Peramalan Kasus Hiv Di Kota Medan Tahun 2012-2016
Lampiran 1 : Grafik Data HIV Asli
70
60
Penderita
50
40
30
20
10
2007
2008
2009
2010
2011
Tahun
Mean
Median
Maximum
Minimum
Std. Dev.
Skewness
Kurtosis
Jarque-Bera
Probability
Sum
Sum Sq. Dev.
Observations
HIV
34.15000
31.50000
60.00000
19.00000
10.45057
0.584866
2.445619
4.189023
0.123130
2049.000
6443.650
60
Universitas Sumatera Utara
Lampiran 2 : Correlogram data HIV Asli
Date: 01/21/13 Time: 01:46
Sample: 2007M01 2011M12
Included observations: 60
Universitas Sumatera Utara
Lampiran 2 Lanjutan
Universitas Sumatera Utara
Lampiran 3 : ADF data HIV Asli
Universitas Sumatera Utara
Lampiran 4: Correlogram Data HIV Differencing
Universitas Sumatera Utara
Universitas Sumatera Utara
Lampiran 5: ADF Data HIV Differencing
Mean
Median
Maximum
Minimum
Std. Dev.
Skewness
Kurtosis
DHIV
0.677966
2.000000
16.00000
-17.00000
6.232398
-0.402584
4.194283
Jarque-Bera
Probability
5.100079
0.078079
Sum
Sum Sq. Dev.
40.00000
2252.881
Observations
59
Universitas Sumatera Utara
Lampiran 6: Grafik Data HIV Differencing
30
20
Penderita
10
0
-10
-20
-30
2007
2008
2009
2010
2011
Tahun
Universitas Sumatera Utara
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
AR(1)
AR(2)
MA(1)
0.516612
0.479244
0.060815
-0.961101
0.142412
0.144181
0.143359
0.037941
3.627590
3.323903
0.424215
-25.33114
0.0006
0.0016
0.6731
0.0000
R-squared
Adjusted R-squared
S.E. of regression
Sum squared resid
Log likelihood
F-statistic
Prob(F-statistic)
Inverted AR Roots
Inverted MA Roots
0.206897
0.162005
5.790038
1776.801
-178.9058
4.608715
0.006136
.58
.96
Mean dependent var
S.D. dependent var
Akaike info criterion
Schwarz criterion
Hannan-Quinn criter.
Durbin-Watson stat
0.684211
6.325001
6.417746
6.561118
6.473466
1.970949
-.10
Universitas Sumatera Utara
b. Uji correlogram Q-Stat
Universitas Sumatera Utara
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
AR(1)
MA(1)
MA(2)
0.521814
0.592176
-1.073412
0.110682
0.155326
0.246973
0.291284
0.267843
3.359470
2.397739
-3.685103
0.413233
0.0014
0.0200
0.0005
0.6811
R-squared
Adjusted R-squared
S.E. of regression
Sum squared resid
Log likelihood
F-statistic
Prob(F-statistic)
Inverted AR Roots
Inverted MA Roots
0.206675
0.162602
5.746038
1782.915
-181.6397
4.689321
0.005548
.59
.96
Mean dependent var
S.D. dependent var
Akaike info criterion
Schwarz criterion
Hannan-Quinn criter.
Durbin-Watson stat
0.637931
6.279173
6.401370
6.543470
6.456721
1.965550
.12
Universitas Sumatera Utara
d. Uji correlogram Q-Stat
Universitas Sumatera Utara
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
AR(1)
AR(2)
MA(1)
MA(2)
0.708005
-0.397783
0.575945
0.032398
-1.463061
0.237330
0.131727
0.135529
0.167087
0.159206
2.983208
-3.019766
4.249604
0.193897
-9.189760
0.0043
0.0039
0.0001
0.8470
0.0000
R-squared
Adjusted R-squared
S.E. of regression
Sum squared resid
Log likelihood
F-statistic
Prob(F-statistic)
Inverted AR Roots
Inverted MA Roots
0.592960
0.561649
4.187661
911.8981
-159.8951
18.93789
0.000000
Mean dependent var
S.D. dependent var
Akaike info criterion
Schwarz criterion
Hannan-Quinn criter.
