iii Universitas Sumatera Utara

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no 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47

bulan JAN FEB MAR APR MEI JUN JUL AGTS SEP OKT NOV DES JAN FEB MAR APR MEI JUN JUL AGTS SEP OKT NOV DES JAN FEB MAR APR MEI JUN JUL AGTS SEP OKT NOV DES JAN FEB MAR APR MEI JUN JUL AGTS SEP OKT NOV

tahun 2002 2002 2002 2002 2002 2002 2002 2002 2002 2002 2002 2002 2003 2003 2003 2003 2003 2003 2003 2003 2003 2003 2003 2003 2004 2004 2004 2004 2004 2004 2004 2004 2004 2004 2004 2004 2005 2005 2005 2005 2005 2005 2005 2005 2005 2005 2005

suhu 26.3 26.7 27.4 26.6 27.6 26.7 27.4 27.6 25.7 26.4 25.8 26.1 26.4 26.6 27.2 27.6 27.9 27.3 27.1 26.7 26.6 26.2 26.5 25.9 26.6 26.7 27 27.3 28 26.5 25.3 26.2 25.6 25.7 26.7 24.7 28.4 27 27.8 28.1 26.4 26 27.5 27.8 25.8 26.6 26.7

Universitas Sumatera Utara

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48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72

DES JAN FEB MAR APR MEI JUN JUL AGTS SEP OKT NOV DES JAN FEB MAR APR MEI JUN JUL AGTS SEP OKT NOV DES

2005 2006 2006 2006 2006 2006 2006 2006 2006 2006 2006 2006 2006 2007 2007 2007 2007 2007 2007 2007 2007 2007 2007 2007 2007

26.2 26.6 27 27.5 27.5 27.5 27.4 27.7 27.2 25.1 26.6 26.4 26.2 26.3 26.6 27.6 27.6 27.7 27.3 27.1 27.1 26.9 26.6 26 26.2


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no 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49

bulan JAN FEB MAR APR MEI JUN JUL AGTS SEP OKT NOV DES JAN FEB MAR APR MEI JUN JUL AGTS SEP OKT NOV DES JAN FEB MAR APR MEI JUN JUL AGTS SEP OKT NOV DES JAN FEB MAR APR MEI JUN JUL AGTS SEP OKT NOV DES JAN

tahun 2002 2002 2002 2002 2002 2002 2002 2002 2002 2002 2002 2002 2003 2003 2003 2003 2003 2003 2003 2003 2003 2003 2003 2003 2004 2004 2004 2004 2004 2004 2004 2004 2004 2004 2004 2004 2005 2005 2005 2005 2005 2005 2005 2005 2005 2005 2005 2005 2006

suhu 26.3 26.7 27.4 26.6 27.6 26.7 27.4 27.6 25.7 26.4 25.8 26.1 26.4 26.6 27.2 27.6 27.9 27.3 27.1 26.7 26.6 26.2 26.5 25.9 26.6 26.7 27 27.3 28 26.5 25.3 26.2 25.6 25.7 26.7 24.7 28.4 27 27.8 28.1 26.4 26 27.5 27.8 25.8 26.6 26.7 26.2 26.6

lag 1 * 26.3 26.7 27.4 26.6 27.6 26.7 27.4 27.6 25.7 26.4 25.8 26.1 26.4 26.6 27.2 27.6 27.9 27.3 27.1 26.7 26.6 26.2 26.5 25.9 26.6 26.7 27 27.3 28 26.5 25.3 26.2 25.6 25.7 26.7 24.7 28.4 27 27.8 28.1 26.4 26 27.5 27.8 25.8 26.6 26.7 26.2

diff 1 * 0.4 0.7 -0.8 1 -0.9 0.7 0.2 -1.9 0.7 -0.6 0.3 0.3 0.2 0.6 0.4 0.3 -0.6 -0.2 -0.4 -0.1 -0.4 0.3 -0.6 0.7 0.1 0.3 0.3 0.7 -1.5 -1.2 0.9 -0.6 0.1 1 -2 3.7 -1.4 0.8 0.3 -1.7 -0.4 1.5 0.3 -2 0.8 0.1 -0.5 0.4


iii

50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72

FEB MAR APR MEI JUN JUL AGTS SEP OKT NOV DES JAN FEB MAR APR MEI JUN JUL AGTS SEP OKT NOV DES

2006 2006 2006 2006 2006 2006 2006 2006 2006 2006 2006 2007 2007 2007 2007 2007 2007 2007 2007 2007 2007 2007 2007

