Lampiran 1 – Data Harian Saham LQ45
Periode Januari 2006 - September 2006
No
SAHAM
No
SAHAM
No
SAHAM
1
256.862
33
273.448
65
300.933
2
259.969
34
274.491
66
302.633
3
266.808
35
271.541
67
302.056
4
266.538
36
270.291
68
305.168
5
266.34
37
268.268
69
307.214
6
274.998
38
266.187
70
308.115
7
278.943
39
271.436
71
315.618
8
277.687
40
270.424
72
325.357
9
276.024
41
272.952
73
328.17
10
272.187
42
275.657
74
326.549
11
266.518
43
278.362
75
322.311
12
261.79
44
278.294
76
325.605
13
271.062
45
273.943
77
330.843
14
269.313
46
270.871
78
328.57
15
263.592
47
272.3
79
325.1
16
265.308
48
274.378
80
328.525
17
271.119
49
273.501
81
328.216
18
270.003
50
273.736
82
333.852
19
271.046
51
272.779
83
331.156
20
271.632
52
281.085
84
330.911
21
273.951
53
289.262
85
336.177
22
274.417
54
295.515
86
342.478
23
274.334
55
294.383
87
344.002
24
274.833
56
287.734
88
346.943
25
278.41
57
288.874
89
340.063
26
273
58
290.36
90
316.522
27
275.141
59
290.418
91
317.406
28
276.33
60
294.013
92
325.229
29
276.191
61
292.57
93
310.648
30
276.324
62
294.577
94
308.108
31
271.896
63
294.107
95
288.271
Sumber : www.yahoofinance.com
No
SAHAM
No
SAHAM
No
SAHAM
97
291.876
131
295.764
165
326.821
98
295.467
132
288.383
166
326.584
99
303.781
133
283.206
167
327.205
100
294.051
134
283.491
168
326.07
101
292.467
135
282.268
169
325.107
102
298.525
136
291.349
170
320.205
103
299.369
137
290.923
171
315.961
104
291.036
138
288.284
172
319.896
105
283.491
139
289.151
173
322.802
106
271.888
140
290.46
174
324.362
107
280.077
141
294.194
175
326.438
108
279.54
142
295.523
176
329.514
109
270.597
143
299.074
177
327.526
110
269.945
144
304.441
178
334.11
111
271.667
145
310.027
179
334.537
112
285.587
146
306.313
180
333.42
113
286.359
147
308.942
181
330.905
114
286.005
148
312.223
182
335.189
115
285.708
149
310.386
183
336.456
116
288.311
150
315.06
184
336.465
117
284.666
151
307.96
118
283.633
152
312.43
119
283.748
153
315.482
120
280.604
154
317.469
121
281.11
155
320.951
122
289.743
156
320.444
123
294.239
157
320.865
124
297.208
158
318.02
125
297.361
159
314.317
126
297.83
160
314.701
127
299.751
161
318.453
128
297.609
162
316.37
129
298.61
163
317.609
Periode Januari 2006 – September 2006
No
RETURN
No
RETURN
No
RETURN
1
0
36
-0.004614
71
0.0240496
2
0.0120351
37
-0.0075015
72
0.0303933
3
0.0259706
38
-0.0077836
73
0.0085995
4
-0.0010125
39
0.0195308
74
-0.0049487
5
-0.0007506
40
-0.0037648
75
-0.0130693
6
0.0319974
41
0.0093123
76
0.0101865
7
0.0142256
42
0.0098796
77
0.0159345
8
-0.0044913
43
0.009747
78
-0.006885
9
-0.0060321
44
-0.0002515
79
-0.0106171
10
-0.013973
45
-0.0157546
80
0.0104649
11
-0.0210511
46
-0.0112701
81
-0.0009136
12
-0.0179066
47
0.0052654
82
0.0170077
13
0.0347975
48
0.0076096
83
-0.0080901
14
-0.0064771
49
-0.0032124
84
-0.0007552
15
-0.0214683
50
0.0008771
85
0.0158003
16
0.0065041
51
-0.0035131
86
