The appendix of Mann & Lees (1996) includes this note regarding fitting a AR(1) process to a power spectrum S(f):
A fit to S(f) will be more weighted towards the low-frequency, high amplitude portion of the spectrum than a fit to log S(f). The latter procedure may provide a preferable alternative when the dynamic range of the spectrum is large. Any significance estimates that are strongly dependent on whether the red noise background is fit to S(f) or log S(f) should not be interpreted with great confidence.
This week I’m in Potsdam working with Kira Rehfeld (the imaginary weasel slayer) and Thomas Laepple to understand the implications of this note for the detection of “significant” periodicities in palaeoclimate data. Initial results suggest that many claims of significant periodicities (including mine from Murray Canyon) should not be “interpreted with great confidence”.
All those claims of significant solar periodicities in palaeodata, how many of them merit “great confidence”? We will find out shortly – manuscript in preparation.
Next week, I’m heading northwest to Bremerhaven to discuss sea-ice reconstructions from dinocyst and diatom assemblages. It is going to be an interesting meeting.
Mann, M.E. and Lees, J.M. 1996: Robust estimation of background noise and signal detection in climatic time series. Climate Change, 33, 409-445.