27 27.5 27.5 27.5 27.4 27.7 27.2 25.1 26.6 26.4 26.2 26.3 26.6 27.6 27.6 27.7 27.3 27.1 27.1 26.9 26.6 26 26.2

26.6 27 27.5 27.5 27.5 27.4 27.7 27.2 25.1 26.6 26.4 26.2 26.3 26.6 27.6 27.6 27.7 27.3 27.1 27.1 26.9 26.6 26

0.4 0.5 0 0 -0.1 0.3 -0.5 -2.1 1.5 -0.2 -0.2 0.1 0.3 1 0 0.1 -0.4 -0.2 0 -0.2 -0.3 -0.6 0.2


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no 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49

bulan JAN FEB MAR APR MEI JUN JUL AGTS SEP OKT NOV DES JAN FEB MAR APR MEI JUN JUL AGTS SEP OKT NOV DES JAN FEB MAR APR MEI JUN JUL AGTS SEP OKT NOV DES JAN FEB MAR APR MEI JUN JUL AGTS SEP OKT NOV DES JAN

tahun 2002 2002 2002 2002 2002 2002 2002 2002 2002 2002 2002 2002 2003 2003 2003 2003 2003 2003 2003 2003 2003 2003 2003 2003 2004 2004 2004 2004 2004 2004 2004 2004 2004 2004 2004 2004 2005 2005 2005 2005 2005 2005 2005 2005 2005 2005 2005 2005 2006

suhu 26.3 26.7 27.4 26.6 27.6 26.7 27.4 27.6 25.7 26.4 25.8 26.1 26.4 26.6 27.2 27.6 27.9 27.3 27.1 26.7 26.6 26.2 26.5 25.9 26.6 26.7 27 27.3 28 26.5 25.3 26.2 25.6 25.7 26.7 24.7 28.4 27 27.8 28.1 26.4 26 27.5 27.8 25.8 26.6 26.7 26.2 26.6

lag 2 * * 26.3 26.7 27.4 26.6 27.6 26.7 27.4 27.6 25.7 26.4 25.8 26.1 26.4 26.6 27.2 27.6 27.9 27.3 27.1 26.7 26.6 26.2 26.5 25.9 26.6 26.7 27 27.3 28 26.5 25.3 26.2 25.6 25.7 26.7 24.7 28.4 27 27.8 28.1 26.4 26 27.5 27.8 25.8 26.6 26.7

diff 2 * * 0.3 -1.5 1.8 -1.9 1.6 -0.5 -2.1 2.6 -1.3 0.9 0 -0.1 0.4 -0.2 -0.1 -0.9 0.4 -0.2 0.3 -0.3 0.7 -0.9 1.3 -0.6 0.2 0 0.4 -2.2 0.3 2.1 -1.5 0.7 0.9 -3 5.7 -5.1 2.2 -0.5 -2 1.3 1.9 -1.2 -2.3 2.8 -0.7 -0.6 0.9


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50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72

FEB MAR APR MEI JUN JUL AGTS SEP OKT NOV DES JAN FEB MAR APR MEI JUN JUL AGTS SEP OKT NOV DES

2006 2006 2006 2006 2006 2006 2006 2006 2006 2006 2006 2007 2007 2007 2007 2007 2007 2007 2007 2007 2007 2007 2007

27 27.5 27.5 27.5 27.4 27.7 27.2 25.1 26.6 26.4 26.2 26.3 26.6 27.6 27.6 27.7 27.3 27.1 27.1 26.9 26.6 26 26.2

26.2 26.6 27 27.5 27.5 27.5 27.4 27.7 27.2 25.1 26.6 26.4 26.2 26.3 26.6 27.6 27.6 27.7 27.3 27.1 27.1 26.9 26.6

0 0.1 -0.5 0 -0.1 0.4 -0.8 -1.6 3.6 -1.7 0 0.3 0.2 0.7 -1 0.1 -0.5 0.2 0.2 -0.2 -0.1 -0.3 0.8


