n F
X MSE
t t
2
8 2.207,095
155.134.00
MSE =
19.391.750.275,887
4.1.2 Pemulusan Eksponensial Ganda
Pada peramalan dengan metode ini digunakan alpha 0.1, 0.6, dan 0.9. Besarnya peramalan forecast bila digunakan alpha 0.1 adalah sebagai berikut.
Tahun 2000 : S
I t
: ditentukan oleh PDRB tahun pertama, yaitu sebesar 915.998,27 S
II t
: ditentukan juga oleh besarnya PDRB tahun pertama, yaitu sebesar 915.998,27. a
t
: belum bisa ditentukan karena merupakan data pertama. b
t
: belum bisa ditentukan karena merupakan data pertama. F
t+m
: peramalan forecasttahun kedua F
2001
ditentukan oleh besarnya PDRB tahun pertama, yaitu sebesar 915.998,27
Tahun 2001 : X
t
= 1.060.634,35 a.
1
1
t I
t t
I
S X
S
= 0.1 x 1.060.634,35 + 1 – 0.1 915.998,27
= 106.063,435 + 0.9 915.998,27 = 106.063,435 + 824.398,443
= 930.461,878
Universitas Sumatera Utara
b.
1
1
t II
t I
t II
S S
S
= 0.1 x 930.461,878 + 1 – 0.1 915.998,27
= 93.046,188 + 0.9 915.998,27 = 93.046,188 + 824.398,443
= 917.444,631
c. a
t
= 2 S
I t
- S
II t
= 2 930.461,878 – 917.444,631 = 1.860.923,756 - 917.444,631
= 943.479,125 d.
t II
t I
t
S S
b
1 =
1 .
1 1
.
930.461,878 - 917.444,631
= 9
. 1
. 13.017,247
= 1.446,361 e. Forecast Peramalan
F
t+m
= a
t
+ b
t
m F
2001+1
= 943.479,125 + 1.446,361 1 F
2002
= 943.479,125 + 1.446,361 = 944.925,486
Universitas Sumatera Utara
Tahun 2002 : X
t
= 1.195.269,54 a.
1
1
t I
t t
I
S X
S
= 0.1 x 1.195.269,54 + 1 – 0.1 930.461,878
= 119.526,954 + 0.9 930.461,878 = 119.526,954 + 837.415,690
= 956.942,644 b.
1
1
t II
t I
t II
S S
S
= 0.1 x 956.942,644 + 1 – 0.1 917.444,631
= 95.694,264 + 0.9 917.444,631 = 95.694,264 + 825.700,168
= 921.394,432 c. a
t
= 2 S
I t
- S
II t
= 2 956.942,644 – 921.394,432 = 1.913.885,288 - 921.394,432
= 992.490,856 d.
t II
t I
t
S S
b
1 =
1 .
1 1
.
956.942,644- 921.394,432
= 9
. 1
. 35.548,212
= 3.949,801 e. Forecast
F
t+m
= a
t
+ b
t
m F
2002+1
= 992.490,856 + 3.949,801 1
Universitas Sumatera Utara
F
2003
= 992.490,856 + 3.949,801 = 996.440,657
Tahun 2003 : X
t
= 1.300.354,52 a.
1
1
t I
t t
I
S X
S
= 0.1 x 1.300.354,52 + 1 – 0.1 996.440,657
= 130.035,452 + 0.9 996.440,657 = 130.035,452 + 861.248,380
= 991.283,832 b.
1
1
t II
t I
t II
S S
S
= 0.1 x 991.283,832 + 1 – 0.1 921.394,432
= 99.128,383 + 0.9 921.394,432 = 99.128,383 + 829.254,989
= 928.383,372 c. a
t
= 2 S
I t
- S
II t
= 2 991.283,832 – 928.383,372 = 1.982.567,664 - 928.383,372
= 1.054.184,291 d.
t II
t I
t
S S
b
1 =
1 .
