iii Universitas Sumatera Utara

no bulan tahun suhu 1 JAN 2002 26.3 2 FEB 2002 26.7 3 MAR 2002 27.4 4 APR 2002 26.6 5 MEI 2002 27.6 6 JUN 2002 26.7 7 JUL 2002 27.4 8 AGTS 2002 27.6 9 SEP 2002 25.7 10 OKT 2002 26.4 11 NOV 2002 25.8 12 DES 2002 26.1 13 JAN 2003 26.4 14 FEB 2003 26.6 15 MAR 2003 27.2 16 APR 2003 27.6 17 MEI 2003 27.9 18 JUN 2003 27.3 19 JUL 2003 27.1 20 AGTS 2003 26.7 21 SEP 2003 26.6 22 OKT 2003 26.2 23 NOV 2003 26.5 24 DES 2003 25.9 25 JAN 2004 26.6 26 FEB 2004 26.7 27 MAR 2004 27 28 APR 2004 27.3 29 MEI 2004 28 30 JUN 2004 26.5 31 JUL 2004 25.3 32 AGTS 2004 26.2 33 SEP 2004 25.6 34 OKT 2004 25.7 35 NOV 2004 26.7 36 DES 2004 24.7 37 JAN 2005 28.4 38 FEB 2005 27 39 MAR 2005 27.8 40 APR 2005 28.1 41 MEI 2005 26.4 42 JUN 2005 26 43 JUL 2005 27.5 44 AGTS 2005 27.8 45 SEP 2005 25.8 46 OKT 2005 26.6 47 NOV 2005 26.7

48 DES 2005 26.2 49 JAN 2006 26.6 50 FEB 2006 27 51 MAR 2006 27.5 52 APR 2006 27.5 53 MEI 2006 27.5 54 JUN 2006 27.4 55 JUL 2006 27.7 56 AGTS 2006 27.2 57 SEP 2006 25.1 58 OKT 2006 26.6 59 NOV 2006 26.4 60 DES 2006 26.2 61 JAN 2007 26.3 62 FEB 2007 26.6 63 MAR 2007 27.6 64 APR 2007 27.6 65 MEI 2007 27.7 66 JUN 2007 27.3 67 JUL 2007 27.1 68 AGTS 2007 27.1 69 SEP 2007 26.9 70 OKT 2007 26.6 71 NOV 2007 26 72 DES 2007 26.2

no bulan tahun suhu lag 1 diff 1 1 JAN 2002 26.3 * * 2 FEB 2002 26.7 26.3 0.4 3 MAR 2002 27.4 26.7 0.7 4 APR 2002 26.6 27.4-0.8 5 MEI 2002 27.6 26.6 1 6 JUN 2002 26.7 27.6-0.9 7 JUL 2002 27.4 26.7 0.7 8 AGTS 2002 27.6 27.4 0.2 9 SEP 2002 25.7 27.6-1.9 10 OKT 2002 26.4 25.7 0.7 11 NOV 2002 25.8 26.4-0.6 12 DES 2002 26.1 25.8 0.3 13 JAN 2003 26.4 26.1 0.3 14 FEB 2003 26.6 26.4 0.2 15 MAR 2003 27.2 26.6 0.6 16 APR 2003 27.6 27.2 0.4 17 MEI 2003 27.9 27.6 0.3 18 JUN 2003 27.3 27.9-0.6 19 JUL 2003 27.1 27.3-0.2 20 AGTS 2003 26.7 27.1-0.4 21 SEP 2003 26.6 26.7-0.1 22 OKT 2003 26.2 26.6-0.4 23 NOV 2003 26.5 26.2 0.3 24 DES 2003 25.9 26.5-0.6 25 JAN 2004 26.6 25.9 0.7 26 FEB 2004 26.7 26.6 0.1 27 MAR 2004 27 26.7 0.3 28 APR 2004 27.3 27 0.3 29 MEI 2004 28 27.3 0.7 30 JUN 2004 26.5 28-1.5 31 JUL 2004 25.3 26.5-1.2 32 AGTS 2004 26.2 25.3 0.9 33 SEP 2004 25.6 26.2-0.6 34 OKT 2004 25.7 25.6 0.1 35 NOV 2004 26.7 25.7 1 36 DES 2004 24.7 26.7-2 37 JAN 2005 28.4 24.7 3.7 38 FEB 2005 27 28.4-1.4 39 MAR 2005 27.8 27 0.8 40 APR 2005 28.1 27.8 0.3 41 MEI 2005 26.4 28.1-1.7 42 JUN 2005 26 26.4-0.4 43 JUL 2005 27.5 26 1.5 44 AGTS 2005 27.8 27.5 0.3 45 SEP 2005 25.8 27.8-2 46 OKT 2005 26.6 25.8 0.8 47 NOV 2005 26.7 26.6 0.1 48 DES 2005 26.2 26.7-0.5 49 JAN 2006 26.6 26.2 0.4

