We show how an autoregressive Gaussian process model incorporating a time scale coefficient can be used to represent irregularly sampled geophysical time series. Selection of this coefficient, together with the order of autoregression, provides flexibility of the model appropriate to the structure of the data. This leads to a valuable improvement in the identification of the periodicities within and dependence between such series, which arise frequently and are often acquired at some cost in time and effort. We carefully explain the modeling procedure and demonstrate its efficacy for identifying periodic behavior in the context of an application to dust flux measurements from lake sediments in a region of subtropical eastern Australia. The model is further applied to the measurements of atmospheric carbon dioxide concentrations and temperature obtained from Antarctic ice cores. The model identifies periods in the glacial-interglacial cycles of these series that are associated with astronomical forcing, determines that they are causally related, and, by application to current measurements, confirms the prediction of climate warming. © 2021 John Wiley & Sons Ltd.