
399Dependent Stochastic Processes and Time Series
Time
1700 1750 1800 1850 1900 1950 2000
−3
−1
1
3
0510 15 20
0.0
0.4
0.8
Lag
ACF of residuals
246810
0.0
0.4
0.8
p-values for Ljung−box statistic
FIGURE 11.22 Diagnostic of ARIMA(9, 1, 0).
Time
1700 1750 1800 1850 1900 1950 2000
−50
0
50
100
150
Data
Pred
Upper and lower
Data
Pred
Upper and lower
1960 1980 2000 2020
−50
0
50
100
150
200
FIGURE 11.23 Sunspots forecast with 22 years horizon.