Lampiran 1 : Grafik Data HIV Asli 70 60 50 Penderita 40 30 20 10 2007 2008 2009 2010 2011 Tahun HIV Mean 34.15000 Median 31.50000 Maximum 60.00000 Minimum 19.00000 Std. Dev. 10.45057 Skewness 0.584866 Kurtosis 2.445619 Jarque-Bera 4.189023 Probability 0.123130 Sum 2049.000 Sum Sq. Dev. 6443.650 Observations 60
Lampiran 2 : Correlogram data HIV Asli Date: 01/21/13 Time: 01:46 Sample: 2007M01 2011M12 Included observations: 60
Lampiran 2 Lanjutan
Lampiran 3 : ADF data HIV Asli
Lampiran 4: Correlogram Data HIV Differencing
Lampiran 5: ADF Data HIV Differencing DHIV Mean 0.677966 Median 2.000000 Maximum 16.00000 Minimum -17.00000 Std. Dev. 6.232398 Skewness -0.402584 Kurtosis 4.194283 Jarque-Bera 5.100079 Probability 0.078079 Sum 40.00000 Sum Sq. Dev. 2252.881 Observations 59
Lampiran 6: Grafik Data HIV Differencing 30 20 10 Penderita 0-10 -20-30 2007 2008 2009 2010 2011 Tahun
Lampiran 7: Estimasi Model a. Arima (2.1.1) Dependent Variable: DHIV Method: Least Squares Date: 01/04/13 Time: 11:32 Sample (adjusted): 2007M04 2011M12 Included observations: 57 after adjustments Convergence achieved after 16 iterations MA Backcast: 2007M03 Variable Coefficient Std. Error t-statistic Prob. C 0.516612 0.142412 3.627590 0.0006 AR(1) 0.479244 0.144181 3.323903 0.0016 AR(2) 0.060815 0.143359 0.424215 0.6731 MA(1) -0.961101 0.037941-25.33114 0.0000 R-squared 0.206897 Mean dependent var 0.684211 Adjusted R-squared 0.162005 S.D. dependent var 6.325001 S.E. of regression 5.790038 Akaike info criterion 6.417746 Sum squared resid 1776.801 Schwarz criterion 6.561118 Log likelihood -178.9058 Hannan-Quinn criter. 6.473466 F-statistic 4.608715 Durbin-Watson stat 1.970949 Prob(F-statistic) 0.006136 Inverted AR Roots.58 -.10 Inverted MA Roots.96
b. Uji correlogram Q-Stat
c. Model Arima (1.1.2) Dependent Variable: DHIV Method: Least Squares Date: 01/04/13 Time: 10:53 Sample (adjusted): 2007M03 2011M12 Included observations: 58 after adjustments Convergence achieved after 51 iterations MA Backcast: 2007M01 2007M02 Variable Coefficient Std. Error t-statistic Prob. C 0.521814 0.155326 3.359470 0.0014 AR(1) 0.592176 0.246973 2.397739 0.0200 MA(1) -1.073412 0.291284-3.685103 0.0005 MA(2) 0.110682 0.267843 0.413233 0.6811 R-squared 0.206675 Mean dependent var 0.637931 Adjusted R-squared 0.162602 S.D. dependent var 6.279173 S.E. of regression 5.746038 Akaike info criterion 6.401370 Sum squared resid 1782.915 Schwarz criterion 6.543470 Log likelihood -181.6397 Hannan-Quinn criter. 6.456721 F-statistic 4.689321 Durbin-Watson stat 1.965550 Prob(F-statistic) 0.005548 Inverted AR Roots.59 Inverted MA Roots.96.12
d. Uji correlogram Q-Stat
e. Model Arima (2.1.2) Dependent Variable: DHIV Method: Least Squares Date: 01/04/13 Time: 11:06 Sample (adjusted): 2007M04 2011M12 Included observations: 57 after adjustments Convergence achieved after 129 iterations MA Backcast: OFF (Roots of MA process too large) Variable Coefficient Std. Error t-statistic Prob. C 0.708005 0.237330 2.983208 0.0043 AR(1) -0.397783 0.131727-3.019766 0.0039 AR(2) 0.575945 0.135529 4.249604 0.0001 MA(1) 0.032398 0.167087 0.193897 0.8470 MA(2) -1.463061 0.159206-9.189760 0.0000 R-squared 0.592960 Mean dependent var 0.684211 Adjusted R-squared 0.561649 S.D. dependent var 6.325001 S.E. of regression 4.187661 Akaike info criterion 5.785793 Sum squared resid 911.8981 Schwarz criterion 5.965008 Log likelihood -159.8951 Hannan-Quinn criter. 5.855442 F-statistic 18.93789 Durbin-Watson stat 2.079200 Prob(F-statistic) 0.000000 Inverted AR Roots.59 -.98 Inverted MA Roots 1.19-1.23 Estimated MA process is noninvertible
f. Uji correlogram Q-Stat
