a) If the end-points are ignored, we obtain the following
results:
|
Year |
Quarter |
Obs |
Simple MA |
Centred MA |
| 1 |
1 |
99 |
|
|
|
|
|
|
|
| 1 |
2 |
88 |
|
|
|
|
|
97.75 |
|
| 1 |
3 |
93 |
|
100.375 |
|
|
|
103 |
|
| 1 |
4 |
111 |
|
105.5 |
|
|
|
108 |
|
| 2 |
1 |
120 |
|
110.25 |
|
|
|
112.5 |
|
| 2 |
2 |
108 |
|
114.875 |
|
|
|
117.25 |
|
| 2 |
3 |
111 |
|
119.625 |
|
|
|
122 |
|
| 2 |
4 |
130 |
|
124.375 |
|
|
|
126.75 |
|
| 3 |
1 |
139 |
|
129.25 |
|
|
|
131.75 |
|
| 3 |
2 |
127 |
|
134.5 |
|
|
|
137.25 |
|
| 3 |
3 |
131 |
|
139.875 |
|
|
|
142.5 |
|
| 3 |
4 |
152 |
|
145.125 |
|
|
|
147.75 |
|
| 4 |
1 |
160 |
|
150.125 |
|
|
|
152.5 |
|
| 4 |
2 |
148 |
|
154.75 |
|
|
|
157 |
|
| 4 |
3 |
150 |
|
|
|
|
|
|
|
| 4 |
4 |
170 |
|
|
b)I Because the centered moving average (CMA) contains no
seasonality and no or little irregularity, the seasonal component
may be estimated by
For example,Seasonal component
=93/100.375=0.9265 and calculate other values
|
Obs |
Centred MA |
Seasonal component |
| 93 |
100.375 |
0.926525529 |
| 111 |
1055 |
0.10521327 |
| 120 |
110.25 |
1.088435374 |
| 108 |
114.875 |
0.940152339 |
| 111 |
119.625 |
0.927899687 |
| 130 |
124.375 |
1.045226131 |
| 139 |
129.25 |
1.075435203 |
| 127 |
134.5 |
0.944237918 |
| 131 |
139.875 |
0.936550492 |
| 152 |
145.125 |
1.047372954 |
| 160 |
150.125 |
1.065778518 |
| 148 |
154.75 |
0.95638126 |
c) End points ignored. Other approaches are possible.
