Seasonal Technique
1. What we have
Transformer table
Transformer
YEAR
January
February
March
April
May
June
July
August
September
October
November
December
SUM OF EACH YEAR
1600
1400
1200
1000
800
600
400
200
0
Transformer sum of each year
Year
Transformer
1(2006)
9614
2(2007)
10784
3(2008)
11884
4(2009)
13002
5(2010)
13214
2006 2007
2008
2009
2010
779
845
857
917
887
802
739
881
956
892
818
871
937
1001
997
888
927
1159
1142
1118
898
1133
1072
1276
1197
902
1124
1246
1356
1256
916
1056
1198
1288
1202
708
889
922
1082
1170
695
857
798
877
982
708
772
879
1009
1297
716
751
945
1100
1163
784
820
990
998
1053
9614 10784 11884 13002 13214
2006
2007
2008
2009
2010
Transformer
15000
10000
5000
0
Transformer
Then we want to forecast total transformer in 2011 by using Linear Trend Equation
t
Sum(Σ)
t^2
1
2
3
4
5
15
y
1
4
9
16
25
55
ty
9,614
10,784
11,884
13,002
13,214
58,498
9,614
21,568
35,652
52,008
66,070
184,912
From equation
Result:
B=941.8
A=8874.2
Equation: Y=8874.2+941.8t
Then try to forecast 2010 from this equation and check whether it works or not
As the result, we get Y=8874.2+941.8(5) = 13,583
Therefore, the forecast of total transformer in 2010 is 13,583 which is not far from the actual (13,214)
Use Seasonal Index to forecast each month
887
AVG(20062009)
849.50
Per
month
943.42
Seasonal
Index
0.90
1,019.23
(actualforecast)^2
17,486.07
956
892
844.50
943.42
0.90
1,013.24
14,698.14
937
1,001
997
906.75
943.42
0.96
1,087.92
8,267.14
927
1,159
1,142
1,118
1,029.00
943.42
1.09
1,234.60
13,595.57
898
1,133
1,072
1,276
1,197
1,094.75
943.42
1.16
1,313.49
13,569.28
June
902
1,124
1,246
1,356
1,256
1,157.00
943.42
1.23
1,388.18
17,470.27
July
916
1,056
1,198
1,288
1,202
1,114.50
943.42
1.18
1,337.18
18,274.56
August
Septembe
r
October
708
889
922
1,082
1,170
900.25
943.42
0.95
1,080.13
8,077.51
695
857
798
877
982
806.75
943.42
0.86
967.94
197.59
708
772
879
1,009
1,297
842.00
943.42
0.89
1,010.24
82,233.38
November
716
751
945
1,100
1,163
878.00
943.42
0.93
1,053.43
12,005.72
December
SUM OF
YEAR
784
820
990
998
1,053
898.00
943.42
0.95
1,077.43
596.60
9,614
10,784
11,884
13,002
13,214
11,321.00
YEAR
2006
2007
2008
2009
2010
January
779
845
857
917
February
802
739
881
March
818
871
April
888
May
2010(F)
13,583.00
Sum (Σ)
(actualforecast)^2
MSE
206,471.83
18,770.17
Moving Average (3 Months)
YEAR
2009
January
917
February
956
March
1,001
April
1,142
May
1,276
June
1,356
July
1,288
August
1,082
September
877
October
1,009
November
1,100
December
998
(actual2010 2010(forecast)
forecast)^2
887
1,035.67
22,101.78
892
995.00
10,609.00
997
925.67
5,088.44
1,118
925.33
37,120.44
1,197
1,002.33
37,895.11
1,256
1,104.00
23,104.00
1,202
1,190.33
136.11
1,170
1,218.33
2,336.11
982
1,209.33
51,680.44
1,297
1,118.00
32,041.00
1,163
1,149.67
177.78
1,053
1,147.33
8,898.78
Sum (Σ) (actualforecast)^2
231,189.00
MSE
21,017.18
Weight Moving Average (3 Months)
We use
Weight = 0.5 for the last month
Weight = 0.3 for the last 2nd month
Weight = 0.2 for the last 3rd month
YEAR
2009
January
917
February
956
March
1,001
April
1,142
May
1,276
June
1,356
July
1,288
August
1,082
September
877
October
1,009
November
1,100
December
998
(actual2010 2010(forecast)
forecast)^2
887
1,030.80
20678.44
892
962.90
5026.81
997
911.70
7276.09
1,118
943.50
30450.25
1,197
1,036.50
25760.25
1,256
1,133.30
15055.29
1,202
1,210.70
75.69
1,170
1,217.20
2227.84
982
1,196.80
46139.04
1,297
1,082.40
46053.16
1,163
1,177.10
198.81
1,053
1,167.00
12,996.00
Sum (Σ) (actualforecast)^2
211,937.67
MSE
19,267.06
We use Mean Squared Error (MSE) to measure accuracy for each technique
MSE of Seasonal Index Technique = 18,770.17
MSE of Moving Average (3 Months) = 21,017.18
MSE of Weight Moving Average (3 Months) = 19,267.06
MSE of Seasonal Index Technique is the lowest, THE BEST then we try to apply to 2011
For the Equation: Y=8874.2+941.8t
Put t=6 in the equation
Year
Transformer
1(2006)
9614
2(2007)
10784
3(2008)
11884
4(2009)
13002
5(2010)
13214
6(2011F)
14525
Then use 14525 as the sum of transformer in 2011 and use seasonal index then we will get this table
YEAR
January
February
March
April
May
June
July
August
September
October
November
December
2006 2007 2008
779
845
857
802
739
881
818
871
937
888
927 1159
898 1133 1072
902 1124 1246
916 1056 1198
708
889
922
695
857
798
708
772
879
716
751
945
784
820
990
Transformer
2009 2010 Seasonal Index
917
887
956
892
1001
997
1142 1118
1276 1197
1356 1256
1288 1202
1082 1170
877
982
1009 1297
1100 1163
998 1053
0.90
0.90
0.96
1.09
1.16
1.23
1.18
0.95
0.86
0.89
0.93
0.95
Sum
2011(Forecast)
1,089.92
1,083.51
1,163.37
1,320.22
1,404.58
1,484.45
1,429.92
1,155.03
1,035.07
1,080.30
1,126.49
1,152.15
14,525.00
For the 3rd question What qualitative factors can be considered to improve the forecast experience?
Don’t know LOL
PS. I use only the first exhibit