g. Model Arima (1.1.1) Dependent Variable: DHIV Method: Least Squares Date: 01/04/13 Time: 11:19 Sample (adjusted): 2007M03 2011M12 Included observations: 58 after adjustments Convergence achieved after 17 iterations MA Backcast: 2007M02 Variable Coefficient Std. Error t-statistic Prob. C 0.514991 0.151157 3.406999 0.0012 AR(1) 0.502622 0.134768 3.729543 0.0005 MA(1) -0.957487 0.053568-17.87409 0.0000 R-squared 0.204036 Mean dependent var 0.637931 Adjusted R-squared 0.175091 S.D. dependent var 6.279173 S.E. of regression 5.703026 Akaike info criterion 6.370209 Sum squared resid 1788.848 Schwarz criterion 6.476784 Log likelihood -181.7361 Hannan-Quinn criter. 6.411722 F-statistic 7.049281 Durbin-Watson stat 2.016798 Prob(F-statistic) 0.001882 Inverted AR Roots.50 Inverted MA Roots.96
h. Uji correlogram Q-stat
Lampiran 8: Peramalan 70 60 50 40 30 20 10 Forecast: HIVF Actual: HIV Forecast sample: 2007M01 2011M12 Adjusted sample: 2007M03 2011M12 Included observations: 58 Root Mean Squared Error 6.753831 Mean Absolute Error 4.906300 Mean Abs. Percent Error 17.25950 Theil Inequality Coefficient 0.091284 Bias Proportion 0.119973 Variance Proportion 0.061675 Covariance Proportion 0.818352 0 2007 2008 2009 2010 2011 HIVF ± 2 S.E. 70 60 50 40 30 20 10 0 2007 2008 2009 2010 2011 HIVF+2*SE_1 HIVF-2*SE_1 HIV
Lampiran 8: Lanjutan 20 10 0 10 5 0-5 -10-20 -10-15 -20 2007 2008 2009 2010 2011 Residual Actual Fitted
Lampiran 9: Hasil Peramalan Jumlah Penderita HIV Tahun 2007-2011 di Kota Medan Periode Aktual Forecast 2007M01 20 NA 2007M02 23 NA 2007M03 21 22,9 2007M04 22 23,1 2007M05 25 23,4 2007M06 30 23,9 2007M07 25 24,3 2007M08 30 24,8 2007M09 29 25,3 2007M10 33 25,8 2007M11 26 26,3 2007M12 27 26,9 2008M01 19 27,4 2008M02 22 27,9 2008M03 24 28,4 2008M04 26 28,9 2008M05 22 29,4 2008M06 29 30,0 2008M07 26 30,5 2008M08 31 31,0 2008M09 39 31,5 2008M10 40 32,0 2008M11 34 32,5 2008M12 35 33,0 2009M01 24 33,6 2009M02 27 34,1 2009M03 37 34,6
Lampiran 9: Lanjutan Lampiran Lanjutan Periode Aktual Forecast 2009M04 28 35,1 2009M05 20 35,6 2009M06 30 36,1 2009M07 31 36,6 2009M08 34 37,2 2009M09 36 37,7 2009M10 30 38,2 2009M11 32 38,7 2009M12 35 39,2 2010M01 28 39,7 2010M02 35 40,3 2010M03 19 40,8 2010M04 35 41,3 2010M05 40 41,8 2010M06 40 42,3 2010M07 44 42,8 2010M08 42 43,3 2010M09 43 43,9 2010M10 42 44,4 2010M11 41 44,9 2010M12 43 45,4 2011M01 26 45,9 2011M02 30 46,4 2011M03 46 46,9 2011M04 48 47,5 2011M05 49 48,0 2011M06 51 48,5 2011M07 52 49,0 2011M08 54 49,5 2011M09 50 50,0 2011M10 54 50,6 2011M11 55 51,1 2011M12 60 51,6 Jumlah 2.049 2.141,7
Lampiran 10: Hasil Peramalan Jumlah Penderita HIV Tahun 2012-2016 di Kota Medan Periode Proyeksi 2012M01 52,1 2012M02 52,6 2012M03 53,1 2012M04 53,6 2012M05 54,2 2012M06 54,7 2012M07 55,2 2012M08 55,7 2012M09 56,2 2012M10 56,7 2012M11 57,2 2012M12 57,8 2013M01 58,3 2013M02 58,8 2013M03 59,3 2013M04 59,8 2013M05 60,3 2013M06 60,9 2013M07 61,4 2013M08 61,9 2013M09 62,4 2013M10 62,9 2013M11 63,4 2013M12 63,9 2014M01 64,5 2014M02 65,0 2014M03 65,5 2014M04 66,0 2014M05 66,5 2014M06 67,0 2014M07 67,5 2014M08 68,1 2014M09 68,6 2014M10 69,1 2014M11 69,6 2014M12 70,1 2015M01 70,6 2015M02 71,1 2015M03 71,7
Lampiran 10: Lanjutan Periode Proyeksi 2015M04 72,2 2015M05 72,7 2015M06 73,2 2015M07 73,7 2015M08 74,2 2015M09 74,8 2015M10 75,3 2015M11 75,8 2015M12 76,3 2016M01 76,8 2016M02 77,3 2016M03 77,8 2016M04 78,4 2016M05 78,9 2016M06 79,4 2016M07 79,9 2016M08 80,4 2016M09 80,9 2016M10 81,4 2016M11 82,0 2016M12 82,5 Jumlah 4.037,3 HIV Mean 67.28752 Median 67.28752 Maximum 82.47975 Minimum 52.09530 Std. Dev. 8.993924 Skewness -8.07E-15 Kurtosis 1.799333 Jarque-Bera 3.604002 Probability 0.164968 Sum 4037.251 Sum Sq. Dev. 4772.549 Observations 60