1. Case study 3: SEASONAL ARIMA MODEL
Average monthly temperatures in Dubuque, Iowa, January 1964 – December 1975
Reference: Cryer [1986], pg. 268.

2. Example 1: Average monthly temperatures in Dubuque, Iowa (January 1964 – December 1975) … [Cryer [1986], pg. 268]
Year
Jan
Feb
Mar
Apr
May
Jun
Jul
Aug
Sept
Oct
Nov
Dec
1964
24.7
25.7
30.6
47.5
62.9
68.5
73.7
67.9
61.1
48.5
39.6
20.0
1965
16.1
19.1
24.2
45.4
61.3
66.5
72.1
68.4
60.2
50.9
37.4
31.1
1966
10.4
21.6
44.7
53.2
68.0
68.2
60.7
50.2
37.2
24.6
1967
21.5
14.7
35.0
48.3
54.0
69.6
65.7
60.8
49.1
33.2
26.0 …
1973
22.5
42.3
45.2
55.5
68.9
72.3
62.5
55.6
38.0
20.4
1974
17.6
20.5
34.2
49.2
54.8
63.8
74.0
57.7
50.8
36.8
25.5
1975
19.6
41.3
61.8
72.0
57.3
52.5
40.6
26.2
Low temperature
Medium temperature
High temperature

3. Example 1: IDENTIFICATION step [stationary, ACF and PACF]
Nonstationer (seasonal) time series
Dies down slowly

4. Example 1: IDENTIFICATION step … Seasonal Difference [Zt = Yt – Yt-12]
Zt  MA(1)12 or
Yt  IMA(1,1)12
Stationary time series
ACF
PACF
Cuts off after lag 12
Dies down at seasonal lag

5. Example 1: ESTIMATION and DIAGNOSTIC CHECK step
Yt = Yt-12 + at – at-12
Estimation and Testing parameter
Diagnostic Check (white noise residual)

6. Example 1: DIAGNOSTIC CHECK step … [Normality test of residuals]

7. Example 1: FORECASTING step [MINITAB output]

8. Example 1: Comparison Actual v.s. Forecast …
Forecast data
Upper
Actual data
Lower