Signal identification in singular spectrum analysis

This paper provides an information theoretic analysis of the signal identification problem in singular spectrum analysis. We present a signal-plus-noise model based on the Karhunen-Loève expansion and use this model to motivate the construction of a minimum description length criterion that can be employed to identify the dimension (rank) of the signal component. We show that under very general regularity conditions the criterion will identify the true signal dimension with probability one as the sample size increases. A by-product of this analysis is a procedure for selecting a window length consistent with the Whitney embedding theorem. The upshot is a modeling strategy that results in a specification that yields a signal-noise reconstruction that minimises mean squared reconstruction error. Empirical results obtained using simulated and real world data series indicate that theoretical properties presented in the paper are reflected in observed behaviour, even in relatively small samples, and that the minimum description length modeling strategy provides the practitioner with an effective addition to the SSA tool box.

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