Stationary Time Series

Abstract

In this chapter we introduce some basic ideas of time series analysis and stochastic processes. Of particular importance are the concepts of stationarity and the autocovariance and sample autocovariance functions. Some standard techniques are described for the estimation and removal of trend and season-ality (of known period) from an observed series. These are illustrated with reference to the data sets in Section 1.1. Most of the topics covered in this chapter will be developed more fully in later sections of the book. The reader who is not already familiar with random vectors and multivariate analysis should first read Section 1.6 where a concise account of the required background is given. Notice our convention that an n-dimensional random vector is assumed (unless specified otherwise) to be a column vector X = (X ₁, X ₂,..., X _n )′ of random variables. If S is an arbitrary set then we shall use the notation S ⁿ to denote both the set of n-component column vectors with components in S and the set of n-component row vectors with components in S.