1 1
.
991.283,832 - 928.383,372
= 9
. 1
. 62.900,460
= 6.988,940
Universitas Sumatera Utara
e. Forecast F
t+m
= a
t
+ b
t
m F
2003+1
= 1.054.184,291 + 6.988,940 1 F
2004
= 1.054.184,291 + 6.988,940 = 1.061.173,231
Tahun 2004 : X
t
= 1.434.960,63 a.
1
1
t I
t t
I
S X
S
= 0.1 x 1.434.960,63 + 1 – 0.1 991.283,832
= 143.496,063 + 0.9 991.283,832 = 143.496,063 + 892.155,449
= 1.035.651,512 b.
1
1
t II
t I
t II
S S
S
= 0.1 x 1.035.651,512 + 1 – 0.1 928.383,372
= 103.565,151 + 0.9 928.383,372 = 103.565,151 + 835.545,035
= 939.110,186 c. a
t
= 2 S
I t
- S
II t
= 2 1.035.651,512 – 939.110,186 = 2.071.303,023 - 939.110,186
= 1.132.192,837
Universitas Sumatera Utara
d.
t II
t I
t
S S
b
1 =
1 .
1 1
.
1.035.651,512 - 939.110,186
= 9
. 1
. 96.541,326
= 10.726,814 e. Forecast
F
t+m
= a
t
+ b
t
m F
2004+1
= 1.132.192,837 + 10.726,814 1 F
2005
= 1.132.192,837 + 10.726,814 = 1.142.919,651
Tahun 2005 : X
t
= 1.562.012,23 a.
1
1
t I
t t
I
S X
S
= 0.1 x 1.562.012,23 + 1 – 0.1 1.035.651,512
= 156.201,223 + 0.9 1.035.651,512 = 156.201,223 + 932.086,360
= 1.088.287,583 b.
1
1
t II
t I
t II
S S
S
= 0.1 x 1.088.287,583 + 1 – 0.1 939.110,186
= 108.828,758 + 0.9 939.110,186 = 108.828,758 + 845.199,167
= 954.027,926
Universitas Sumatera Utara
c. a
t
= 2 S
I t
- S
II t
= 2 1.088.287,583 – 954.027,926 = 2.176.575,167 - 954.027,926
= 1.222.547,241 d.
t II
t I
t
S S
b
1 =
1 .
1 1
.
1.088.287,583 - 954.027,926
= 9
. 1
. 134.259,658
= 14.917,740 e. Forecast
F
t+m
= a
t
+ b
t
m F
2005+1
= 1.222.547,241 + 14.917,740 1 F
2006
= 1.222.547,241 + 14.917,740 = 1.237.464,981
Tahun 2006 : X
t
= 1.666.274,17 a.
1
1
t I
t t
I
S X
S
= 0.1 x 1.666.274,17 + 1 – 0.1 1.088.287,583
= 166.627,417 + 0.9 1.088.287,583 = 166.627,417 + 979.458,825
= 1.146.086,242 b.
1
1
t II
t I
t II
S S
S
= 0.1 x 1.146.086,242 + 1 – 0.1 954.027,926
Universitas Sumatera Utara
= 114.608,624 + 0.9 954.027,926 = 114.608,624 + 858.625,133
= 973.233,757 c. a
t
= 2 S
I t
- S
II t
= 2 1.146.086,242 – 973.233,757 = 2.292.172,484 - 973.233,757
= 1.318.938,727 d.
t II
t I
t
S S
b
1 =
1 .
1 1
.
1.146.086,242 - 973.233,757
= 9
. 1
. 172.852,485
= 19.205,832 e. Forecast
F
t+m
= a
t
+ b
t
m F
2006+1
= 1.318.938,727 + 19.205,832 1 F
2007
= 1.318.938,727 + 19.205,832 = 1.338.144,558
Tahun 2007 : X
t
= 1.805.008,01 a.
