum analysis (SSA), is illustrated using synthetic datas in three situations: 1) where there is prior knowledge of the power-spectral characteristics of the noise, a situation expected in some laboratory and engineering applications, or when the 'noise' against which the data is being tested consists of the output of an independently specified model, such as a climate model; ii) where a simple hypothetical noise model is tested, namely, that the data consists only of white or colored noise; and iii) where a composite hypothetical noise model is tested, assuming some deterministic components have already been found in the data such as a trend or annual cycle, and it needs to be established whether the remainder may be attributed to noise. The authors examine two historical temperature records and show that the strength of the evidence provided by SSA for interannual and interdecadal climate oscillations in such data has been considerably overestimated.