Pemulusan Eksponensial Ganda Analisa Data

n F X MSE t t 2 ∑ − = 10 .863.958,9 17.204.367 = MSE = 1.720.436.786.395,89

4.1.2 Pemulusan Eksponensial Ganda

Pada peramalan dengan metode ini digunakan alpha 0.1, 0.6, dan 0.9. Besarnya peramalan forecastbila digunakan alpha 0.1 adalah sebagai berikut. Tahun 1997 : S I t : ditentukan oleh PDRB tahun pertama, yaitu sebesar 1.875.287,45 S II t : ditentukan juga oleh besarnya PDRB tahun pertama, yaitu sebesar 1.875.287,45 . 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 1998 ditentukan oleh besarnya PDRB tahun pertama, yaitu sebesar 1.875.287,45 Tahun 1998 : X t = 2.983.978,36 Universitas Sumatera Utara a. 1 1 − − + = t I t t I S X S α α = 0.1 x 2.983.978,36 + 1 – 0.1 1.875.287,45 = 298.397,836 + 0.9 1.875.287,45 = 298.397,836 + 1.687.758,705 = 1.986.156,541 b. 1 1 − − + = t II t I t II S S S α α = 0.1 x 1.986.156,541 + 1 – 0.1 1.875.287,45 = 198.615,6541 + 0.9 1.875.287,45 = 198.615,6541 + 1.687.758,705 = 1.886.374,359 c. a t = 2 S I t - S II t = 2 1.986.156,541 – 1.886.374,359 = 3.972.313,082 - 1.886.374,359 = 2.085.938,723 d. t II t I t S S b − − = α α 1 = 1 . 1 1 . − 1.986.156,541-1.886.374,359 = 9 . 1 . 99.782,1819 = 11.086,9091 Universitas Sumatera Utara e. Forecast F t+m = a t + b t m F 1998+1 = 2.085.938,723 + 11.086,90911 F 1999 = 2.085.938,723 + 11.086,9091 = 2.097.025,632 Tahun 1999 : X t = 3.378.471,43 a. 1 1 − − + = t I t t I S X S α α = 0.1 x 3.378.471,43 + 1 – 0.1 1986156.541 = 337.847,143 + 0.9 1986156.541 = 337.847,143 + 1787540.887 = 2.125.388,03 b. 1 1 − − + = t II t I t II S S S α α = 0.1 x 2.125.388,03 + 1 – 0.1 1.886.374,359 = 212.538,803 + 0.9 1.886.374,359 = 212.538,803 + 1.697.736,923 = 1.910.275,726 c. a t = 2 S I t - S II t = 2 2.125.388,03 – 1.910.275,726 Universitas Sumatera Utara = 4.250.776,06 - 1.910.275,726 = 2.340.500,334 d. t II t I t S S b − − = α α 1 = 1 . 1 1 . − 2.125.388,03 -1.910.275,726 = 9 . 1 . 215.112,304 = 23.901,3671 e. Peramalan Forecast F t+m = a t + b t m F 1999+1 = 2.340.500,334 + 23.901,3671 1 F 2000 = 2.340.500,334 + 23.901,3671 = 2.364.401,701 Tahun 2000 : X t = 4.563.228,26 a. 1 1 − − + = t I t t I S X S α α = 0.1 x 4.563.228,26 + 1 – 0.1 2.125.388,03 = 456.322,826 + 0.9 2.125.388,03 = 456.322,826 + 1.912.849,227 = 2.369.172,053 Universitas Sumatera Utara b. 1 1 − − + = t II t I t II S S S α α = 0.1 x 2.369.172,053 + 1 – 0.1 1.910.275,726 = 236.917,2053 + 0.9 1.910.275,726 = 236.917,2053 + 1.719.248,154 = 1.956.165,359 c. a t = 2 S I t - S II t = 2 2.369.172,053 – 1.956.165,359 = 4.738.344,106 - 1.956.165,359 = 2.782.178,747 d. t II t I t S S b − − = α α 1 = 1 . 1 1 . − 2.369.172,053 -1.956.165,359 = 9 . 1 . 413.006,694 = 45.889,634 e. Forecast F t+m = a t + b t m F 2000+1 = 2.782.178,747 + 45.889,634 1 F 2001 = 2.782.178,747 + 45.889,634 Universitas Sumatera Utara = 2.828.068,38 Tahun 2001 : X t = 5.510.135,7 a. 1 1 − − + = t I t t I S X S α α = 0.1 x 5.510.135,7 + 1 – 0.1 2.369.172,053 = 551.013,57 + 0.9 2.369.172,053 = 551.013,57 + 2.132.254,848 = 2.683.268,418 b. 1 1 − − + = t II t I t II S S S α α = 0.1 x 2.683.268,418 + 1 – 0.1 1.956.165,359 = 268.326,8418 + 0.9 1.956.165,359 = 236.917,2053 + 1.760.548,823 = 2.028.875,665 c. a t = 2 S I t - S II t = 2 2.683.268,418 – 2.028.875,665 = 5.366.536,835 - 2.028.875,665 = 3.337.661,171 d. t II t I t S S b − − = α α 1 Universitas Sumatera Utara = 1 . 