The analysis of indexed astronomical time series – I. Basic methods

Abstract

The application of autoregressive moving-average (ARMA) modelling to discrete time or indexed data is discussed. An essential tool is the autocorrelation function, and its utility is demonstrated with some examples. Extensions of the ARMA models to include non-stationarity are described; variability in both the series mean and the ARMA coefficients can be dealt with by recursively calculated or ‘state space’ models. A number of tests for non-stationarity of the series mean are described in detail. Particular attention is devoted to the effects of serial dependence of the data. A problem with the O – C (observed – calculated) method as traditionally used in astronomy is pointed out. Non-stationarity in the data variance and the identification of outlying observations are dealt with at some length. Tests designed to discriminate between different outlier types are described. Brief mention is made of a few other important topics, particularly non-linearity and data transformation.