Durbin-Watson stat
0.684211
6.325001
5.785793
5.965008
5.855442
2.079200
.59
-.98
1.19
-1.23
Estimated MA process is noninvertible
Universitas Sumatera Utara
f. Uji correlogram Q-Stat
Universitas Sumatera Utara
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
AR(1)
MA(1)
0.514991
0.502622
-0.957487
0.151157
0.134768
0.053568
3.406999
3.729543
-17.87409
0.0012
0.0005
0.0000
R-squared
Adjusted R-squared
S.E. of regression
Sum squared resid
Log likelihood
F-statistic
Prob(F-statistic)
Inverted AR Roots
Inverted MA Roots
0.204036
0.175091
5.703026
1788.848
-181.7361
7.049281
0.001882
Mean dependent var
S.D. dependent var
Akaike info criterion
Schwarz criterion
Hannan-Quinn criter.
Durbin-Watson stat
0.637931
6.279173
6.370209
6.476784
6.411722
2.016798
.50
.96
Universitas Sumatera Utara
h. Uji correlogram Q-stat
Universitas Sumatera Utara
Lampiran 8: Peramalan
70
Forecast: HIVF
Actual: HIV
Forecast sample: 2007M01 2011M12
Adjusted sample: 2007M03 2011M12
Included observations: 58
60
50
40
Root Mean Squared Error
Mean Absolute Error
Mean Abs. Percent Error
Theil Inequality Coefficient
Bias Proportion
Variance Proportion
Covariance Proportion
30
20
10
6.753831
4.906300
17.25950
0.091284
0.119973
0.061675
0.818352
0
2007
2008
2009
HIVF
2010
2011
± 2 S.E.
70
60
50
40
30
20
10
0
2007
2008
HI VF+2 *SE_ 1
2009
2010
HI VF- 2 *SE_ 1
2011
HI V
Universitas Sumatera Utara
Lampiran 8: Lanjutan
20
10
0
-10
10
-20
5
0
-5
-10
-15
-20
2007
2008
Residual
2009
Actual
2011
2010
Fitted
Universitas Sumatera Utara
Lampiran 9: Hasil Peramalan Jumlah Penderita HIV Tahun 2007-2011 di
Kota Medan
Periode
2007M01
2007M02
2007M03
2007M04
2007M05
2007M06
2007M07
2007M08
2007M09
2007M10
2007M11
2007M12
2008M01
2008M02
2008M03
2008M04
2008M05
2008M06
2008M07
2008M08
2008M09
2008M10
2008M11
2008M12
2009M01
2009M02
2009M03
Aktual
20
23
21
22
25
30
25
30
29
33
26
27
19
22
24
26
22
29
26
31
39
40
34
35
24
27
37
Forecast
NA
NA
22,9
23,1
23,4
23,9
24,3
24,8
25,3
25,8
26,3
26,9
27,4
27,9
28,4
28,9
29,4
30,0
30,5
31,0
31,5
32,0
32,5
33,0
33,6
34,1
34,6
Universitas Sumatera Utara
Lampiran 9: Lanjutan
Lampiran Lanjutan
Periode
2009M04
2009M05
2009M06
2009M07
2009M08
2009M09
2009M10
2009M11
2009M12
2010M01
2010M02
2010M03
2010M04
2010M05
2010M06
2010M07
2010M08
2010M09
2010M10
2010M11
2010M12
2011M01
2011M02
2011M03
2011M04
2011M05
2011M06
2011M07
2011M08
2011M09
2011M10
2011M11
2011M12
Jumlah
Aktual
28
20
30
31
34
36
30
32
35
28
35
19
35
40
40
44
42
43
42
41
43
26
30
46
48
49
51
52
54
50
54
55
60
2.049
Forecast
35,1
35,6
36,1
36,6
37,2
37,7
38,2
38,7
39,2
39,7
40,3
40,8
41,3
41,8
42,3
42,8
43,3
43,9
44,4
44,9
45,4
45,9
46,4
46,9
47,5
48,0
48,5
49,0
49,5
50,0
50,6
51,1
51,6
2.141,7
Universitas Sumatera Utara
Lampiran 10: Hasil Peramalan Jumlah Penderita HIV Tahun 2012-2016 di