1 1 . − 2.683.268,418 -2.028.875,665 = 9 . 1 . 654.392 = 45.889,694 e. Forecast F t+m = a t + b t m F 2001+1 = 3.337.661,171 + 45.889,694 1 F 2002 = 3.337.661,171 + 45.889,694 = 3.410.371,476 Tahun 2002 : X t = 6.135.245,81 a. 1 1 − − + = t I t t I S X S α α = 0.1 x 6.135.245,81 + 1 – 0.1 2.683.268,418 = 613.524,581 + 0.9 2.683.268,418 = 613.524,581 + 2.414.941,576 = 3.028.466,157 b. 1 1 − − + = t II t I t II S S S α α = 0.1 x 3.028.466,157 + 1 – 0.1 2.028.875,665 = 302.846,6157 + 0.9 2.028.875,665 Universitas Sumatera Utara = 302.846,6157 + 1.825.988,098 = 2.128.834,714 c. a t = 2 S I t - S II t = 2 3.028.466,157 – 2.128.834,714 = 6.056.932,314 - 2.128.834,714 = 3.928.097,6 d. t II t I t S S b − − = α α 1 = 1 . 1 1 . − 3.028.466,157 - 2.128.834,714 = 9 . 1 . 899.631,443 = 99.959,0492 e. Forecast F t+m = a t + b t m F 2002+1 = 3.928.097,6 + 99.959,0492 1 F 2003 = 3.928.097,6 + 99.959,0492 = 4.028.056,649 Tahun 2003 : X t = 6.569.556,17 Universitas Sumatera Utara a. 1 1 − − + = t I t t I S X S α α = 0.1 x 6.569.556,17 + 1 – 0.1 3.028.466,157 = 656.955,617 + 0.9 3.028.466,157 = 656.955,617 + 2.725.619,541 = 3.382.575,158 b. 1 1 − − + = t II t I t II S S S α α = 0.1 x 3.382.575,158 + 1 – 0.1 2.128.834,714 = 338.257,5158 + 0.9 2.128.834,714 = 338.257,5158 + 1.915.951,243 = 2.254.208,758 c. a t = 2 S I t - S II t = 2 3.382.575,158 – 2.254.208,758 = 6.765.150,316 - 2.254.208,758 = 4.510.941,558 d. t II t I t S S b − − = α α 1 = 1 . 1 1 . − 3.382.575,158 - 2.254.208,758 = 9 . 1 . 1.128.366,4 = 125.374,044 Universitas Sumatera Utara e. Forecast F t+m = a t + b t m F 2003+1 = 4.510.941,558 + 125.374,044 1 F 2004 = 4.510.941,558 + 125.374,044 = 4.636.315,602 Tahun 2004 : X t = 7.313.398,82 a. 1 1 − − + = t I t t I S X S α α = 0.1 x 7.313.398,82 + 1 – 0.1 3.382.575,158 = 731.339,882 + 0.9 3.382.575,158 = 731.339,882 + 3.044.317,642 = 3.775.657,524 b. 1 1 − − + = t II t I t II S S S α α = 0.1 x 3.775.657,524 + 1 – 0.1 2.254.208,758 = 377.565,7524 + 0.9 2.254.208,758 = 377.565,7524 + 2.028.787,883 = 2.406.353.635 c. a t = 2 S I t - S II t = 2 3.775.657,524 – 2.406.353.635 Universitas Sumatera Utara = 7.551.315,049 - 2.406.353.635 = 5.144.961,414 d. t II t I t S S b − − = α α 1 = 1 . 1 1 . − 3.775.657,524 - 2.406.353.635 = 9 . 1 . 1.369.303,89 = 152.144,877 e. Forecast F t+m = a t + b t m F 2004+1 = 5.144.961,414 + 152.144,877 1 F 2005 = 5.144.961,414 + 152.144,877 = 5.297.106,29 Tahun 2005 : X t = 9.209.143,29 a. 1 1 − − + = t I t t I S X S α α = 0.1 x 9.209.143,29 + 1 – 0.1 3.775.657,524 = 920.914,329 + 0.9 3.775.657,524 = 920.914,329 + 3.398.091,772 = 4.319.006,101 Universitas Sumatera Utara b. 1 1 − − + = t II t I t II S S S α α = 0.1 x 4.319.006,101 + 1 – 0.1 2.406.353.635 = 431.900,6101 + 0.9 2.406.353.635 = 431.900,6101 + 2.165.718,271 = 2.597.618,882 c. a t = 2 S I t - S II t = 2 4.319.006,101 – 2.597.618,882 = 8.638.012,202 - 2.597.618,882 = 6.040.393,32 d. t II t I t S S b − − = α α 1 = 1 . 