A Stochastic Model for Ice Core Time Series

Abstract

Ice cores provide a proxy for climatic records over a period of nearly half a million years, and are a valuable source of information about past climate changes. The deuterium content in the 1999 Lake Vostok and 2004 EPICA Dome C ice cores, and the Delta-O-18 measurement in the 2003 NGRIP ice core, are analysed and time series models are fitted. The procedure is to fit Milankovitch cycles in regression models and take residuals from these models as cycle adjusted (decycled) time series; interpolate the decycled series from Lake Vostok and EPICA to obtain evenly spaced data, at 50 and 100 years respectively (the NGRIP series is evenly spaced at 50 years); fit a fractionally differenced autoregressive moving average (FARIMA) model to the three decycled time series; and investigate the residuals. The Milankovitch cycles account for 65% of the variance in the Vostok series, 59% of the variance in the EPICA series and 74% of the variance of the NGRIP series. The spectra of the decycled time series provide evidence that fractional differencing is appropriate, and fractional differencing is followed by fitting autoregressive moving average (ARMA) models according to a minimum AIC criterion, to give FARIMA models. The fitted ARMA models were of low order (up to six coefficients), and the residuals from these FARIMA models are consistent with their being a realisation of independent random variation. However, the distribution of the residuals is noticeably non-Gaussian, which accounts for a small degree of directionality, and there is evidence of volatility. The analysis is discussed in the context of known environmental disturbances.