Chapter 1Introduction
A (discrete-time) time series is a set of observations
, which are recorded at times
stemming from a discrete and linearly ordered set
. An example of such a time series is plotted in Figure 1.1. This is the annual number of lynx fur returns for the MacKenzie River district in north-west Canada. The source is the Hudson's Bay Company, 1821–1934; see Elton & Nicholson (1942). These lynx data are discussed in many textbooks about time series analysis, to illustrate that real time series may exhibit quite complex seasonal patterns. Another famous example from the time series literature is the passenger data of Box & Jenkins (1970), which gives the monthly totals of international airline passengers (in thousands) for the period 1949–1960. These data (see Figure 1.2 for a plot) are often used to demonstrate the possible need for variance-stabilizing transformations.
Figure 1.1 Annual number of lynx fur returns (1821–1934); see Elton & Nicholson (1942).