1 1 . − 4.319.006,101 - 2.597.618,882 = 9 . 1 . 1.721.387,22 = 191.265,247 e. Forecast F t+m = a t + b t m F 2005+1 = 6.040.393,32 + 191.265,247 1 F 2006 = 6.040.393,32 + 191.265,247 Universitas Sumatera Utara = 6.231.658,567 Tahun 2006 : X t = 10.242.023,94 a. 1 1 − − + = t I t t I S X S α α = 0.1 x 10.242.023,94 + 1 – 0.1 4.319.006,101 = 1.024.202,394 + 0.9 4.319.006,101 = 1.024.202,394 + 3.887.105,491 = 4.911.307,885 b. 1 1 − − + = t II t I t II S S S α α = 0.1 x 4.911.307,885 + 1 – 0.1 2.597.618,882 = 491.130,7885 + 0.9 2.597.618,882 = 491.130,7885 + 2.337.856,993 = 2.828.987,782 c. a t = 2 S I t - S II t = 2 4.911.307,885 – 2.828.987,782 = 9.822.615,77 - 2.828.987,782 = 6.993.627,988 d. t II t I t S S b − − = α α 1 Universitas Sumatera Utara = 1 . 1 1 . − 4.911.307,885 - 2.828.987,782 = 9 . 1 . 2.082.320,1 = 231.368,9 e. Forecast F t+m = a t + b t m F 2006+1 = 6.993.627,988 + 231.368,9 1 F 2007 = 6.993.627,988 + 231.368,9 = 7.224.996,888 Tahun 2007 : X t = 11.362.637,09 a. 1 1 − − + = t I t t I S X S α α = 0.1 x 11.362.637,09 + 1 – 0.1 4.911.307,885 = 1.136.263,709 + 0.9 4.911.307,885 = 1.136.263,709 + 4.420.177,096 = 5.556.440,805 b. 1 1 − − + = t II t I t II S S S α α = 0.1 x 5.556.440,805 + 1 – 0.1 2.828.987,782 = 555.644.0805 + 0.9 2.828.987,782 Universitas Sumatera Utara = 555.644.0805 + 2.546.089,004 = 3.101.733,084 c. a t = 2 S I t - S II t = 2 5.556.440,805 – 3.101.733,084 = 11.112.881,61 - 3.101.733,084 = 8.011.148,526 d. t II t I t S S b − − = α α 1 = 1 . 1 1 . − 5.556.440,805 - 3.101.733,084 = 9 . 1 . 2.454.707,72 = 272.745,302 e. Forecast F t+m = a t + b t m F 2007+1 = 8.011.148,526 + 272.745,302 1 F 2008 = 8.011.148,526 + 272.745,302 = 8.283.893,829 n F X MAE t t ∑ − = Universitas Sumatera Utara 10 ,45 31.547.188 = MAE = 3.154.718,845 n F X MSE t t 2 ∑ − = 10 .902.605,0 112187.409 = MSE = 11.218.740.990.260,50 Besarnya forecast bila digunakan alpha 0.6 adalah sebagai berikut. Tahun 1997 : S I t : ditentukan oleh PDRB tahun pertama, yaitu sebesar 1.875.287,45 S II t : ditentukan juga oleh besarnya PDRB tahun pertama, yaitu sebesar 1.875.287,45 a t : belum bisa ditentukan karena merupakan data pertama. b t : belum bisa ditentukan karena merupakan data pertama. F t+m : peramalan forecast tahun kedua F 2001 ditentukan oleh besarnya PDRB tahun pertama, yaitu sebesar 1.875.287,45 Tahun 1998 : X t = 2.983.978,36 a. 1 1 − − + = t I t t I S X S α α Universitas Sumatera Utara = 0.6 x 2.983.978,36 + 1 – 0.6 1.875.287,45 = 1.790.387,016 + 0.4 1.875.287,45 = 1.790.387,016 + 750.114,98 = 2.540.501,996 b. 1 1 − − + = t II t I t II S S S α α = 0.6 x 2.540.501,996 + 1 – 0.6 2.540.501,996 = 1.524.301,198 + 0.4 2.540.501,996 = 1.524.301,198 + 750.114,98 = 2.274.416,178 c. a t = 2 S I t - S II t = 2 2.540.501,996 – 2.274.416,178 = 5.081.003,992 - 2.274.416,178 = 2.806.587,814 d. t II t I t S S b − − = α α 1 = 6 . 