1
1
t I
t t
I
S X
S
= 0.1 x 1.805.008,01 + 1 – 0.1 1.146.086,242
= 180.500,801 + 0.9 1.146.086,242 = 180.500,801 + 1.031.477,618
Universitas Sumatera Utara
= 1.211.978,419 b.
1
1
t II
t I
t II
S S
S
= 0.1 x 1.211.978,419 + 1 – 0.1 973.233,757
= 121.197,842 + 0.9 973.233,757 = 121.197,842 + 875.910,382
= 997.108,224 c. a
t
= 2 S
I t
- S
II t
= 2 1.211.978,419 – 997.108,224 = 2.423.956,838 - 997.108,224
= 1.426.848,614 d.
t II
t I
t
S S
b
1 =
1 .
1 1
.
1.211.978,419 - 997.108,224
= 9
. 1
. 214.870,195
= 23.874,466 e. Forecast
F
t+m
= a
t
+ b
t
m F
2007+1
= 1.426.848,614 + 23.874,466 1 F
2008
= 1.426.848,614 + 23.874,466 = 1.450.723,080
Tahun 2008 : X
t
= 1.929.695,13 a.
1
1
t I
t t
I
S X
S
Universitas Sumatera Utara
= 0.1 x 1.929.695,13 + 1 – 0.1 1.211.978,419 = 192.969,513 + 0.9 1.211.978,419
= 192.969,513 + 1.090.780,577 = 1.283.750,090
b.
1
1
t II
t I
t II
S S
S
= 0.1 x 1.283.750,090 + 1 – 0.1 997.108,224
= 128.375,009 + 0.9 997.108,224 = 128.375,009 + 897.397,401
= 1.025.772,410 c. a
t
= 2 S
I t
- S
II t
= 2 1.283.750,090 – 1.025.772,410 = 2.567.500,180 - 1.025.772,410
= 1.541.727,770 d.
t II
t I
t
S S
b
1 =
1 .
1 1
.
1.283.750,090 - 1.025.772,410
= 9
. 1
. 257.977,680
= 28.664,187 e. Forecast
F
t+m
= a
t
+ b
t
m F
2008+1
= 1.541.727,770 + 28.664,187 1 F
2009
= 1.541.727,770 + 28.664,187 = 1.570.391,956
Universitas Sumatera Utara
n F
X MAE
t t
8 778
3.210.988,
MAE = 401.373,597
n F
X MSE
t t
2
8 117.484,57
1.340.967.
MSE = 167.620.889.685,571
Besarnya forecast bila digunakan alpha 0.6 adalah sebagai berikut. Tahun 2000 :
S
I t
: ditentukan oleh PDRB tahun pertama, yaitu sebesar 915.998,27 S
II t
: ditentukan juga oleh besarnya PDRB tahun pertama, yaitu sebesar 915.998,27. a
t
: belum bisa ditentukan karena merupakan data pertama. b
t
: belum bisa ditentukan karena merupakan data pertama. F
t+m
: peramalan forecasttahun kedua F
2001
ditentukan oleh besarnya PDRB tahun pertama, yaitu sebesar 915.998,27
Tahun 2001 : X
t
= 1.060.634,35 a.
1
1
t I
t t
I
S X
S
= 0.6 x 1.060.634,35 + 1 – 0.6 915.998,27
= 636.380,610 + 0.4 915.998,27
Universitas Sumatera Utara
= 636.380,610 + 366.399,308 = 1.002.779,918
b.
1
1
t II
t I
t II
S S
S
= 0.6 x 1.002.779,918 + 1 – 0.6 915.998,27
= 601.667,951+ 0.4 915.998,27 = 601.667,951 + 366.399,308
= 968.067,259 c. a
t
= 2 S
I t
- S
II t
= 2 1.002.779,918 – 968.067,259 = 2.005.559,836 - 968.067,259
= 1.037.492,577 d.
t II
t I
t
S S
b
1 =
6 .
