36 Table 4.17 Calculation Exponential Smoothing the Population data
Population Period
n Population
actual data Population
Forecast ES Error
ABS Error Cumulatif
ABS Error MAD
2000 1
5,231,189.00 5,785,868
-554,679 554,679.27
554,679.27 277,339.64
2001 2
5,331,311.00 5,286,657
44,654 599,333.35
599,333.35 199,777.78
2002 3
5,434,293.00 5,326,846
107,447 706,780.75
706,780.75 176,695.19
2003 4
5,541,062.00 5,423,548
117,514 824,294.49
824,294.49 164,858.90
2004 5
5,652,797.00 5,529,311
123,486 947,780.87
947,780.87 157,963.48
2005 6
5,769,709.00 5,640,448
129,261 1,077,041.50
1,077,041.50 153,863.07
2006 7
5,893,738.00 5,756,783
136,955 1,213,996.57
1,213,996.57 151,749.57
2007 8
6,023,053.00 5,880,042
143,011 1,357,007.08
1,357,007.08 150,778.56
2008 9
6,149,620.00 6,008,752
140,868 1,497,875.13
1,497,875.13 149,787.51
2009 10
6,262,667.00 6,135,533
127,134 1,625,008.93
1,625,008.93 147,728.08
2010 11
6,355,112.00 6,249,954
105,158 1,730,167.31
1,730,167.31 157,287.94
6,344,596 Mean
5785868.273
4.3.10 Calculation of Exponential Smoothing
1. First step, input actual data, calculate average actual data then we will get the average
2. Put average as forecast the first time 3. The second time until the next time with calculate by ES formulation
= F
t
= F
t-1
+ α A
t-1
- F
t-1
Ft = Forecasting value period t
F
t-1
= Forecasting value period t-1 A
t-1
= Actual value forecasting value period t-1 α = smoothing constant
4. Until here, calculate about forecasting, and the next step, analysis to make sure forecasting used Mean Absolute Deviation MAD so, the calculate the error
actual data – forecasting data change the error by absolute data, the absolute
error is move symbol front of numbers, cumulative is calculation absolute error
5. The mad calculate is number cumulative in the last number divided count of all period
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37
4.3.11 Error Calculation Of Moving Average
Table 4.18 Error Calculation Of Moving Average Production
Years Actual
Production Data Forecast MA=4
Absolute deviation
Forecast MA=5 Absolute
deviation 2000
235,846,163.00 2001
246,466,479.00 2002
269,796,996.00 2003
291,526,568.00 2004
310,905,610.00 260,909,051.50 49,996,558.50
2005 345,503,222.00
279,673,913.25 65,829,308.75 270,908,363.20 74,594,858.80 2006
369,243,682.00 304,433,099.00 64,810,583.00 292,839,775.00 76,403,907.00
2007 392,661,722.00
329,294,770.50 63,366,951.50 317,395,215.60 75,266,506.40 2008
441,171,910.00 354,578,559.00 86,593,351.00 341,968,160.80 99,203,749.20
2009 468,261,988.00
387,145,134.00 81,116,854.00 371,897,229.20 96,364,758.80 2010
500,655,953.00 417,834,825.50 82,821,127.50 403,368,504.80 97,287,448.20
2011 450,687,893.25
434,399,051.00 MAD
45,068,789.33 43,439,905.10
Table 4.19 Error Calculation Of Moving Average Generated
Years Generated
Actual Data Forecast MA=4
Absolute deviation
Forecast MA=5 Absolute
deviation 2000
15,324,637.00 2001
16,014,716.00 2002
17,530,669.00 2003
18,942,597.00 2004
20,201,794.00 16,953,154.75
3,248,639.25 2005
22,449,852.00 18,172,444.00
4,277,408.00 17,602,882.60
4,846,969.40 2006
23,992,442.00 19,781,228.00
4,211,214.00 19,027,925.60
4,964,516.40 2007
25,514,082.00 21,396,671.25
4,117,410.75 20,623,470.80
4,890,611.20 2008
28,666,141.00 23,039,542.50
5,626,598.50 22,220,153.40
6,445,987.60 2009
30,426,380.00 25,155,629.25
5,270,750.75 24,164,862.20
6,261,517.80 2010
32,531,251.00 27,149,761.25
5,381,489.75 26,209,779.40
6,321,471.60 2011
29,284,463.50 28,226,059.20
MAD 2,928,446.35
2,822,605.92
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38 Table 4.20 Error Calculation Of Moving Average Consumption
Years Consumption
Actual Data Forecast MA=4
Absolute deviation
Forecast MA=5 Absolute
deviation 2000
14,522,025.00 2001
15,208,543.00 2002
15,445,816.00 2003
16,702,230.00 2004
17,931,957.00 15,469,653.50
2,462,303.50 2005
19,909,502.00 16,322,136.50
3,587,365.50 15,962,114.20
3,947,387.80 2006
21,730,193.00 17,497,376.25
4,232,816.75 17,039,609.60
4,690,583.40 2007
23,016,749.00 19,068,470.50
3,948,278.50 18,343,939.60
4,672,809.40 2008
27,748,242.00 20,647,100.25
7,101,141.75 19,858,126.20
7,890,115.80 2009
29,427,305.00 23,101,171.50
6,326,133.50 22,067,328.60
7,359,976.40 2010
31,680,704.00 25,480,622.25
6,200,081.75 24,366,398.20
7,314,305.80 2011
27,968,250.00 26,720,638.60
MAD 2,796,825
2,672,064
Table 4.21 Error Calculation Of Moving Average Population
Years Population
Actual Data Forecast MA=4
Absolute deviation
Forecast MA=5 Absolute
deviation 2000
5,231,189.00 2001
5,331,311.00 2002
5,434,293.00 2003
5,541,062.00 2004
5,652,797.00 5,384,463.75
268,333.25 2005
5,769,709.00 5,489,865.75
279,843.25 5,438,130.40
331,578.60 2006
5,893,738.00 5,599,465.25
294,272.75 5,545,834.40
347,903.60 2007
6,023,053.00 5,714,326.50
308,726.50 5,658,319.80
364,733.20 2008
6,149,620.00 5,834,824.25
314,795.75 5,776,071.80
373,548.20 2009
6,262,667.00 5,959,030.00
303,637.00 5,897,783.40
364,883.60 2010
6,355,112.00 6,082,269.50
272,842.50 6,019,757.40
335,354.60 2011
6,197,613.00 6,136,838.00
MAD 619,761
613,684
The describ in detail to calculate the error of forecasting in 2022. Next, the calculate error forecasting uses Moving Average and make sure uses MAD.
4.3.12 Calculation of ARIMA
