Description Length Based Signal Detection in singular Spectrum Analysis

This paper provides an information theoretic analysis of the signal-noise separation 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 select both the window length and the signal. We show that under very general regularity conditions the criterion will identify the true signal dimension with probability one as the sample size increases, and will choose the smallest window length consistent with the Whitney embedding theorem. Empirical results obtained using simulated and real world data sets indicate that the asymptotic theory is reflected in observed behaviour, even in relatively small samples.