0.0185665
17
0.0216626
52
0.0299737
87
0.0044284
18
-0.0041396
53
0.0286866
88
0.0085102
19
0.0038813
54
0.0213767
89
-0.0200298
20
0.0021375
55
-0.0038312
90
-0.0717356
21
0.0085048
56
-0.0228489
91
0.0028079
22
0.0017142
57
0.0039542
92
0.0243383
23
-0.000328
58
0.0051448
93
-0.0458657
24
0.001821
59
0.0002066
94
-0.00821
25
0.0129421
60
0.0122856
95
-0.0665593
26
-0.0196231
61
-0.0049098
96
0.0145671
27
0.0078083
62
0.0068467
97
-0.0021219
28
0.0043157
63
-0.0015968
98
0.0122246
29
-0.0005068
64
0.0155194
99
0.0277364
30
0.0004706
65
0.0074045
100
-0.0325539
31
-0.0161253
66
0.0056333
101
-0.0053877
32
0.000625
67
-0.0018853
102
0.0204748
33
0.0050594
68
0.0102433
103
0.0028433
34
0.003796
69
0.0066626
104
-0.0282196
107
0.0296777
142
0.0045107
177
-0.006027
108
-0.0019299
143
0.0119411
178
0.0198906
109
-0.0325037
144
0.0177964
179
0.0012862
110
-0.002442
145
0.018195
180
-0.0033535
111
0.0063884
146
-0.0120714
181
-0.0075867
112
0.0499691
147
0.0085494
182
0.0128813
113
0.0026925
148
0.010561
183
0.0037817
114
-0.001223
149
-0.0058785
184
0
115
-0.0010495
150
0.0149335
116
0.009059
151
-0.0227932
117
-0.0127057
152
0.0144105
118
-0.00366
153
0.0097148
119
0.000423
154
0.006288
120
-0.0111634
155
0.010902
121
0.0018159
156
-0.0015903
122
0.0302379
157
0.001341
123
0.0154118
158
-0.0089218
124
0.0100432
159
-0.0117027
125
0.0005046
160
0.0012082
126
0.0015793
161
0.0118457
127
0.0064259
162
-0.0065531
128
-0.0071649
163
0.0039118
129
0.0033545
164
0.0094012
130
0.0004018
165
0.0191841
131
-0.0099918
166
-0.0007346
132
-0.0252693
167
0.0018967
133
-0.0180904
168
-0.0034595
134
0.0009882
169
-0.0029485
135
-0.0043128
170
-0.0152178
136
0.0316612
171
-0.0133302
137
-0.001477
172
0.0123928
138
-0.0091161
173
0.0090245
139
0.0030134
174
0.0048211
Lampiran 3 – Estimasi Parameter Model ARIMA
Return
Saham LQ45
1.
ARIMA ([5], 0)
Variable Coefficient Std. Error t-Statistic Prob.
AR(5) 0.180571 0.073250 2.465134 0.0146
R-squared 0.026533 Mean dependent var 0.001306 Adjusted R-squared 0.026533 S.D. dependent var 0.015994 S.E. of regression 0.015780 Akaike info criterion -5.454542 Sum squared resid 0.044325 Schwarz criterion -5.436735 Log likelihood 489.1815 Durbin-Watson stat 1.750462
2.
ARIMA (0, [5])
Variable Coefficient Std. Error t-Statistic Prob.
MA(5) 0.166659 0.073160 2.278019 0.0239
R-squared 0.021197 Mean dependent var 0.001467 Adjusted R-squared 0.021197 S.D. dependent var 0.015900 S.E. of regression 0.015730 Akaike info criterion -5.461024 Sum squared resid 0.045282 Schwarz criterion -5.443552 Log likelihood 503.4142 Durbin-Watson stat 1.759836
3.
ARIMA ([5], [5])
Variable Coefficient Std. Error t-Statistic Prob.
AR(5) 0.736867 0.164414 4.481786 0.0000 MA(5) -0.605137 0.196774 -3.075285 0.0024
Log likelihood 490.9138 Durbin-Watson stat 1.812693
4.
ARIMA ([11], 0)
Variable Coefficient Std. Error t-Statistic Prob.
