We present a Monte Carlo based method for the determination of errors associated with frequency spectra produced by the CLEAN transformation of Roberts et al. (1987). The Monte Carlo procedure utilises three different types of simulation involving a data stripping operation and the addition of white and red noise to the analysed time series. The simulations are tested on both synthetic and real data sets demonstrating the ability of the procedures to extract coherent information from time series characterised by the low signal-to-noise-ratio that is typical of many palaeoclimatic records. Significance levels derived for the Monte Carlo spectra of four time series from the Vostok ice core are utilised in the study of eccentricity components contained within the palaeoclimatic archive since ∼420 ka. Inversion of the Vostok frequency spectra into the time domain reveals the differing influence of orbital parameters in the palaeoclimatic proxy records as well as the relative magnitudes of the eccentricity components contained in the time series of greenhouse gas concentration, ice volume and local temperature.