50 FEB 2006 27 26.6 0.4 51 MAR 2006 27.5 27 0.5 52 APR 2006 27.5 27.5 0 53 MEI 2006 27.5 27.5 0 54 JUN 2006 27.4 27.5-0.1 55 JUL 2006 27.7 27.4 0.3 56 AGTS 2006 27.2 27.7-0.5 57 SEP 2006 25.1 27.2-2.1 58 OKT 2006 26.6 25.1 1.5 59 NOV 2006 26.4 26.6-0.2 60 DES 2006 26.2 26.4-0.2 61 JAN 2007 26.3 26.2 0.1 62 FEB 2007 26.6 26.3 0.3 63 MAR 2007 27.6 26.6 1 64 APR 2007 27.6 27.6 0 65 MEI 2007 27.7 27.6 0.1 66 JUN 2007 27.3 27.7-0.4 67 JUL 2007 27.1 27.3-0.2 68 AGTS 2007 27.1 27.1 0 69 SEP 2007 26.9 27.1-0.2 70 OKT 2007 26.6 26.9-0.3 71 NOV 2007 26 26.6-0.6 72 DES 2007 26.2 26 0.2

no bulan tahun suhu lag 2 diff 2 1 JAN 2002 26.3 * * 2 FEB 2002 26.7 * * 3 MAR 2002 27.4 26.3 0.3 4 APR 2002 26.6 26.7-1.5 5 MEI 2002 27.6 27.4 1.8 6 JUN 2002 26.7 26.6-1.9 7 JUL 2002 27.4 27.6 1.6 8 AGTS 2002 27.6 26.7-0.5 9 SEP 2002 25.7 27.4-2.1 10 OKT 2002 26.4 27.6 2.6 11 NOV 2002 25.8 25.7-1.3 12 DES 2002 26.1 26.4 0.9 13 JAN 2003 26.4 25.8 0 14 FEB 2003 26.6 26.1-0.1 15 MAR 2003 27.2 26.4 0.4 16 APR 2003 27.6 26.6-0.2 17 MEI 2003 27.9 27.2-0.1 18 JUN 2003 27.3 27.6-0.9 19 JUL 2003 27.1 27.9 0.4 20 AGTS 2003 26.7 27.3-0.2 21 SEP 2003 26.6 27.1 0.3 22 OKT 2003 26.2 26.7-0.3 23 NOV 2003 26.5 26.6 0.7 24 DES 2003 25.9 26.2-0.9 25 JAN 2004 26.6 26.5 1.3 26 FEB 2004 26.7 25.9-0.6 27 MAR 2004 27 26.6 0.2 28 APR 2004 27.3 26.7 0 29 MEI 2004 28 27 0.4 30 JUN 2004 26.5 27.3-2.2 31 JUL 2004 25.3 28 0.3 32 AGTS 2004 26.2 26.5 2.1 33 SEP 2004 25.6 25.3-1.5 34 OKT 2004 25.7 26.2 0.7 35 NOV 2004 26.7 25.6 0.9 36 DES 2004 24.7 25.7-3 37 JAN 2005 28.4 26.7 5.7 38 FEB 2005 27 24.7-5.1 39 MAR 2005 27.8 28.4 2.2 40 APR 2005 28.1 27-0.5 41 MEI 2005 26.4 27.8-2 42 JUN 2005 26 28.1 1.3 43 JUL 2005 27.5 26.4 1.9 44 AGTS 2005 27.8 26-1.2 45 SEP 2005 25.8 27.5-2.3 46 OKT 2005 26.6 27.8 2.8 47 NOV 2005 26.7 25.8-0.7 48 DES 2005 26.2 26.6-0.6 49 JAN 2006 26.6 26.7 0.9

