Time Series Concepts

Abstract

This chapter brings together a number of concepts that are essential in characterising and analysing time series models. The reader is likely to be familiar with series of observations that are ordered by time and arranged into a sequence; for example quarterly observations on GDP from 1950ql to 2009q4 (T = 240 observations). In practice we observe one set of observations, but conceptualise these as outcomes from a process that is inherently capable of replication. In order to do this, each sample point of the 240 is viewed as an outcome, or ‘draw’, from a random variable; there are, therefore, in the conceptual scheme, 240 random variables, arranged in a sequence, Y = (y₁, y₂, …, y₂₀₄), each with a sample space corresponding to the multiplicity of possible outcomes for each random variable, and a sample space for the entire sequence. In Chapter 1, this sequence was referred to as a stochastic process, where an outcome of such a process is a path function or sample path, not a single point.