Final_1.pdf

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