whenb= 0, this is the same as the white noise series. In Figure 2.2a is a plot
of a time series of this type. This specific time series was generated from the
white noise sequence in Figure 2.1 using the formula yt=et+ 0.8et–1. The cor-
relogram of the series is plotted in Figure 2.2b. In the correlogram, note that
there is a steep drop in the value after t= 1. To see why that is, let us con-
sider the time series values for the three consecutive time steps t,t+ 1, and
t+ 2.
yt=et+bet–1 (2.3)
yt+1=et+1+bet
yt+2=et+2+bet+1
18 BACKGROUND MATERIAL
FIGURE 2.2A MA(1) Series.
10 30 50 70 90
–3
–2
–1
0
1
2
3
FIGURE 2.2B MA(1) Series ACF.
0510 15 20
Lag
–0.2
–0.0
0.2
0.4
0.6
0.8
1.0
Auto Correlation