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Correlations: AKTUAL, 001;100 Pearson correlation of AKTUAL and 001;100 = 0.600 P-Value = 0.039

ARIMA Model: SUHU ARIMA model for SUHU Estimates at each iteration Iteration SSE Parameters 0 101.954 0.100 0.100 1 72.250 -0.035 0.235 2 66.581 0.052 0.385 3 59.962 0.122 0.535 4 51.815 0.161 0.685 5 44.604 0.139 0.768 6 39.421 0.101 0.801 7 39.372 0.049 0.836 8 37.530 -0.022 0.800 9 37.146 -0.011 0.818 10 37.123 0.006 0.830 11 37.121 0.009 0.833 12 37.120 0.011 0.835 13 37.120 0.012 0.836 14 37.120 0.012 0.836 Final Estimates of Parameters Type Coef SE Coef AR 1 0.0122 0.1184 MA 1 0.8363 0.0652 SMA 12 0.8793 0.0822 Constant 0.002258 0.002332

T 0.10 12.83 10.70 0.97

0.100 0.250 0.301 0.371 0.485 0.635 0.785 0.935 0.909 0.882 0.881 0.879 0.880 0.879 0.879

0.094 0.001 0.002 0.003 0.004 0.005 0.004 0.004 0.001 0.002 0.002 0.002 0.002 0.002 0.002

P 0.918 0.000 0.000 0.335

Differencing: 1 regular, 1 seasonal of order 12 Number of observations: Original series 120, after differencing 107 Residuals: SS = 34.4928 (backforecasts excluded) MS = 0.3349 DF = 103 Modified Box-Pierce (Ljung-Box) Chi-Square statistic Lag 12 24 36 48 Chi-Square 4.8 16.5 29.6 44.3 DF 8 20 32 44 P-Value 0.780 0.685 0.587 0.457 Forecasts from period 120 Period 121 122 123 124 125 126 127 128 129 130 131 132

Forecast 26.8284 27.0742 27.5321 27.6195 27.6925 27.2130 27.2672 27.2581 26.2394 26.6839 26.5959 26.1890

95 Percent Limits Lower Upper 25.6940 27.9629 25.9223 28.2261 26.3650 28.6992 26.4374 28.8017 26.4955 28.8895 26.0014 28.4247 26.0410 28.4933 26.0176 28.4986 24.9847 27.4940 25.4152 27.9525 25.3134 27.8784 24.8928 27.4852

Actual

Correlations: AKTUAL, 111;011


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Pearson correlation of AKTUAL and 111;011 = 0.633 P-Value = 0.027

ARIMA Model: SUHU ARIMA model for SUHU Estimates at each iteration Iteration SSE Parameters 0 67.5129 0.100 0.100 0.075 1 54.5810 -0.050 0.250 -0.015 2 52.3584 0.064 0.400 -0.012 3 49.8203 0.169 0.550 -0.009 4 46.7227 0.258 0.700 -0.008 5 41.6239 0.260 0.850 -0.005 6 38.2031 0.110 0.860 -0.000 7 36.1059 -0.040 0.893 0.001 Unable to reduce sum of squares any further Final Estimates of Parameters Type Coef SE Coef SAR 12 -0.0405 0.1131 SMA 12 0.8931 0.0923 Constant 0.00106 0.01125

T -0.36 9.67 0.09

P 0.721 0.000 0.925

Differencing: 0 regular, 1 seasonal of order 12 Number of observations: Original series 120, after differencing 108 Residuals: SS = 32.4045 (backforecasts excluded) MS = 0.3086 DF = 105 Modified Box-Pierce (Ljung-Box) Chi-Square statistic Lag 12 24 36 48 Chi-Square 8.0 19.8 31.0 46.0 DF 9 21 33 45 P-Value 0.536 0.531 0.567 0.431 Forecasts from period 120 Period 121 122 123 124 125 126 127 128 129 130 131 132

Forecast 26.6844 26.9236 27.3378 27.4110 27.4789 26.9986 27.0616 27.0287 25.9388 26.4313 26.3517 25.9486

