Quadratic-Inverse Spectrum Estimates: Applications to Palaeoclimatology

This paper describes some new methods for the analysis of time series and their application to find new results in palaeoclimate. The new statistical theory includes a quadratic inverse theory for unbiased estimation of power spectra, an associated test for spectral resolution, maximum-likelihood spectrum estimates, and detailed explanations of some topics in the detection and estimation of periodic components. A new technique for estimating transfer functions is described. This methodology is used to analyse series describing global ice volume over the past 700000 years as recorded by proxy oxygen isotope ratios from deep-sea cores. We find many of the periodic components predicted by the Milankovitch theory. However, systematic departures are found from the predicted frequencies. These are accompanied by phase modulation that can be attributed to changes in the precession constant of the Earth caused by glaciation-induced changes in the Earth's principal moments. An estimate of the transfer function from ice volume to precession implies that the Earth's crust requires more than 160000 years to compensate for mass redistribution, and overcompensates with a delay of about 24000 years.