Time series analysis of geological data

Time series analysis is being applied to the following geological data: tree rings, Sr isotope data for Phanerozoic seawater, and the El Nino phenomenon. First the data are treated by ARIMA models that enable, for stationary time series, to construct a stochastic model that can be utilized to forecast future values of the series. The subsequent R/S analysis allows detection of short or long range dependence in the data, furthermore it can also distinguish random from non-random series. It has been applied for El Nino data as well, as to tree rings. For El Nino events we obtain evidence of the presence of "cycles" of nearly 30 years. In the case of tree ring width, their increments are independent random variables. The next technique, Neural Network analysis is a deterministic approach which overcomes the restriction of the ARIMA model and permits the reconstruction of the function that gives rise to the data series. We also outline the last approach, the Local Methods, which takes into account the topological structure of the data and enables predictions that approximate the evolution of a dynamical system generating the data. The long range component in the tree ring width data, as well as in the (Sr) isotope data, has been corrected for by first order subtraction in order to apply the ARIMA model. In these cases the Neural Network approach gives the same past predictions as the ARIMA model. The major contributions of our statistical approach for geological applications are the following: (1) recognition of qualitative changes within a given dataset, (2) evaluation of the (in)dependency of increments, (3) characterization of the random process that describes the evolution of the data, (4) recognition of cycles.