50 FEB 2006 27 26.2 0 51 MAR 2006 27.5 26.6 0.1 52 APR 2006 27.5 27-0.5 53 MEI 2006 27.5 27.5 0 54 JUN 2006 27.4 27.5-0.1 55 JUL 2006 27.7 27.5 0.4 56 AGTS 2006 27.2 27.4-0.8 57 SEP 2006 25.1 27.7-1.6 58 OKT 2006 26.6 27.2 3.6 59 NOV 2006 26.4 25.1-1.7 60 DES 2006 26.2 26.6 0 61 JAN 2007 26.3 26.4 0.3 62 FEB 2007 26.6 26.2 0.2 63 MAR 2007 27.6 26.3 0.7 64 APR 2007 27.6 26.6-1 65 MEI 2007 27.7 27.6 0.1 66 JUN 2007 27.3 27.6-0.5 67 JUL 2007 27.1 27.7 0.2 68 AGTS 2007 27.1 27.3 0.2 69 SEP 2007 26.9 27.1-0.2 70 OKT 2007 26.6 27.1-0.1 71 NOV 2007 26 26.9-0.3 72 DES 2007 26.2 26.6 0.8

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 0.100 0.094 1 72.250-0.035 0.235 0.250 0.001 2 66.581 0.052 0.385 0.301 0.002 3 59.962 0.122 0.535 0.371 0.003 4 51.815 0.161 0.685 0.485 0.004 5 44.604 0.139 0.768 0.635 0.005 6 39.421 0.101 0.801 0.785 0.004 7 39.372 0.049 0.836 0.935 0.004 8 37.530-0.022 0.800 0.909 0.001 9 37.146-0.011 0.818 0.882 0.002 10 37.123 0.006 0.830 0.881 0.002 11 37.121 0.009 0.833 0.879 0.002 12 37.120 0.011 0.835 0.880 0.002 13 37.120 0.012 0.836 0.879 0.002 14 37.120 0.012 0.836 0.879 0.002 Final Estimates of Parameters Type Coef SE Coef T P AR 1 0.0122 0.1184 0.10 0.918 MA 1 0.8363 0.0652 12.83 0.000 SMA 12 0.8793 0.0822 10.70 0.000 Constant 0.002258 0.002332 0.97 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 95 Percent Limits Period Forecast Lower Upper Actual 121 26.8284 25.6940 27.9629 122 27.0742 25.9223 28.2261 123 27.5321 26.3650 28.6992 124 27.6195 26.4374 28.8017 125 27.6925 26.4955 28.8895 126 27.2130 26.0014 28.4247 127 27.2672 26.0410 28.4933 128 27.2581 26.0176 28.4986 129 26.2394 24.9847 27.4940 130 26.6839 25.4152 27.9525 131 26.5959 25.3134 27.8784 132 26.1890 24.8928 27.4852 Correlations: AKTUAL, 111;011

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 T P SAR 12-0.0405 0.1131-0.36 0.721 SMA 12 0.8931 0.0923 9.67 0.000 Constant 0.00106 0.01125 0.09 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 95 Percent Limits Period Forecast Lower Upper Actual 121 26.6844 25.5954 27.7735 122 26.9236 25.8345 28.0126 123 27.3378 26.2488 28.4269 124 27.4110 26.3220 28.5001 125 27.4789 26.3899 28.5680 126 26.9986 25.9096 28.0877 127 27.0616 25.9726 28.1507 128 27.0287 25.9397 28.1178 129 25.9388 24.8498 27.0279 130 26.4313 25.3422 27.5203 131 26.3517 25.2627 27.4408 132 25.9486 24.8595 27.0376 Correlations: AKTUAL, 000;111

