Distinguishing modulated oscillations from coloured noise in multivariate datasets. Climate Dynamics.


Extended empirical orthogonal functions (EEOFS), alternatively known as multi- channel singular systems (or singular spectrum) analysis (MSSA), provide a natural method of extracting oscillatory modes of variability from multivariate data. The eigenfunctions of some simple non-oscillatory noise processes are, however, also solutions to the wave equation, so the occurrence of stable, wave-like patterns in EEOF/MSSA is not sufficient grounds for concluding that the data exhibits oscillations. We present a generalisation of the "Monte Carlo SSA" algorithm which allows an objective test for the presence of oscillations at low signal-to-noise ratios in multivariate data. The test issimilar to those used in standard regression, examining directions in state-space to determine whether they contain more varaince than would be expected if the noise null-hypothesis were valid. We demonstrate the application of the test to the analysis of interannual variability in tropical Pacific sea-surface temperatures.

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