Kota Medan
Periode
2012M01
2012M02
2012M03
2012M04
2012M05
2012M06
2012M07
2012M08
2012M09
2012M10
2012M11
2012M12
2013M01
2013M02
2013M03
2013M04
2013M05
2013M06
2013M07
2013M08
2013M09
2013M10
2013M11
2013M12
2014M01
2014M02
2014M03
2014M04
2014M05
2014M06
2014M07
2014M08
2014M09
2014M10
2014M11
2014M12
2015M01
2015M02
2015M03
Proyeksi
52,1
52,6
53,1
53,6
54,2
54,7
55,2
55,7
56,2
56,7
57,2
57,8
58,3
58,8
59,3
59,8
60,3
60,9
61,4
61,9
62,4
62,9
63,4
63,9
64,5
65,0
65,5
66,0
66,5
67,0
67,5
68,1
68,6
69,1
69,6
70,1
70,6
71,1
71,7
Universitas Sumatera Utara
Lampiran 10: Lanjutan
Periode
2015M04
2015M05
2015M06
2015M07
2015M08
2015M09
2015M10
2015M11
2015M12
2016M01
2016M02
2016M03
2016M04
2016M05
2016M06
2016M07
2016M08
2016M09
2016M10
2016M11
2016M12
Jumlah
Mean
Median
Maximum
Minimum
Std. Dev.
Skewness
Kurtosis
Jarque-Bera
Probability
Sum
Sum Sq. Dev.
Observations
Proyeksi
72,2
72,7
73,2
73,7
74,2
74,8
75,3
75,8
76,3
76,8
77,3
77,8
78,4
78,9
79,4
79,9
80,4
80,9
81,4
82,0
82,5
4.037,3
HIV
67.28752
67.28752
82.47975
52.09530
8.993924
-8.07E-15
1.799333
3.604002
0.164968
4037.251
4772.549
60
Universitas Sumatera Utara
Universitas Sumatera Utara
Universitas Sumatera Utara
70
60
Penderita
50
40
30
20
10
2007
2008
2009
2010
2011
Tahun
Mean
Median
Maximum
Minimum
Std. Dev.
Skewness
Kurtosis
Jarque-Bera
Probability
Sum
Sum Sq. Dev.
Observations
HIV
34.15000
31.50000
60.00000
19.00000
10.45057
0.584866
2.445619
4.189023
0.123130
2049.000
6443.650
60
Universitas Sumatera Utara
Lampiran 2 : Correlogram data HIV Asli
Date: 01/21/13 Time: 01:46
Sample: 2007M01 2011M12
Included observations: 60
Universitas Sumatera Utara
Lampiran 2 Lanjutan
Universitas Sumatera Utara
Lampiran 3 : ADF data HIV Asli
Universitas Sumatera Utara
Lampiran 4: Correlogram Data HIV Differencing
Universitas Sumatera Utara
Universitas Sumatera Utara
Lampiran 5: ADF Data HIV Differencing
Mean
Median
Maximum
Minimum
Std. Dev.
Skewness
Kurtosis
DHIV
0.677966
2.000000
16.00000
-17.00000
6.232398
-0.402584
4.194283
Jarque-Bera
Probability
5.100079
0.078079
Sum
Sum Sq. Dev.
40.00000
2252.881
Observations
59
Universitas Sumatera Utara
Lampiran 6: Grafik Data HIV Differencing
30
20
Penderita
10
0
-10
-20
-30
2007
2008
2009
2010
2011
Tahun
Universitas Sumatera Utara
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
AR(1)
AR(2)
MA(1)
0.516612
0.479244
0.060815
-0.961101
0.142412
0.144181
0.143359
0.037941
3.627590
3.323903
0.424215
-25.33114
0.0006
0.0016
0.6731
0.0000
R-squared
Adjusted R-squared
S.E. of regression
Sum squared resid
Log likelihood
F-statistic
Prob(F-statistic)
Inverted AR Roots
Inverted MA Roots
0.206897
0.162005
5.790038
1776.801
-178.9058
4.608715
0.006136
.58
.96
Mean dependent var
S.D. dependent var
Akaike info criterion
Schwarz criterion
Hannan-Quinn criter.