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 0.100 0.084 1 96.179-0.050 0.071-0.004 0.117 0.083 2 92.595-0.200 0.043-0.124 0.131 0.086 3 89.598-0.350 0.012-0.248 0.144 0.089 4 86.775-0.500-0.022-0.373 0.159 0.091 5 83.975-0.650-0.060-0.498 0.176 0.091 6 76.790-0.561-0.090-0.348 0.232 0.064 7 75.323-0.425-0.071-0.198 0.245 0.054 8 73.943-0.289-0.049-0.048 0.256 0.045 9 72.631-0.153-0.024 0.102 0.267 0.037 10 71.450-0.019 0.002 0.252 0.272 0.030 11 69.645 0.111 0.029 0.402 0.285 0.025 12 67.264 0.235 0.057 0.552 0.303 0.018 13 63.701 0.344 0.085 0.702 0.333 0.012 14 56.383 0.399 0.107 0.852 0.406 0.005 15 47.226 0.270 0.091 0.867 0.556 0.003 16 41.477 0.198 0.085 0.874 0.706 0.003 17 37.457 0.149 0.085 0.888 0.856 0.003 18 37.017 0.048 0.071 0.870 0.871 0.002 19 37.010 0.048 0.072 0.875 0.876 0.002 20 37.009 0.045 0.071 0.874 0.873 0.002 21 37.008 0.048 0.073 0.876 0.875 0.002 22 37.008 0.047 0.073 0.875 0.874 0.002 23 37.008 0.048 0.073 0.876 0.874 0.002 24 37.008 0.048 0.073 0.876 0.874 0.002 Unable to reduce sum of squares any further Final Estimates of Parameters Type Coef SE Coef T P AR 1 0.0476 0.1201 0.40 0.693 AR 2 0.0734 0.1151 0.64 0.525 MA 1 0.8762 0.0678 12.92 0.000 SMA 12 0.8739 0.0846 10.33 0.000 Constant 0.001668 0.001931 0.86 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 95 Percent Limits Period Forecast Lower Upper Actual 121 26.7819 25.6433 27.9205 122 27.0654 25.9102 28.2207 123 27.5156 26.3370 28.6943 124 27.6040 26.4136 28.7943 125 27.6720 26.4701 28.8739 126 27.1874 25.9748 28.4000

127 27.2393 26.0161 28.4626 128 27.2331 25.9994 28.4669 129 26.2202 24.9760 27.4643 130 26.6509 25.3965 27.9054 131 26.5615 25.2968 27.8261 132 26.1574 24.8826 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 0.100 0.075 1 66.3828 0.211 0.083 0.250 0.122 0.055 2 58.4540 0.227 0.027 0.400 0.106 0.064 3 50.5070 0.077-0.019 0.376 0.176 0.041 4 45.2826 0.117-0.051 0.526 0.206 0.019 5 42.5261-0.033-0.070 0.453 0.274 0.022 6 40.4538-0.183-0.086 0.368 0.350 0.020 7 38.9434-0.333-0.097 0.272 0.443 0.019 8 37.7168-0.483-0.107 0.174 0.542 0.016 9 37.1654-0.482-0.134 0.288 0.516 0.013 10 36.5810-0.632-0.131 0.150 0.634 0.015 Unable to reduce sum of squares any further Final Estimates of Parameters Type Coef SE Coef T P SAR 12-0.6317 0.6892-0.92 0.362 MA 1-0.1305 0.0976-1.34 0.184 SMA 12 0.1500 0.6758 0.22 0.825 SMA 24 0.6338 0.5484 1.16 0.250 Constant 0.01540 0.01728 0.89 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 95 Percent Limits Period Forecast Lower Upper Actual 121 26.9107 25.7999 28.0215 122 26.9499 25.8297 28.0701 123 27.4689 26.3487 28.5891 124 27.5723 26.4521 28.6925 125 27.4289 26.3087 28.5491 126 26.9545 25.8343 28.0747 127 27.1207 26.0005 28.2409

128 27.1477 26.0275 28.2679 129 26.2643 25.1441 27.3845 130 26.5061 25.3859 27.6263 131 26.3759 25.2557 27.4961 132 25.9706 24.8504 27.0908

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 : MHD.FADLI Nim : 062407141 Judul Tugas Akhir : 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 Paraf Dosen Pembimbing Keterangan Diketahui/Disetujui oleh Departemen Matematika FMIPA USU Ketua, Pembimbing, Dr. Saib Suwilo, M.Sc Drs. Marwan Harahap, M.Eng NIP. 131 796 149 NIP. 130 422 443

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 : MHD.FADLI NIM : 062407141 Program Studi : D3 Statistika Judul TA : 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