1 6 . − 2.540.501,996 - 2.274.416,178 = 4 . 6 . 266.085,818 = 399.128,728 e. Forecast Universitas Sumatera Utara F t+m = a t + b t m F 1998+1 = 2.806.587,814 + 399.128,728 1 F 1999 = 2.806.587,814 + 399.128,728 = 3.205.716,542 Tahun 1999 : X t = 3.378.471,43 a. 1 1 − − + = t I t t I S X S α α = 0.6 x 3.378.471,43 + 1 – 0.6 2.540.501,996 = 2.027.082,858 + 0.4 2.540.501,996 = 2.027.082,858 + 1.016.200,798 = 3.043.283,656 b. 1 1 − − + = t II t I t II S S S α α = 0.6 x 3.043.283,656 + 1 – 0.6 2.274.416,178 = 1.825.970,194 + 0.4 2.274.416,178 = 1.825.970,194 + 909.766,471 = 2.735.736,665 c. a t = 2 S I t - S II t = 2 3.043.283,656 – 2.735.736,665 Universitas Sumatera Utara = 6.086.567,313 - 2.735.736,665 = 3.350.830,648 d. t II t I t S S b − − = α α 1 = 6 . 1 6 . − 3.043.283,656 - 2.735.736,665 = 4 . 6 . 307.546,992 = 461.320,487 e. Forecast F t+m = a t + b t m F 1999+1 = 3.350.830,648 + 461.320,487 1 F 2000 = 3.350.830,648 + 461.320,487 = 3.812.151,135 Tahun 2000 : X t = 4.563.228,26 a. 1 1 − − + = t I t t I S X S α α = 0.6 x 4.563.228,26 + 1 – 0.6 3.043.283,656 = 2.737.936,956 + 0.4 3.043.283,656 = 2.737.936,956 + 1.217.313,463 = 3.955.250,419 Universitas Sumatera Utara b. 1 1 − − + = t II t I t II S S S α α = 0.6 x 3.955.250,419 + 1 – 0.6 2.735.736,665 = 2.737.150,251 + 0.4 2.735.736,665 = 2.737.150,251 + 1.094,294,666 = 3.467.444,917 c. a t = 2 S I t - S II t = 2 3.955.250,419 – 3.467.444,917 = 7.910.500,837 - 3.467.444,917 = 4.443.055,92 d. t II t I t S S b − − = α α 1 = 6 . 1 6 . − 3.955.250,419 - 3.467.444,917 = 4 . 6 . 487.805,501 = 731.708,252 e. Forecast F t+m = a t + b t m F 2000+1 = 4.443.055,92 + 731.708,252 1 F 2001 = 4.443.055,92 + 731.708,252 Universitas Sumatera Utara = 5.174.764,172 Tahun 2001 : X t = 5.510.135,7 a. 1 1 − − + = t I t t I S X S α α = 0.6 x 5.510.135,7 + 1 – 0.6 3.955.250,419 = 3.306.081,42 + 0.4 3.955.250,419 = 3.306.081,42 + 1.582.100,167 = 4.888.181,587 b. 1 1 − − + = t II t I t II S S S α α = 0.6 x 4.888.181,587 + 1 – 0.6 3.467.444,917 = 2.932.908,952 + 0.4 3.467.444,917 = 2.932.908,952 + 1.386.977,967 = 4.319.886,919 c. a t = 2 S I t - S II t = 2 4.888.181,587 – 4.319.886,919 = 9.776.363,175 - 4.319.886,919 = 5.456.476,256 d. t II t I t S S b − − = α α 1 Universitas Sumatera Utara = 6 . 1 6 . − 4.888.181,587 - 4.319.886,919 = 4 . 6 . 568.294,668 = 852.442,002 e. Forecast F t+m = a t + b t m F 2001+1 = 5.456.476,256 + 852.442,002 1 F 2002 = 5.456.476,256 + 852.442,002 = 6.308.918,258 Tahun 2002 : X t = 6.135.245,81 a. 1 1 − − + = t I t t I S X S α α = 0.6 x 6.135.245,81 + 1 – 0.6 4.888.181,587 = 3.681.147,486 + 0.4 4.888.181,587 = 3.681.147,486 + 1.955.272,635 = 5.636.420,121 b. 1 1 − − + = t II t I t II S S S α α Universitas Sumatera Utara = 0.6 x 5.636.420,121 + 1 – 0.6 4.319.886,919 = 3.381.852,073 + 0.4 4.319.886,919 = 3.381.852,073 + 1.727.954,768 = 5.109.806,84 c. a t = 2 S I t - S II t = 2 5.636.420,121 – 5.109.806,84 = 11.272.840,24 - 5.109.806,84 = 6.163.033,402 d. t II t I t S S b − − = α α 1 = 6 . 