Homework 10

The Strontium data file linked to the course homepage contains a short time series of measurements on a strontium isotope ratio (Sr87 to Sr86) derived from seawater measurements from the Indian ocean. These data represent approximate levels of the strontium ratio at equal spacings of 3kyr (3000 years); thus the time interval represents approximately the last 450,000 years. They are of interest as climatic indicators, driven by changes in seawater chemistry due, largely, to input from the weathering of continental crust. The series has been preprocessed to remove an underlying trend. Of interest in the application context of this series are inferences about underlying latent structure in the series, and particularly about quasi-cyclical behaviour related to patterns of climatic change. To explore this, fit reference analyses of AR(p) models and explore the component root/eigenstructure and corresponding decompositions of the data. You can use my skeleton S-Plus code for this. You should explore various possible AR models and aim to summarise your exploration with some commentary and graphics from a "final" analysis, as well as a general overview of your explorations. You might, for example, include informal examination of questions about