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Stationary and non-stationary time series

Time series analysis is about the study of data collected through time. The field of time series is a vast one that pervades many areas of science and engineering particularly statistics and signal processing: this short article can only be an advertisement. Hence, the first thing to say is that there are several excellent texts on time series analysis. Most statistical books concentrate on stationary time series and some texts have good coverage of “globally non-stationary” series such as those often used in financial time series. For a general, elementary introduction to time series analysis the author highly recommends the book by (Chatfield 2003). The core of Chatfield’s book is a highly readable account of various topics in time series including time series models, forecasting, time series in the frequency domain and spectrum estimation and also linear systems. More recent editions contain useful, well-presented and well-referenced information on important new research areas. Of course, there are many other books: ones the author finds useful are Priestley (1983), Diggle (1990), Brockwell and Davis (1991), and Hamilton (1994). The book by Hannan (1960) is concise (but concentrated) and Pole et al. (1994) is a good introduction to a Bayesian way of doing time series analysis. There are undoubtedly many more books. This article is a brief survey of several kinds of time series model and analysis. Section 11.1 covers stationary time series which, loosely speaking, are those whose statistical properties remain constant over time. Of course, for many real applications the stationarity assumption is not valid. Gener-