Testing astronomically tuned age models

Astrochronology is fundamental to many paleoclimate studies, but a standard statistical test has yet to be established for validating stand-alone astronomically tuned time scales (those lacking detailed independent time control) against their astronomical insolation tuning curves. Shackleton et al. (1995) proposed that the modulation of precession's amplitude by eccentricity can be used as an independent test for the successful tuning of paleoclimate data. Subsequent studies have demonstrated that eccentricity-like amplitude modulation can be artificially generated in random data, following astronomical tuning. Here we introduce a new statistical approach that circumvents the problem of introducing amplitude modulations during tuning and data processing, thereby allowing the use of amplitude modulations for astronomical time scale evaluation. The method is based upon the use of the Hilbert transform to calculate instantaneous amplitude following application of a wide band precession filter and subsequent low-pass filtering of the instantaneous amplitude to extract potential eccentricity modulations. Statistical significance of the results is evaluated using phase-randomized surrogates that preserve the power spectrum structure of the data but have randomized amplitude modulations. Application of the new testing algorithm to two astronomically tuned data sets demonstrates the efficacy of the technique and confirms the presence of astronomical signals. Additionally, it is demonstrated that a minimal tuning approach using (at maximum) one precession cycle per ~100 kyr eccentricity cycle does not introduce systematic frequency modulations, even when a narrow band-pass filter is applied, allowing direct comparison of data amplitudes and orbital eccentricity.