Frequency selection in paleoclimate time series: A model‐based approach incorporating possible time uncertainty

A key aspect of paleoclimate time series analysis is the identification of frequency behavior. Commonly, this is achieved by calculating a power spectrum and comparing this spectrum with that of a simplified model. Traditional hypothesis testing method can then be used to find statistically significant peaks that correspond to different frequencies. Complications occur when the data are multivariate or suffer from time uncertainty. In particular, the presence of joint uncertainties surrounding observations and their timing makes traditional hypothesis testing impractical. In this paper, we reexpress the frequency identification problem in the time domain as a variable selection model where each variable corresponds to a different frequency. We place this problem in a Bayesian framework that allows us to place shrinkage prior distributions on the weighting of each frequency, as well as include informative prior information through which we can take account of time uncertainty. We validate our approach with simulated data and illustrate it with analysis of mid‐ to late Holocene water table records from two sites in Northern Ireland—Dead Island and Slieveanorra. Both case studies also show the extent of the challenges that researchers may face. We therefore present one case that shows a good model fit with a clear frequency pattern and the other case where the identification of frequency behavior is impossible. We contrast our results with that of the extant methodology, known as REDFIT.