95 Percent Limits Lower Upper 25.5954 27.7735 25.8345 28.0126 26.2488 28.4269 26.3220 28.5001 26.3899 28.5680 25.9096 28.0877 25.9726 28.1507 25.9397 28.1178 24.8498 27.0279 25.3422 27.5203 25.2627 27.4408 24.8595 27.0376

Actual

Correlations: AKTUAL, 000;111


iii

Pearson correlation of AKTUAL and 000;111 = 0.614 P-Value = 0.034

ARIMA Model: SUHU ARIMA model for SUHU Estimates at each iteration Iteration SSE Parameters 0 101.836 0.100 0.100 0.100 1 96.179 -0.050 0.071 -0.004 2 92.595 -0.200 0.043 -0.124 3 89.598 -0.350 0.012 -0.248 4 86.775 -0.500 -0.022 -0.373 5 83.975 -0.650 -0.060 -0.498 6 76.790 -0.561 -0.090 -0.348 7 75.323 -0.425 -0.071 -0.198 8 73.943 -0.289 -0.049 -0.048 9 72.631 -0.153 -0.024 0.102 10 71.450 -0.019 0.002 0.252 11 69.645 0.111 0.029 0.402 12 67.264 0.235 0.057 0.552 13 63.701 0.344 0.085 0.702 14 56.383 0.399 0.107 0.852 15 47.226 0.270 0.091 0.867 16 41.477 0.198 0.085 0.874 17 37.457 0.149 0.085 0.888 18 37.017 0.048 0.071 0.870 19 37.010 0.048 0.072 0.875 20 37.009 0.045 0.071 0.874 21 37.008 0.048 0.073 0.876 22 37.008 0.047 0.073 0.875 23 37.008 0.048 0.073 0.876 24 37.008 0.048 0.073 0.876 Unable to reduce sum of squares any further Final Estimates of Parameters Type Coef SE Coef AR 1 0.0476 0.1201 AR 2 0.0734 0.1151 MA 1 0.8762 0.0678 SMA 12 0.8739 0.0846 Constant 0.001668 0.001931

T 0.40 0.64 12.92 10.33 0.86

0.100 0.117 0.131 0.144 0.159 0.176 0.232 0.245 0.256 0.267 0.272 0.285 0.303 0.333 0.406 0.556 0.706 0.856 0.871 0.876 0.873 0.875 0.874 0.874 0.874

0.084 0.083 0.086 0.089 0.091 0.091 0.064 0.054 0.045 0.037 0.030 0.025 0.018 0.012 0.005 0.003 0.003 0.003 0.002 0.002 0.002 0.002 0.002 0.002 0.002

P 0.693 0.525 0.000 0.000 0.390

Differencing: 1 regular, 1 seasonal of order 12 Number of observations: Original series 120, after differencing 107 Residuals: SS = 34.4082 (backforecasts excluded) MS = 0.3373 DF = 102 Modified Box-Pierce (Ljung-Box) Chi-Square statistic Lag 12 24 36 48 Chi-Square 4.6 17.3 30.6 45.2 DF 7 19 31 43 P-Value 0.706 0.571 0.488 0.381 Forecasts from period 120 Period 121 122 123 124 125 126

Forecast 26.7819 27.0654 27.5156 27.6040 27.6720 27.1874

95 Percent Limits Lower Upper 25.6433 27.9205 25.9102 28.2207 26.3370 28.6943 26.4136 28.7943 26.4701 28.8739 25.9748 28.4000

Actual


iii

127 128 129 130 131 132

27.2393 27.2331 26.2202 26.6509 26.5615 26.1574

26.0161 25.9994 24.9760 25.3965 25.2968 24.8826

28.4626 28.4669 27.4643 27.9054 27.8261 27.4321

Correlations: AKTUAL, 110;011 Pearson correlation of AKTUAL and 110;011 = 0.620 P-Value = 0.032