AR(11) 0.240213 0.072363 3.319542 0.0011
R-squared 0.053443 Mean dependent var 0.001347 Adjusted R-squared 0.053443 S.D. dependent var 0.015922 S.E. of regression 0.015491 Akaike info criterion -5.491403 Sum squared resid 0.041273 Schwarz criterion -5.473176 Log likelihood 476.0063 Durbin-Watson stat 1.850501
5.
ARIMA (0, [11])
Variable Coefficient Std. Error t-Statistic Prob.
MA(11) 0.351038 0.068849 5.098654 0.0000
R-squared 0.078439 Mean dependent var 0.001467 Adjusted R-squared 0.078439 S.D. dependent var 0.015900 S.E. of regression 0.015263 Akaike info criterion -5.521286 Sum squared resid 0.042634 Schwarz criterion -5.503813 Log likelihood 508.9583 Durbin-Watson stat 1.844499
6.
ARIMA ([11], [11])
Variable Coefficient Std. Error t-Statistic Prob.
AR(11) -0.253647 0.167500 -1.514315 0.1318 MA(11) 0.567371 0.144264 3.932870 0.0001
Sum squared resid 0.039505 Schwarz criterion -5.487171 Log likelihood 479.7935 Durbin-Watson stat 1.874573
7.
ARIMA ([5], [11])
Variable Coefficient Std. Error t-Statistic Prob.
AR(5) 0.185825 0.073200 2.538583 0.0120 MA(11) 0.366218 0.069158 5.295396 0.0000
Lampiran 4 – Uji
White Noise
Model ARIMA ([5],[11]) dengan
Correlogram of
Residuals
MODEL ARIMA ([5], [11])
Autocorrelation Partial Correlation AC PAC Q-Stat Prob
.|* | .|* | 1 0.091 0.091 1.4910 .|. | .|. | 2 -0.026 -0.035 1.6194
Lag
A
u
to
c
o
rr
e
la
ti
o
n
45 40 35 30 25 20 15 10 5 1 1.0
0.8
0.6
0.4
0.2
0.0
-0.2
-0.4
-0.6
-0.8
-1.0
Autocorrelation Function for residual kuadrat (with 5% significance limits for the autocorrelations)
Lampiran 5 - Uji Heteroskedastisitas Model ARIMA ([5], [11]) dengan
Correlogram of Residuals
Squared
Autocorrelation Partial Correlation AC PAC Q-Stat Prob
.|. | .|. | 1 0.008 0.008 0.0126 .|* | .|* | 2 0.111 0.111 2.2786
.|** | .|** | 3 0.209 0.209 10.283 0.001 .|. | .|. | 4 0.017 0.007 10.338 0.006 .|*** | .|** | 5 0.342 0.314 32.128 0.000 .|. | .|. | 6 0.038 0.004 32.403 0.000 .|. | *|. | 7 -0.000 -0.064 32.403 0.000 .|. | *|. | 8 -0.001 -0.153 32.403 0.000 .|. | .|. | 9 0.061 0.052 33.107 0.000 .|. | *|. | 10 0.018 -0.081 33.167 0.000 .|* | .|* | 11 0.086 0.116 34.598 0.000 .|. | .|. | 12 -0.009 -0.002 34.613 0.000 .|. | .|* | 13 0.039 0.115 34.908 0.000
Atau gambar diatas dapat diperjelas melalui plot ACF dan PACF dengan bantuan
paket program MINITAB 14.
