Enhanced Monte Carlo SSA for Detection of Modes with Nontrivial Dynamics Embedded in Colored Noise

Milan PALUS, Institue of Computer Science AS CR, Prague

Singular spectrum analysis (SSA) is a useful tool for identification and extraction of oscillatory or other signals from noisy background. Its basic form, however, is reliable when a signal is embedded in white noise, while presence of ``colored'' noises could lead to spurious results. Recently, Monte Carlo SSA, based on so-called surrogate data technique, has been introduced in order to increase reliability of detecting signals embedded in colored noises, which are usually present in geophysical data. We propose to enhance the Monte Carlo SSA by evaluating and testing regularity of dynamics (quantified by so-called coarse-grained entropy rates, a tool suitable for characterization of complex experimental time series) of the SSA modes against the colored noise null hypothesis, in addition to the test based on variance (eigenvalues). We demonstrate that such an approach can enhance the test reliability in detection of relatively more regular dynamical modes than those obtained by decomposition of colored noises, in particular, in detection of irregular oscillations embedded in red noise. The method is demonstrated in detection of 7.8-year oscillations in historical temperature records obtained from several European locations, as well as in detection of approximately 5-year oscillations in the global temperature series.

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