1 6 . − 5.636.420,121 - 5.109.806,84 = 4 . 6 . 526.613,281 = 789.919,921 e. Forecast F t+m = a t + b t m F 2002+1 = 6.163.033,402 + 789.919,921 1 F 2003 = 6.163.033,402 + 789.919,921 = 6.952.953,323 Universitas Sumatera Utara Tahun 2003 : X t = 6.569.556,17 a. 1 1 − − + = t I t t I S X S α α = 0.6 x 6.569.556,17 + 1 – 0.6 5.636.420,121 = 3.941.733,702 + 0.4 5.636.420,121 = 3.941.733,702 + 2.254.568,048 = 6.196.301,75 b. 1 1 − − + = t II t I t II S S S α α = 0.6 x 6.196.301,75 + 1 – 0.6 5.109.806,84 = 3.717.781,05 + 0.4 5.109.806,84 = 3.717.781,05 + 2.043.922,736 = 5.761.703,786 c. a t = 2 S I t - S II t = 2 6.196.301,75 – 5.761.703,786 = 12.392.603,5 - 5.761.703,786 = 6.630.899,714 d. t II t I t S S b − − = α α 1 = 6 . 1 6 . − 6.196.301,75 - 5.761.703,786 Universitas Sumatera Utara = 4 . 6 . 434.597,964 = 651.896,946 e. Forecast F t+m = a t + b t m F 2003+1 = 6.630.899,714 + 651.896,946 1 F 2004 = 6.630.899,714 + 651.896,946 = 7.282.796,66 Tahun 2004 : X t = 7.313.398,82 a. 1 1 − − + = t I t t I S X S α α = 0.6 x 7.313.398,82 + 1 – 0.6 6.196.301,75 = 4.388.039,292 + 0.4 6.196.301,75 = 4.388.039,292 + 2.478.520,7 = 6.866.559,992 b. 1 1 − − + = t II t I t II S S S α α = 0.6 x 6.866.559,992 + 1 – 0.6 5.761.703,786 = 4.119.935,995 + 0.4 5.761.703,786 = 4.119.935,995 + 2.304.681,515 = 6.424.617,51 Universitas Sumatera Utara c. a t = 2 S I t - S II t = 2 6.866.559,992 – 6.424.617,51 = 13.733.119,98 - 6.424.617,51 = 7.308.502,474 d. t II t I t S S b − − = α α 1 = 6 . 1 6 . − 6.866.559,992 - 6.424.617,51 = 4 . 6 . 441.942,482 = 662.913,723 e. Forecast F t+m = a t + b t m F 2004+1 = 7.308.502,474 + 662.913,723 1 F 2005 = 7.308.502,474 + 662.913,723 = 7.971.416,198 Tahun 2005 : X t = 9.209.143,29 a. 1 1 − − + = t I t t I S X S α α Universitas Sumatera Utara = 0.6 x 9.209.143,29 + 1 – 0.6 6.866.559,992 = 5.525.485,974 + 0.4 6.866.559,992 = 5.525.485,974 + 2.746.623,997 = 8.272.109,971 b. 1 1 − − + = t II t I t II S S S α α = 0.6 x 8.272.109,971 + 1 – 0.6 6.424.617,51 = 4.963.265,983 + 0.4 6.424.617,51 = 4.963.265,983 + 2.569.847,004 = 7.533.112,986 c. a t = 2 S I t - S II t = 2 8.272.109,971 – 7.533.112,986 = 16.544.219,94 - 7.533.112,986 = 9.011.106,955 d. t II t I t S S b − − = α α 1 = 6 . 1 6 . − 8.272.109,971 - 7.533.112,986 = 4 . 6 . 738.996,984 = 1.108.495,48 e. Forecast Universitas Sumatera Utara F t+m = a t + b t m F 2005+1 = 9.011.106,955 + 1.108.495,48 1 F 2006 = 9.011.106,955 + 1.108.495,48 = 10.119.602,43 Tahun 2006 : X t = 10.242.023,94 a. 1 1 − − + = t I t t I S X S α α = 0.6 x 10.242.023,94 + 1 – 0.6 8.272.109,971 = 6.145.214,364 + 0.4 8.272.109,971 = 6.145.214,364 + 3.308.843,988 = 9.454.058,352 b. 1 1 − − + = t II t I t II S S S α α = 0.6 x 9.454.058,352 + 1 – 0.6 7.533.112,986 = 5.672.435,011 + 0.4 7.533.112,986 = 5.672.435,011 + 3.013.245,195 = 8.685.680,206 c. a t = 2 S I t - S II t = 2 9.454.058,352 – 8.685.680,206 = 18.908.116,7 - 8.685.680,206 Universitas Sumatera Utara = 10.222.436,5 d. t II t I t S S b − − = α α 1 = 6 . 1 6 . − 9.454.058,352 - 8.685.680,206 = 4 . 6 . 