1 6
.
1.002.779,918 - 968.067,259
= 4
. 6
. 34.712,659
= 52.068,989 e. Forecast
F
t+m
= a
t
+ b
t
m F
2001+1
= 1.037.492,577 + 52.068,989 1 F
2002
= 1.037.492,577 + 52.068,989 = 1.089.561,566
Universitas Sumatera Utara
Tahun 2002 : X
t
= 1.195.269,54 a.
1
1
t I
t t
I
S X
S
= 0.6 x 1.195.269,54 + 1 – 0.6 1.002.779,918
= 717.161,724 + 0.4 1.002.779,918 = 717.161,724 + 401.111,967
= 1.118.273,691 b.
1
1
t II
t I
t II
S S
S
= 0.6 x 1.118.273,691 + 1 – 0.6 968.067,259
= 670.964,215 + 0.4 968.067,259 = 670.964,215 + 387.226,904
= 1.058.191,118
c. a
t
= 2 S
I t
- S
II t
= 2 1.118.273,691 – 1.058.191,118 = 2.236.547,382 - 1.058.191,118
= 1.178.356,264 d.
t II
t I
t
S S
b
1 =
6 .
1 6
.
1.118.273,691 - 1.058.191,118
= 4
. 6
. 60.082,573
= 90.123,859
Universitas Sumatera Utara
e. Forecast F
t+m
= a
t
+ b
t
m F
2002+1
= 1.178.356,264 + 90.123,859 1 F
2003
= 1.178.356,264 + 90.123,859 = 1.268.480,124
Tahun 2003 : X
t
= 1.300.354,52 a.
1
1
t I
t t
I
S X
S
= 0.6 x 1.300.354,52 + 1 – 0.6 1.118.273,691
= 780.212,712 + 0.4 1.118.273,691 = 780.212,712 + 447.309,476
= 1.227.522,188 b.
1
1
t II
t I
t II
S S
S
= 0.6 x 1.227.522,188 + 1 – 0.6 1.058.191,118
= 736.513,313 + 0.4 1.058.191,118 = 736.513,313 + 423.276,447
= 1.159.789,760 c. a
t
= 2 S
I t
- S
II t
= 2 1.227.522,188 – 1.159.789,760 = 2.455.044,377 - 1.159.789,760
= 1.295.254,617 d.
t II
t I
t
S S
b
1
Universitas Sumatera Utara
= 6
. 1
6 .
1.227.522,188 - 1.159.789,760
= 4
. 6
. 67.732,428
= 101.598,642 e. Forecast
F
t+m
= a
t
+ b
t
m F
2003+1
= 1.295.254,617 + 101.598,642 1 F
2004
= 1.295.254,617 + 101.598,642 = 1.396.853,259
Tahun 2004 : X
t
= 1.434.960,63 a.
1
1
t I
t t
I
S X
S
= 0.6 x 1.434.960,63 + 1 – 0.6 1.227.522,188
= 860.976,378 + 0.4 1.227.522,188 = 860.976,378 + 491.008,875
= 1.351.985,253 b.
1
1
t II
t I
t II
S S
S
= 0.6 x 1.351.985,253 + 1 – 0.6 1.159.789,760
= 811.191,152 + 0.4 1.159.789,760 = 811.191,152 + 463.915,904
= 1.275.107,056 c. a
t
= 2 S
I t
- S
II t
= 2 1.351.985,253 – 1.275.107,056
Universitas Sumatera Utara
= 2.703.970,507- 1.275.107,056 = 1.428.863,451
d.
t II
t I
t
S S
b
1 =
6 .
1 6
.
1.351.985,253 - 1.275.107,056
= 4
. 6
. 76.878,197
= 115.317,296 e. Forecast
F
t+m
= a
t
+ b
t
m F
2004+1
= 1.428.863,451 + 115.317,296 1 F
2005
= 1.428.863,451 + 115.317,296 = 1.544.180,746
Tahun 2005 : X
t
= 1.562.012,23 a.