Lag
P
a
rt
ia
l
A
u
to
c
o
rr
e
la
ti
o
n
45 40 35 30 25 20 15 10 5 1 1.0
0.8
0.6
0.4
0.2
0.0
-0.2
-0.4
-0.6
-0.8
-1.0
Partial Autocorrelation Function for residual kuadrat
(with 5% significance limits for the partial autocorrelations)
Gambar plot PACF residual kuadrat ARMA ([5],[11])
Dari plot ACF dan PACF diatas terlihat bahwa ada lag yang keluar dari batas margin
Lampiran 6 - Uji
White Noise
Model EGARCH(1,1) dengan
Correlogram of
Residuals
MODEL EGARCH(1,1)
Autocorrelation Partial Correlation AC PAC Q-Stat Prob
.|* | .|* | 1 0.184 0.184 6.1721 .|. | .|. | 2 -0.018 -0.054 6.2333
Lampiran 7 – Data
Return
Saham LQ45 Setelah Penghapusan
Outlier
Periode Januari 2006 – September 2006
No
RETURN
No
RETURN
No
RETURN
1
0
33
0.0050594
65
0.0074045
2
0.0120351
34
0.003796
66
0.0056333
3
0.0259706
35
-0.0108054
67
-0.0018853
4
-0.0010125
36
-0.004614
68
0.0102433
5
-0.0007506
37
-0.0075015
69
0.0066626
6
0.0319974
38
-0.0077836
70
0.0029578
7
0.0142256
39
0.0195308
71
0.0240496
8
-0.0044913
40
-0.0037648
72
0.0303933
9
-0.0060321
41
0.0093123
73
0.0085995
10
-0.013973
42
0.0098796
74
-0.0049487
11
-0.0210511
43
0.009747
75
-0.0130693
12
-0.0179066
44
-0.0002515
76
0.0101865
13
0
45
-0.0157546
77
0.0159345
14
-0.0064771
46
-0.0112701
78
-0.006885
15
-0.0214683
47
0.0052654
79
-0.0106171
16
0.0065041
48
0.0076096
80
0.0104649
17
0.0216626
49
-0.0032124
81
-0.0009136
18
-0.0041396
50
0.0008771
82
0.0170077
19
0.0038813
51
-0.0035131
83
-0.0080901
20
0.0021375
52
0.0299737
84
-0.0007552
21
0.0085048
53
0.0286866
85
0.0158003
22
0.0017142
54
0.0213767
86
0.0185665
23
-0.000328
55
-0.0038312
87
0.0044284
24
0.001821
56
-0.0228489
88
0.0085102
25
0.0129421
57
0.0039542
89
-0.0200298
26
-0.0196231
58
0.0051448
90
0
27
0.0078083
59
0.0002066
91
0.0028079
28
0.0043157
60
0.0122856
92
0.0243383
29
-0.0005068
61
-0.0049098
93
0
30
0.0004706
62
0.0068467
94
-0.00821
31
-0.0161253
63
-0.0015968
95
0
No
RETURN
No
RETURN
No
RETURN
97
-0.0021219
132
-0.0252693
167
0.0018967
98
0.0122246
133
-0.0180904
168
-0.0034595
99
0.0277364
134
0.0009882
169
-0.0029485
100
0
135
-0.0043128
170
-0.0152178
101
-0.0053877
136
0.0316612
171
-0.0133302
102
0.0204748
137
-0.001477
172
0.0123928
103
0.0028433
138
-0.0091161
173
0.0090245
104
-0.0282196
139
0.0030134
174
0.0048211
105
-0.0262839
140
0.0045203
175
0.0063922
106
0
141
0.0127599
176
0.0093605
107
0.0296777
142
0.0045107
177
-0.006027
108
-0.0019299
143
0.0119411
178
0.0198906
109
0
144
0.0177964
179
0.0012862
110
-0.002442
145
0.018195
180
-0.0033535
111
0.0063884
146
-0.0120714
181
-0.0075867
112
0
147
0.0085494
182
0.0128813
113
0.0026925
148
0.010561
183
0.0037817
114
-0.001223
149
-0.0058785
184
0
115
-0.0010495
150
0.0149335
116
0.009059
151
-0.0227932
117
-0.0127057
152
0.0144105
118
-0.00366
153
0.0097148
119
0.000423
154
0.006288
120
-0.0111634
155
0.010902
121
0.0018159
156
-0.0015903
122
0.0302379
157
0.001341
123
0.0154118
158
-0.0089218
124
0.0100432
159
-0.0117027
125
0.0005046
160
0.0012082
126
0.0015793
161
0.0118457
127
0.0064259
162
-0.0065531
128
-0.0071649
163
0.0039118
129
0.0033545
164
0.0094012
130
0.0004018
165
0.0191841
Lampiran 8 –
Correlogram of
Return
Saham LQ45 Setelah Penghapusan
Outlier
Autocorrelation Partial Correlation AC PAC Q-Stat Prob
Lampiran 9 –
Estimasi Parameter Model ARIMA Terbaik
Return
Saham LQ45
Setelah Penghapusan
Outlier
1.