Durbin-Watson stat
0.684211
6.325001
6.417746
6.561118
6.473466
1.970949
-.10
Universitas Sumatera Utara
b. Uji correlogram Q-Stat
Universitas Sumatera Utara
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
AR(1)
MA(1)
MA(2)
0.521814
0.592176
-1.073412
0.110682
0.155326
0.246973
0.291284
0.267843
3.359470
2.397739
-3.685103
0.413233
0.0014
0.0200
0.0005
0.6811
R-squared
Adjusted R-squared
S.E. of regression
Sum squared resid
Log likelihood
F-statistic
Prob(F-statistic)
Inverted AR Roots
Inverted MA Roots
0.206675
0.162602
5.746038
1782.915
-181.6397
4.689321
0.005548
.59
.96
Mean dependent var
S.D. dependent var
Akaike info criterion
Schwarz criterion
Hannan-Quinn criter.
Durbin-Watson stat
0.637931
6.279173
6.401370
6.543470
6.456721
1.965550
.12
Universitas Sumatera Utara
d. Uji correlogram Q-Stat
Universitas Sumatera Utara
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
AR(1)
AR(2)
MA(1)
MA(2)
0.708005
-0.397783
0.575945
0.032398
-1.463061
0.237330
0.131727
0.135529
0.167087
0.159206
2.983208
-3.019766
4.249604
0.193897
-9.189760
0.0043
0.0039
0.0001
0.8470
0.0000
R-squared
Adjusted R-squared
S.E. of regression
Sum squared resid
Log likelihood
F-statistic
Prob(F-statistic)
Inverted AR Roots
Inverted MA Roots
0.592960
0.561649
4.187661
911.8981
-159.8951
18.93789
0.000000
Mean dependent var
S.D. dependent var
Akaike info criterion
Schwarz criterion
Hannan-Quinn criter.
Durbin-Watson stat
0.684211
6.325001
5.785793
5.965008
5.855442
2.079200
.59
-.98
1.19
-1.23
Estimated MA process is noninvertible
Universitas Sumatera Utara
f. Uji correlogram Q-Stat
Universitas Sumatera Utara
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
AR(1)
MA(1)
0.514991
0.502622
-0.957487
0.151157
0.134768
0.053568
3.406999
3.729543
-17.87409
0.0012
0.0005
0.0000
R-squared
Adjusted R-squared
S.E. of regression
Sum squared resid
Log likelihood
F-statistic
Prob(F-statistic)
Inverted AR Roots
Inverted MA Roots
0.204036
0.175091
5.703026
1788.848
-181.7361
7.049281
0.001882
Mean dependent var
S.D. dependent var
Akaike info criterion
Schwarz criterion
Hannan-Quinn criter.
Durbin-Watson stat
0.637931
6.279173
6.370209
6.476784
6.411722
2.016798
.50
.96
Universitas Sumatera Utara
h. Uji correlogram Q-stat
Universitas Sumatera Utara
Lampiran 8: Peramalan
70
Forecast: HIVF
Actual: HIV
Forecast sample: 2007M01 2011M12
Adjusted sample: 2007M03 2011M12
Included observations: 58
60
50
40
Root Mean Squared Error
Mean Absolute Error
Mean Abs. Percent Error
Theil Inequality Coefficient
Bias Proportion
Variance Proportion
Covariance Proportion
30
20
10
6.753831
4.906300
17.25950
0.091284
0.119973
0.061675
0.818352
0
2007
2008
2009
HIVF
2010
2011
± 2 S.E.