1
1
t I
t t
I
S X
S
= 0.6 x 1.562.012,23 + 1 – 0.6 1.351.985,253
= 937.207,338 + 0.4 1.351.985,253 = 937.207,338 + 540.794,101
= 1.478.001,439 b.
1
1
t II
t I
t II
S S
S
= 0.6 x 1.478.001,439 + 1 – 0.6 1.275.107,056
= 886.800,864 + 0.4 1.275.107,056 = 886.800,864 + 510.042,822
Universitas Sumatera Utara
= 1.396.843,686 c. a
t
= 2 S
I t
- S
II t
= 2 1.478.001,439 – 1.396.843,686 = 2.956.002,879 - 1.396.843,686
= 1.559.159,193 d.
t II
t I
t
S S
b
1 =
6 .
1 6
.
1.478.001,439 - 1.396.843,686
= 4
. 6
. 81.157,753
= 121.736,630 e. Forecast
F
t+m
= a
t
+ b
t
m F
2005+1
= 1.559.159,193 + 121.736,630 1 F
2006
= 1.559.159,193 + 121.736,630 = 1.680.895,823
Tahun 2006 : X
t
= 1.666.274,17 a.
1
1
t I
t t
I
S X
S
= 0.6 x 1.666.274,17 + 1 – 0.6 1.478.001,439
= 999.764,502 + 0.4 1.478.001,439 = 999.764,502 + 591.200,576
= 1.590.965,078
Universitas Sumatera Utara
b.
1
1
t II
t I
t II
S S
S
= 0.6 x 1.590.965,078 + 1 – 0.6 1.396.843,686
= 954.579,047 + 0.4 1.396.843,686 = 954.579,047 + 558.737,474
= 1.513.316,521 c. a
t
= 2 S
I t
- S
II t
= 2 1.590.965,078 – 1.513.316,521 = 3.181.930,155 - 1.513.316,521
= 1.668.613,634 d.
t II
t I
t
S S
b
1 =
6 .
1 6
.
1.590.965,078 - 1.513.316,521
= 4
. 6
. 77.648,557
= 116.472,835 e. Forecast
F
t+m
= a
t
+ b
t
m F
2006+1
= 1.668.613,634 + 116.472,835 1 F
2007
= 1.668.613,634 + 116.472,835 = 1.785.086,469
Tahun 2007 : X
t
= 1.805.008,01 a.
1
1
t I
t t
I
S X
S
= 0.6 x 1.805.008,01 + 1 – 0.6 1.590.965,078
Universitas Sumatera Utara
= 1.083.004,806 + 0.4 1.590.965,078 = 1.083.004,806 + 636.386,031
= 1.719.390,837 b.
1
1
t II
t I
t II
S S
S
= 0.6 x 1.719.390,837 + 1 – 0.6 1.513.316,521
= 1.031.634,502 + 0.4 1.513.316,521 = 1.031.634,502 + 605.326,608
= 1.636.961,111 c. a
t
= 2 S
I t
- S
II t
= 2 1.719.390,837 – 1.636.961,111 = 3.438.781,674 - 1.636.961,111
= 1.801.820,564 d.
t II
t I
t
S S
b
1 =
6 .
1 6
.
1.719.390,837 - 1.636.961,111
= 4
. 6
. 82.429,726
= 123.644,590 e. Forecast
F
t+m
= a
t
+ b
t
m F
2007+1
= 1.801.820,564 + 123.644,590 1 F
2008
= 1.801.820,564 + 123.644,590 = 1.925.465,153
Universitas Sumatera Utara
Tahun 2008 : X
t
= 1.929.695,13 a.
1
1
t I
t t
I
S X
S
= 0.6 x 1.929.695,13 + 1 – 0.6 1.719.390,837
= 1.157.817,078 + 0.4 1.719.390,837 = 1.157.817,078 + 687.756,335
= 1.845.573,413 b.
