• On-line estimation;
  • Kalman filter and Kalman smoother;
  • variation decomposition;
  • local linear Gaussian model;
  • non-Gaussian state space model;
  • GISP2;


Statistical modelling of six time series of geological ice core chemical data from Greenland is discussed. We decompose the total variation into long time-scale (trend) and short time-scale variations (fluctuations around the trend), and a pure noise component. Too heavy tails of the short-term variation makes a standard time-invariant linear Gaussian model inadequate. We try non-Gaussian state space models, which can be efficiently approximated by time-dependent Gaussian models. In essence, these time-dependent Gaussian models result in a local smoothing, in contrast to the global smoothing provided by the time-invariant model. To describe the mechanism of this local smoothing, we utilise the concept of a local variance function derived from a heavy-tailed density. The time-dependent error variance expresses the uncertainty about the dynamical development of the model state, and it controls the influence of observations on the estimates of the model state components. The great advantage of the derived time-dependent Gaussian model is that the Kalman filter and the Kalman smoother can be used as efficient computational tools for performing the variation decomposition. One of the main objectives of the study is to investigate how the distributional assumption on the model error component of the short time-scale variation affects the decomposition. Copyright © 2009 John Wiley & Sons, Ltd.