Pemulusan Eksponensial Ganda Analisa Data

  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