1
1
t II
t I
t II
S S
S
= 0.6 x 1.845.573,413 + 1 – 0.6 1.636.961,111
= 1.107.344,048 + 0.4 1.636.961,111 = 1.107.344,048 + 654.784,444
= 1.762.128,492 c. a
t
= 2 S
I t
- S
II t
= 2 1.845.573,413 – 1.762.128,492 = 3.691.146,826- 1.762.128,492
= 1.929.018,334 d.
t II
t I
t
S S
b
1 =
6 .
1 6
.
1.845.573,413 - 1.762.128,492
= 4
. 6
. 83.444,921
= 125.167,381 e. Forecast
F
t+m
= a
t
+ b
t
m F
2008+1
= 1.929.018,334 + 125.167,381 1
Universitas Sumatera Utara
F
2009
= 1.929.018,334 + 125.167,381 = 2.054.185,715
n F
X MAE
t t
8 237.706,83
MAE
= 29.713,354
n F
X MSE
t t
2
8 .126,136
14.618.134
MSE = 1.827.266.765,767
Besarnya forecast bila digunakan alpha 0.9 adalah sebagai berikut. Tahun 2000 :
S
I t
: ditentukan oleh PDRB tahun pertama, yaitu sebesar 915.998,27 S
II t
: ditentukan juga oleh besarnya PDRB tahun pertama, yaitu sebesar 915.998,27. a
t
: belum bisa ditentukan karena merupakan data pertama. b
t
: belum bisa ditentukan karena merupakan data pertama. F
t+m
: peramalan forecasttahun kedua F
2001
ditentukan oleh besarnya PDRB tahun pertama, yaitu sebesar 915.998,27
Tahun 2001 : X
t
= 1.060.634,35
Universitas Sumatera Utara
a.
1
1
t I
t t
I
S X
S
= 0.9 x 1.060.634,35 + 1 – 0.9 915.998,27
= 954.570,915 + 0.1 915.998,27 = 954.570,915 + 91.599,827
= 1.046.170,742 b.
1
1
t II
t I
t II
S S
S
= 0.9 x 1.046.170,742 + 1 – 0.9 915.998,27
= 941.553,668+ 0.1 915.998,27 = 941.553,668 + 91.599,827
= 1.033.153,495 c. a
t
= 2 S
I t
- S
II t
= 2 1.046.170,742 – 1.033.153,495 = 2.092.341,484 - 1.033.153,495
= 1.059.187,989 d.
t II
t I
t
S S
b
1 =
9 .
1 9
.
1.046.170,742 - 1.033.153,495
= 1
. 9
. 13.017,247
= 117.155,225 e. Forecast
F
t+m
= a
t
+ b
t
m F
2001+1
= 1.059.187,989 + 117.155,225 1 F
2002
= 1.059.187,989 + 117.155,225
Universitas Sumatera Utara
= 1.176.343,214
Tahun 2002 : X
t
= 1.195.269,54 a.
1
1
t I
t t
I
S X
S
= 0.9 x 1.195.269,54 + 1 – 0.9 1.046.170,742
= 1.075.742,586 + 0.1 1.046.170,742 = 1.075.742,586 + 104.617,074
= 1.180.359,660
b.
1
1
t II
t I
t II
S S
S
= 0.9 x 1.180.359,660 + 1 – 0.9 1.033.153,495
= 1.062.323,694 + 0.1 1.033.153,495 = 1.062.323,694 + 103.315,349
= 1.165.639,043 c. a
t
= 2 S
I t
- S
II t
= 2 1.180.359,660 – 1.165.639,043 = 2.360.719,320 - 1.165.639,043
= 1.195.080,277 d.
t II
t I
t
S S
b
1 =
9 .
1 9
.
