Interpolating a palaeoclimatic time series: nonlinearity, persistence and trending in the Cenozoic

Some climatic time series are available only at irregular frequencies, or may show discontinuities. This paper investigates the issues involved in interpolating the CENBEN (Cenozoic-Benthic) series, covering 68 m.y., to a regular frequency. Since no single physical model explains this data, interpolation requires fitting a statistical model on the time series itself. The properties of the synthetic series depend critically on the model used. Several methods are tried, Gaussian filters, frequency and time domain models, and a Kalman filter. The frequency domain model mainly picks up the long-term properties of the data; however, when the window is widened to accommodate movements at shorter horizons, the result is often to generate spurious cycles. This model also tends to mask out nonlinearity, while inducing greater persistence than is justified by the underlying dataset. The Gaussian filter can be set to capture either long or intermediate-term movements, but typically does not pick up high frequency variation. Time domain methods such as ARIMA models capture more of the high-frequency variations. The best result is obtained using a Kalman filter, which preserves evidence of nonlinear oscillations.