768.378,146 = 1.152.567,22 e. Forecast F t+m = a t + b t m F 2006+1 = 10.222.436,5+ 1.152.567,22 1 F 2007 = 10.222.436,5 + 1.152.567,22 = 11.375.003,72 Tahun 2007 : X t = 11.362.637,09 a. 1 1 − − + = t I t t I S X S α α = 0.6 x 11.362.637,09 + 1 – 0.6 9.454.058,352 = 6.817.582,254 + 0.4 9.454.058,352 = 6.817.582,254 + 3.781.623,341 = 10.599.205,59 Universitas Sumatera Utara b. 1 1 − − + = t II t I t II S S S α α = 0.6 x 10.599.205,59 + 1 – 0.6 8.685.680,206 = 6.359.523,357 + 0.4 8.685.680,206 = 6.359.523,357 + 3.474.272,082 = 9.833.795,439 c. a t = 2 S I t - S II t = 2 10.599.205,59 – 9.833.795,439 = 21.198.411,19 - 9.833.795,439 = 11.364.615,75 d. t II t I t S S b − − = α α 1 = 6 . 1 6 . − 10.599.205,59 - 9.833.795,439 = 4 . 6 . 765.410,156 = 1.148.115,23 e. Forecast F t+m = a t + b t m F 2007+1 = 11.364.615,75+ 1.148.115,23 1 F 2008 = 11.364.615,75 + 1.148.115,23 Universitas Sumatera Utara = 12.512.730,98 n F X MAE t t ∑ − = 10 495 4.371.902, = MAE = 437.190,2495 n F X MSE t t 2 ∑ − = 10 293.841,07 3.759.919. = MSE = 375.991.929.384,11 Besarnya peramalan forecast bila digunakan alpha 0.9 adalah sebagai berikut. Tahun 1997 : S I t : ditentukan oleh PDRB tahun pertama, yaitu sebesar 1.875.287,45 S II t : ditentukan juga oleh besarnya PDRB tahun pertama, yaitu sebesar 1.875.287,45 a t : belum bisa ditentukan karena merupakan data pertama. b t : belum bisa ditentukan karena merupakan data pertama. F t+m : peramalan forecast tahun kedua F 2001 ditentukan oleh besarnya PDRB tahun pertama, yaitu sebesar 1.875.287,45 Universitas Sumatera Utara Tahun 1998 : X t = 2.983.978,36 a. 1 1 − − + = t I t t I S X S α α = 0.9 x 2.983.978,36 + 1 – 0.9 1.875.287,45 = 2.685.580,524 + 0.1 1.875.287,45 = 2.685.580,524 + 187.528,745 = 2.873.109,269 b. 1 1 − − + = t II t I t II S S S α α = 0.9 x 2.873.109,269 + 1 – 0.9 1.875.287,45 = 2.585.798,342 + 0.1 1.875.287,45 = 2.585.798,342 + 187.528,745 = 2.773.327,087 c. a t = 2 S I t - S II t = 2 2.873.109,269 – 2.773.327,087 = 5.746.218,538 - 2.773.327,087 = 2.972.891,451 d. t II t I t S S b − − = α α 1 = 9 . 1 9 . − 2.873.109,269 - 2.773.327,087 Universitas Sumatera Utara = 1 . 9 . 99.782,1819 = 898.039,637 e. Forecast F t+m = a t + b t m F 1998+1 = 2.972.891,451 + 898.039,637 1 F 1999 = 2.972.891,451 + 898.039,637 = 3.870.931,088 Tahun 1999 : X t = 3.378.471,43 a. 1 1 − − + = t I t t I S X S α α = 0.9 x 3.378.471,43 + 1 – 0.9 2.873.109,269 = 3.040.624,287 + 0.1 2.873.109,269 = 3.040.624,287 + 287.310,9269 = 3.327.935,214 b. 1 1 − − + = t II t I t II S S S α α = 0.9 x 3.327.935,214 + 1 – 0.9 2.773.327,087 = 2.995.141,693 + 0.1 2.773.327,087 = 2.995.141,693 + 277.332,7087 = 3.272.474,401 Universitas Sumatera Utara c. a t = 2 S I t - S II t = 2 3.327.935,214 – 3.272.474,401 = 6.655.870,428 - 3.272.474,401 = 3.383.396,027 d. t II t I t S S b − − = α α 1 = 9 . 1 9 . − 3.327.935,214 - 3.272.474,401 = 1 . 9 . 