1.180.359,660 - 1.165.639,043
= 1
. 9
. 14.720,617
= 132.485,549
Universitas Sumatera Utara
e. Forecast F
t+m
= a
t
+ b
t
m F
2002+1
= 1.195.080,277 + 132.485,549 1 F
2003
= 1.195.080,277 + 132.485,549 = 1.327.565,826
Tahun 2003 : X
t
= 1.300.354,52 a.
1
1
t I
t t
I
S X
S
= 0.9 x 1.300.354,52 + 1 – 0.9 1.180.359,660
= 1.170.319,068 + 0.1 1.180.359,660 = 1.170.319,068 + 118.035,966
= 1.288.355,034 b.
1
1
t II
t I
t II
S S
S
= 0.9 x 1.288.355,034 + 1 – 0.9 1.165.639,044
= 1.159.519,531 + 0.1 1.165.639,044 = 1.159.519,531 + 116.563,904
= 1.276.083,435 c. a
t
= 2 S
I t
- S
II t
= 2 1.288.355,034 – 1.276.083,435 = 2.576.710,068 - 1.276.083,435
= 1.300.626,633
Universitas Sumatera Utara
d.
t II
t I
t
S S
b
1 =
9 .
1 9
.
1.288.355,034 - 1.276.083,435
= 1
. 9
. 12.271,599
= 110.444,391 e. Forecast
F
t+m
= a
t
+ b
t
m F
2003+1
= 1.300.626,633 + 110.444,391 1 F
2004
= 1.300.626,633 + 110.444,391 = 1.411.071,024
Tahun 2004 : X
t
= 1.434.960,63 a.
1
1
t I
t t
I
S X
S
= 0.9 x 1.434.960,63 + 1 – 0.9 1.288.355,034
= 1.291.464,567 + 0.1 1.288.355,034 = 1.291.464,567 + 128.835,503
= 1.420.300,070 b.
1
1
t II
t I
t II
S S
S
= 0.9 x 1.420.300,070 + 1 – 0.9 1.276.083,435
= 1.278.270,063 + 0.1 1.276.083,435 = 1.278.270,063 + 127.608,343
= 1.405.878,407
Universitas Sumatera Utara
c. a
t
= 2 S
I t
- S
II t
= 2 1.420.300,070 – 1.405.878,407 = 2.840.600,141 - 1.405.878,407
= 1.434.721,734 d.
t II
t I
t
S S
b
1 =
9 .
1 9
.
1.420.300,070 - 1.434.721,734
= 1
. 9
. 14.421,664
= 129.794,972 e. Forecast
F
t+m
= a
t
+ b
t
m F
2004+1
= 1.434.721,734 + 129.794,972 1 F
2005
= 1.434.721,734 + 129.794,972 = 1.564.516,706
Tahun 2005 : X
t
= 1.562.012,23 a.
1
1
t I
t t
I
S X
S
= 0.9 x 1.562.012,23 + 1 – 0.9 1.420.300,070
= 1.405.811,007 + 0.1 1.420.300,070 = 1.405.811,007 + 142.030,007
= 1.547.841,014 b.
1
1
t II
t I
t II
S S
S
= 0.9 x 1.547.841,014+ 1 – 0.9 1.405.878,407
Universitas Sumatera Utara
= 1.393.056,913 + 0.1 1.405.878,407 = 1.393.056,913 + 140.587,841
= 1.533.644,753 c. a
t
= 2 S
I t
- S
II t
= 2 1.547.841,014 – 1.533.644,753 = 3.095.682,028 - 1.533.644,753
= 1.562.037,275 d.
t II
t I
t
S S
b
1 =
9 .
1 9
.
1.547.841,014 - 1.533.644,753
= 1
. 9
. 14.196,261
= 127.766,346 e. Forecast
F
t+m
= a
t
+ b
t
m F
2005+1
= 1.562.037,275 + 127.766,346 1 F
2006
= 1.562.037,275 + 127.766,346 = 1.689.803,621
Tahun 2006 : X
t
= 1.666.274,17 a.
