Time series decomposition and analysis in a study of oxygen isotope records

Some methodological developments in Bayesian time series analysis are discussed and illustrated in analyses of an oxygen isotope record of some geological interest. The developments include the implementation of Bayesian simulation analyses of auto-regressions, and state-space autoregressions, with a particular focus on spectral characteristics; various such analyses are summarised. A useful time series decomposition result is developed and illustrated in connection with exploring latent cyclical components in the time series; though almost transparent and evidently very useful in practical time series analysis, this decomposition method does not seem to have surfaced signi cantly in the literature to date. Analyses incorporating additive time series outlier components are discussed, as are questions of time variation in time series parameters and structure.