55.460,8127 = 499.147,314 e. Forecast F t+m = a t + b t m F 1999+1 = 3.383.396,027 + 499.147,314 1 F 2000 = 3.383.396,027 + 499.147,314 = 3.882.543,341 Tahun 2000 : X t = 4.563.228,26 a. 1 1 − − + = t I t t I S X S α α = 0.9 x 4.563.228,26 + 1 – 0.9 3.327.935,214 Universitas Sumatera Utara = 4.106.905,434 + 0.1 3.327.935,214 = 4.106.905,434 + 332.793,5214 = 4.439.698,955 b. 1 1 − − + = t II t I t II S S S α α = 0.9 x 4.439.698,955 + 1 – 0.9 3.272.474,401 = 3.995.729,06 + 0.1 3.272.474,401 = 3.995.729,06 + 327.247,4401 = 4.322.976,5 c. a t = 2 S I t - S II t = 2 4.439.698,955 – 4.322.976,5 = 8.879.397,911 - 4.322.976,5 = 4.556.421,411 d. t II t I t S S b − − = α α 1 = 9 . 1 9 . − 4.439.698,955 - 4.322.976,5 = 1 . 9 . 116.722,455 = 1.050.502,1 e. Forecast F t+m = a t + b t m Universitas Sumatera Utara F 2000+1 = 4.556.421,411 + 1.050.502,1 1 F 2001 = 4.556.421,411 + 1.050.502,1 = 5.606.923,51 Tahun 2001 : X t = 5.510.135,7 a. 1 1 − − + = t I t t I S X S α α = 0.9 x 5.510.135,7 + 1 – 0.9 4.439.698,955 = 4.959.122.13 + 0.1 4.439.698,955 = 4.959.122.13 + 443.969.8955 = 5.403.092,026 b. 1 1 − − + = t II t I t II S S S α α = 0.9 x 5.403.092,026 + 1 – 0.9 4.322.976,5 = 4.862.782,823 + 0.1 4.322.976,5 = 4.862.782,823 + 432.297,65 = 5.295.080,473 c. a t = 2 S I t - S II t = 2 5.403.092,026 – 5.295.080,473 = 10.806.184,05 - 5.295.080,473 Universitas Sumatera Utara = 5.511.103,578 d. t II t I t S S b − − = α α 1 = 9 . 1 9 . − 5.403.092,026 - 5.295.080,473 = 1 . 9 . 108.011,553 = 972.103,973 e. Forecast F t+m = a t + b t m F 2001+1 = 5.511.103,578 + 972.103,973 1 F 2002 = 5.511.103,578 + 972.103,973 = 6.483.207,551 Tahun 2002 : X t = 6.135.245,81 a. 1 1 − − + = t I t t I S X S α α = 0.9 x 6.135.245,81 + 1 – 0.9 5.403.092,026 = 5.521.721,229 + 0.1 5.403.092,026 = 5.521.721,229 + 540.309,2026 = 6.062.030,432 Universitas Sumatera Utara b. 1 1 − − + = t II t I t II S S S α α = 0.9 x 6.062.030,432 + 1 – 0.9 5.295.080,473 = 5.455.827,388 + 0.1 5.295.080,473 = 5.455.827,388 + 529.508,0473 = 5.985.335,436 c. a t = 2 S I t - S II t = 2 6.062.030,432 – 5.985.335,436 = 12.124.060,86 - 5.985.335,436 = 6.138.725,427 d. t II t I t S S b − − = α α 1 = 9 . 1 9 . − 6.062.030,432 - 5.985.335,436 = 1 . 9 . 76.694,9959 = 690.254,963 e. Forecast F t+m = a t + b t m F 2002+1 = 6.138.725,427 + 690.254,963 1 F 2003 = 6.138.725,427 + 690.254,963 Universitas Sumatera Utara = 6.828.980,39 Tahun 2003 : X t = 6.569.556,17 a. 1 1 − − + = t I t t I S X S α α = 0.9 x 6.569.556,17 + 1 – 0.9 6.062.030,432 = 5.912.600,553 + 0.1 6.062.030,432 = 5.912.600,553 + 606.203,0432 = 6.518.803,596 b. 1 1 − − + = t II t I t II S S S α α = 0.9 x 6.518.803,596 + 1 – 0.9 5.985.335,43 = 5.866.923,237 + 0.1 5.985.335,436 = 5.866.923,237 + 598.533,5436 = 6.465.456,78 c. a t = 2 S I t - S II t = 2 6.518.803,596 – 6.465.456,78 = 13.037.607,19 - 6.465.456,78 = 6.572.150,412 d. t II t I t S S b − − = α α 1 Universitas Sumatera Utara = 9 . 1 9 . − 6.518.803,596 - 6.465.456,78 = 1 . 9 . 