1
1
t I
t t
I
S X
S
= 0.9 x 1.666.274,17 + 1 – 0.9 1.547.841,014
= 1.499.646,753 + 0.1 1.547.841,014 = 1.499.646,753 + 154.784,101
= 1.654.430,854
Universitas Sumatera Utara
b.
1
1
t II
t I
t II
S S
S
= 0.9 x 1.654.430,854 + 1 – 0.9 1.533.644,753
= 1.488.987,769 + 0.1 1.533.644,753 = 1.488.987,769 + 153.364,475
= 1.642.352,244 c. a
t
= 2 S
I t
- S
II t
= 2 1.654.430,854 – 1.642.352,244 = 3.308.861,709 - 1.642.352,244
= 1.666.509,465 d.
t II
t I
t
S S
b
1 =
9 .
1 9
.
1.654.430,854 - 1.642.352,244
= 1
. 9
. 12.078,610
= 108.707,491 e. Forecast
F
t+m
= a
t
+ b
t
m F
2006+1
= 1.666.509,465 + 108.707,491 1 F
2007
= 1.666.509,465 + 108.707,491 = 1.775.216,955
Tahun 2007 : X
t
= 1.805.008,01 a.
1
1
t I
t t
I
S X
S
= 0.9 x 1.805.008,01 + 1 – 0.9 1.654.430,854
Universitas Sumatera Utara
= 1.624.507,209 + 0.1 1.654.430,854 = 1.624.507,209 + 165.443,085
= 1.789.950,294 b.
1
1
t II
t I
t II
S S
S
= 0.9 x 1.789.950,294 + 1 – 0.9 1.642.352,244
= 1.610.955,265 + 0.1 1.642.352,244 = 1.610.955,265 + 164.235,224
= 1.775.190,489 c. a
t
= 2 S
I t
- S
II t
= 2 1.789.950,294 – 1.775.190,489 = 3.579.900,589 - 1.775.190,489
= 1.804.710,099 d.
t II
t I
t
S S
b
1 =
9 .
1 9
.
1.789.950,294 - 1.775.190,489
= 1
. 9
. 14.759,805
= 132.838,245 e. Forecast
F
t+m
= a
t
+ b
t
m F
2007+1
= 1.804.710,099 + 132.838,245 1 F
2008
= 1.804.710,099 + 132.838,245 = 1.937.548,345
Universitas Sumatera Utara
Tahun 2008 : X
t
= 1.929.695,13 a.
1
1
t I
t t
I
S X
S
= 0.9 x 1.929.695,13 + 1 – 0.9 1.789.950,294
= 1.736.725,617 + 0.1 1.789.950,294 = 1.736.725,617 + 178.995,029
= 1.915.720,646 b.
1
1
t II
t I
t II
S S
S
= 0.9 x 1.915.720,646 + 1 – 0.9 1.775.190,489
= 1.724.148,582 + 0.1 1.775.190,489 = 1.724.148,582 + 177.519,049
= 1.901.667,631 c. a
t
= 2 S
I t
- S
II t
= 2 1.915.720,646 – 1.901.667,631 = 3.831.441,293 - 1.901.667,631
= 1.929.773,662 d.
t II
t I
t
S S
b
1 =
9 .
1 9
.
1.915.720,646 - 1.901.667,631
= 1
. 9
. 14.053,016
= 126.477,141 e. Forecast
F
t+m
= a
t
+ b
t
m F
2008+1
= 1.929.773,662 + 126.477,141 1
Universitas Sumatera Utara
F
2009
= 1.929.773,662 + 126.477,141 = 2.056.250,803
n F
X MAE
t t
8 137.052,78
MAE
= 17.131,597
n F
X MSE
t t
2
8 336,078
3.189.666.
MSE = 398.708.292,010
4.2 Evaluasi Data