ARIMA Model: SUHU ARIMA model for SUHU Estimates at each iteration Iteration SSE Parameters 0 69.5633 0.100 0.100 0.100 1 66.3828 0.211 0.083 0.250 2 58.4540 0.227 0.027 0.400 3 50.5070 0.077 -0.019 0.376 4 45.2826 0.117 -0.051 0.526 5 42.5261 -0.033 -0.070 0.453 6 40.4538 -0.183 -0.086 0.368 7 38.9434 -0.333 -0.097 0.272 8 37.7168 -0.483 -0.107 0.174 9 37.1654 -0.482 -0.134 0.288 10 36.5810 -0.632 -0.131 0.150 Unable to reduce sum of squares any further Final Estimates of Parameters Type Coef SE Coef SAR 12 -0.6317 0.6892 MA 1 -0.1305 0.0976 SMA 12 0.1500 0.6758 SMA 24 0.6338 0.5484 Constant 0.01540 0.01728

T -0.92 -1.34 0.22 1.16 0.89

0.100 0.122 0.106 0.176 0.206 0.274 0.350 0.443 0.542 0.516 0.634

0.075 0.055 0.064 0.041 0.019 0.022 0.020 0.019 0.016 0.013 0.015

P 0.362 0.184 0.825 0.250 0.375

Differencing: 0 regular, 1 seasonal of order 12 Number of observations: Original series 120, after differencing 108 Residuals: SS = 33.0678 (backforecasts excluded) MS = 0.3210 DF = 103 Modified Box-Pierce (Ljung-Box) Chi-Square statistic Lag 12 24 36 48 Chi-Square 7.3 15.1 25.6 39.3 DF 7 19 31 43 P-Value 0.395 0.714 0.742 0.631 Forecasts from period 120 Period 121 122 123 124 125 126 127

Forecast 26.9107 26.9499 27.4689 27.5723 27.4289 26.9545 27.1207

95 Percent Limits Lower Upper 25.7999 28.0215 25.8297 28.0701 26.3487 28.5891 26.4521 28.6925 26.3087 28.5491 25.8343 28.0747 26.0005 28.2409

Actual


iii

128 129 130 131 132

27.1477 26.2643 26.5061 26.3759 25.9706

26.0275 25.1441 25.3859 25.2557 24.8504

28.2679 27.3845 27.6263 27.4961 27.0908


iii

DEPARTEMEN PENDIDIKAN DAN KEBUDAYAAN UNIVERSITAS SUMATERA UTARA FAKULTAS MATEMATIKA DAN ILMU PENGETAHUAN ALAM

Jl. Bioteknologi No. 1 Kampus USU Telp. (061) 8211212, 8211298, 8211414 Medan 20155

KARTU BIMBINGAN TUGAS AKHIR MAHASISWA Nama Nim Judul Tugas Akhir

: MHD.FADLI : 062407141 : Peramalan Suhu Udara Bulanan di Kota Medan Dengan Metode Box-Jenkins. Dosen Pembimbing : Drs. Marwan Harahap, M.Eng Tanggal Mulai Bimbingan : Tanggal Selesai Bimbingan :

No Tanggal Asistensi Bimbingan

Pembahasan Asistensi Mengenai, Pada Bab

Diketahui/Disetujui oleh Departemen Matematika FMIPA USU Ketua,

Dr. Saib Suwilo, M.Sc NIP. 131 796 149

Paraf Dosen Pembimbing

Keterangan

Pembimbing,

Drs. Marwan Harahap, M.Eng NIP. 130 422 443


iii

SURAT KETERANGAN Hasil Uji Program Tugas Akhir

Yang bertanda tangan dibawah ini, menerangkan bahwa Mahasiswa Tugas Akhir Program Studi Diploma III Ilmu Komputer/Statistika: Nama NIM Program Studi Judul TA

: : : :

MHD.FADLI 062407141 D3 Statistika Peramalan Suhu Udara Bulanan di Kota Medan Dengan Metode Box-Jenkins.

Telah melaksanakan test program Tugas Akhir Mahasiswa tersebut di atas pada tanggal…../…./2009

Dengan Hasil: Sukses/Gagal

Demikian diterangkan untuk digunakan melengkapi syarat pendaftaran Ujian Meja Hijau Tugas Akhir Mahasiswa bersangkutan di Jurusan Matematika FMIPA USU Medan.

Medan,…../…../2009 Dosen Pembimbing/Kepala Lab Komputer Program D3 Ilmu Komputer/Statistika

Drs. Marwan Harahap, M.Eng NIP. 130 422 443


iii Universitas Sumatera Utara

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