53.346,816 = 480.121.,344 e. Forecast F t+m = a t + b t m F 2003+1 = 6.572.150,412 + 480.121.,344 1 F 2004 = 6.572.150,412 + 480.121.,344 = 7.052.271,757 Tahun 2004 : X t = 7.313.398,82 a. 1 1 − − + = t I t t I S X S α α = 0.9 x 7.313.398,82 + 1 – 0.9 6.518.803,596 = 6.582.058,938 + 0.1 6.518.803,596 = 6.582.058,938 + 651.880,3596 = 7.233.939,298 b. 1 1 − − + = t II t I t II S S S α α = 0.9 x 7.233.393,9298 + 1 – 0.9 6.465.456,78 = 6.510.545,368 + 0.1 6.465.456,78 Universitas Sumatera Utara = 6.510.545,368 + 646.545,678 = 7.157.091,046 c. a t = 2 S I t - S II t = 2 7.233.393,9298 – 7.157.091,046 = 14.467.878,6 - 7.157.091,046 = 7.310.787,549 d. t II t I t S S b − − = α α 1 = 9 . 1 9 . − 7.233.393,9298 - 7.157.091,046 = 1 . 9 . 76.848,2518 = 691.634,266 e. Forecast F t+m = a t + b t m F 2004+1 = 7.310.787,549 + 691.634,266 1 F 2005 = 7.310.787,549 + 691.634,266 = 8.002.421,815 Tahun 2005 : X t = 9.209.143,29 Universitas Sumatera Utara a. 1 1 − − + = t I t t I S X S α α = 0.9 x 9.209.143,29 + 1 – 0.9 7.233.939,298 = 8.288.228,961 + 0.1 7.233.939,298 = 8.288.228,961 + 723.393,9298 = 9.011.622,891 b. 1 1 − − + = t II t I t II S S S α α = 0.9 x 9.011.622,891 + 1 – 0.9 7.157.091,046 = 8.110.460,602 + 0.1 7.157.091,046 = 8.110.460,602 + 715.709,1046 = 8.826.169,706 c. a t = 2 S I t - S II t = 2 9.011.622,891 – 8.826.169,706 = 18.023.245,78 - 8.826.169,706 = 9.197.076,075 d. t II t I t S S b − − = α α 1 = 9 . 1 9 . − 9.011.622,891 - 8.826.169,706 = 1 . 9 . 185.453,184 = 1.669.078,66 Universitas Sumatera Utara e. Forecast F t+m = a t + b t m F 2005+1 = 9.197.076,075 + 1.669.078,66 1 F 2006 = 9.197.076,075 + 1.669.078,66 = 10.866.154,74 Tahun 2006 : X t = 10.242.023,94 a. 1 1 − − + = t I t t I S X S α α = 0.9 x 10.242.023,94 + 1 – 0.9 9.011.622,891 = 9.217.821,546 + 0.1 9.011.622,891 = 9.217.821,546 + 901.162,2891 = 10.118.983,84 b. 1 1 − − + = t II t I t II S S S α α = 0.9 x 10.118.983,84 + 1 – 0.9 8.826.169,706 = 9.107.085,452 + 0.1 8.826.169,706 = 9.107.085,452 + 882.616,9706 = 9.989.702,422 c. a t = 2 S I t - S II t = 2 10.118.983,84 – 9.989.702,422 Universitas Sumatera Utara = 20.237.967,67 - 9.989.702,422 = 10.248.265,25 d. t II t I t S S b − − = α α 1 = 9 . 1 9 . − 9.011.622,891 - 9.989.702,422 = 1 . 9 . 129.281,413 = 1.163.532,72 e. Forecast F t+m = a t + b t m F 2006+1 = 10.248.265,25 + 1.163.532,72 1 F 2007 = 10.248.265,25 + 1.163.532,72 = 11.411.797,96 Tahun 2007 : X t = 11.362.637,09 a. 1 1 − − + = t I t t I S X S α α = 0.9 x 11.362.637,09 + 1 – 0.9 10.118.983,84 = 10.226.373,38 + 0.1 10.118.983,84 = 10.226.373,38 + 1.011.898,384 = 11.238.271,76 Universitas Sumatera Utara b. 1 1 − − + = t II t I t II S S S α α = 0.9 x 11.238.271,76 + 1 – 0.9 9.989.702,422 = 10.114.444,59 + 0.1 9.989.702,422 = 10.114.444,59 + 998.970,2422 = 11.113.414,83 c. a t = 2 S I t - S II t = 2 11.238.271,76 – 11.113.414,83 = 22.476.543,53 - 11.113.414,83 = 11.363.128,7 d. t II t I t S S b − − = α α 1 = 9 . 1 9 . − 11.238.271,76 - 11.113.414,83 = 1 . 9 . 129.281,413 = 1.163.532,72 e. Forecast F t+m = a t + b t m F 2007+1 = 11.363.128,7 + 1.163.532,72 1 F 2008 = 11.363.128,7 + 1.163.532,72 Universitas Sumatera Utara = 12.486.841.11 n F X MAE t t ∑ − = 10 519.860,99 = MAE = 519.686,0399 n F X MSE t t 2 ∑ − = 10 60.246,02 4208.545.6 = MSE = 420.854.566.024,60

4.2 Evaluasi Data