70
60
50
40
30
20
10
0
2007
2008
HI VF+2 *SE_ 1
2009
2010
HI VF- 2 *SE_ 1
2011
HI V
Universitas Sumatera Utara
Lampiran 8: Lanjutan
20
10
0
-10
10
-20
5
0
-5
-10
-15
-20
2007
2008
Residual
2009
Actual
2011
2010
Fitted
Universitas Sumatera Utara
Lampiran 9: Hasil Peramalan Jumlah Penderita HIV Tahun 2007-2011 di
Kota Medan
Periode
2007M01
2007M02
2007M03
2007M04
2007M05
2007M06
2007M07
2007M08
2007M09
2007M10
2007M11
2007M12
2008M01
2008M02
2008M03
2008M04
2008M05
2008M06
2008M07
2008M08
2008M09
2008M10
2008M11
2008M12
2009M01
2009M02
2009M03
Aktual
20
23
21
22
25
30
25
30
29
33
26
27
19
22
24
26
22
29
26
31
39
40
34
35
24
27
37
Forecast
NA
NA
22,9
23,1
23,4
23,9
24,3
24,8
25,3
25,8
26,3
26,9
27,4
27,9
28,4
28,9
29,4
30,0
30,5
31,0
31,5
32,0
32,5
33,0
33,6
34,1
34,6
Universitas Sumatera Utara
Lampiran 9: Lanjutan
Lampiran Lanjutan
Periode
2009M04
2009M05
2009M06
2009M07
2009M08
2009M09
2009M10
2009M11
2009M12
2010M01
2010M02
2010M03
2010M04
2010M05
2010M06
2010M07
2010M08
2010M09
2010M10
2010M11
2010M12
2011M01
2011M02
2011M03
2011M04
2011M05
2011M06
2011M07
2011M08
2011M09
2011M10
2011M11
2011M12
Jumlah
Aktual
28
20
30
31
34
36
30
32
35
28
35
19
35
40
40
44
42
43
42
41
43
26
30
46
48
49
51
52
54
50
54
55
60
2.049
Forecast
35,1
35,6
36,1
36,6
37,2
37,7
38,2
38,7
39,2
39,7
40,3
40,8
41,3
41,8
42,3
42,8
43,3
43,9
44,4
44,9
45,4
45,9
46,4
46,9
47,5
48,0
48,5
49,0
49,5
50,0
50,6
51,1
51,6
2.141,7
Universitas Sumatera Utara
Lampiran 10: Hasil Peramalan Jumlah Penderita HIV Tahun 2012-2016 di
Kota Medan
Periode
2012M01
2012M02
2012M03
2012M04
2012M05
2012M06
2012M07
2012M08
2012M09
2012M10
2012M11
2012M12
2013M01
2013M02
2013M03
2013M04
2013M05
2013M06
2013M07
2013M08
2013M09
2013M10
2013M11
2013M12
2014M01
2014M02
2014M03
2014M04
2014M05
2014M06
2014M07
2014M08
2014M09
2014M10
2014M11
2014M12
2015M01
2015M02
2015M03
Proyeksi
52,1
52,6
53,1
53,6
54,2
54,7
55,2
55,7
56,2
56,7
57,2
57,8
58,3
58,8
59,3
59,8
60,3
60,9
61,4
61,9
62,4
62,9
63,4
63,9
64,5
65,0
65,5
66,0
66,5
67,0
67,5
68,1
68,6
69,1
69,6
70,1
70,6
71,1
71,7
Universitas Sumatera Utara
Lampiran 10: Lanjutan
Periode
2015M04
2015M05
2015M06
2015M07
2015M08
2015M09
2015M10
2015M11
2015M12
2016M01
2016M02
2016M03
2016M04
2016M05
2016M06
2016M07
2016M08
2016M09
2016M10
2016M11
2016M12
Jumlah
Mean
Median
Maximum
Minimum
Std. Dev.
Skewness
Kurtosis
Jarque-Bera
Probability
Sum
Sum Sq. Dev.
Observations
Proyeksi
72,2
72,7
73,2
73,7
74,2
74,8
75,3
75,8
76,3
76,8
77,3
77,8
78,4
78,9
79,4
79,9
80,4
80,9
81,4
82,0
82,5
4.037,3
HIV
67.28752
67.28752
82.47975
52.09530
8.993924
-8.07E-15
1.799333
3.604002
0.164968
4037.251
4772.549
60
Universitas Sumatera Utara
Universitas Sumatera Utara
Universitas Sumatera Utara