ARMA ( [1], 0)
Variable Coefficient Std. Error t-Statistic Prob.
AR(1) 0.215543 0.072383 2.977824 0.0033
R-squared 0.001313 Mean dependent var 0.002602 Adjusted R-squared 0.001313 S.D. dependent var 0.011991 S.E. of regression 0.011984 Akaike info criterion -6.005103 Sum squared resid 0.026137 Schwarz criterion -5.987564 Log likelihood 550.4669 Durbin-Watson stat 1.945860
2.
ARMA (0, [1])
Variable Coefficient Std. Error t-Statistic Prob.
MA(1) 0.250253 0.071571 3.496580 0.0006
R-squared 0.010302 Mean dependent var 0.002588 Adjusted R-squared 0.010302 S.D. dependent var 0.011960 S.E. of regression 0.011898 Akaike info criterion -6.019396 Sum squared resid 0.025908 Schwarz criterion -6.001924 Log likelihood 554.7845 Durbin-Watson stat 2.018583
3.
ARMA ([1], [1])
Variable Coefficient Std. Error t-Statistic Prob.
AR(1) -0.100063 0.295829 -0.338247 0.7356 MA(1) 0.341741 0.279462 1.222855 0.2230
Log likelihood 551.3673 Durbin-Watson stat 1.999901
4.
ARMA ([11] , 0)
Variable Coefficient Std. Error t-Statistic Prob.
AR(11) 0.172748 0.072271 2.390282 0.0179
R-squared -0.013683 Mean dependent var 0.002539 Adjusted R-squared -0.013683 S.D. dependent var 0.011702 S.E. of regression 0.011782 Akaike info criterion -6.038785 Sum squared resid 0.023875 Schwarz criterion -6.020558 Log likelihood 523.3549 Durbin-Watson stat 1.607740
5.
ARMA (0, [11])
Variable Coefficient Std. Error t-Statistic Prob.
MA(11) 0.198966 0.072928 2.728262 0.0070
R-squared -0.011942 Mean dependent var 0.002588 Adjusted R-squared -0.011942 S.D. dependent var 0.011960 S.E. of regression 0.012031 Akaike info criterion -5.997169 Sum squared resid 0.026490 Schwarz criterion -5.979696 Log likelihood 552.7395 Durbin-Watson stat 1.547105
6.
ARMA ([11], [11])
Variable Coefficient Std. Error t-Statistic Prob.
AR(11) -0.153716 0.196679 -0.781556 0.4356 MA(11) 0.344644 0.194818 1.769056 0.0787
Lampiran 10
–
Uji
White Noise
Model ARMA ([1],0) Setelah Penghapusan
Outlier
dengan
Correlogram of Residuals
ARMA ([1], 0)
Autocorrelation Partial Correlation AC PAC Q-Stat Prob
.|. | .|. | 1 -0.004 -0.004 0.0034
LAMPIRAN 11 – Uji Heteroskedastisitas Model ARMA ([1],0) Setelah
Penghapusan
Outlier
dengan
Correlogram of Residuals
Squared
ARMA ([1], 0)
Autocorrelation Partial Correlation AC PAC Q-Stat Prob
.|. | .|. | 1 0.005 0.005 0.0049
LAMPIRAN 12 - Uji Normalitas
Model EGARCH(1,1) dengan Histogram
%
5
=
α
0
H
: Residual berdistribusi normal
1
H
: Residual tidak berdistribusi normal
Keputusan : P-value >
α
maka terima
H
0sehingga residual EGARCH(1,1) berdistribusi
normal.
0 4 8 12 16 20 24-2 -1 0 1 2 3
Series: Standardized Residuals Sample 2 184
Observations 183
Mean 0.205436 Median 0.171973 Maximum 3.731255 Minimum -2.335133 Std. Dev. 1.004014 Skewness 0.177054 Kurtosis 3.462131
Lampiran 13 – Program S-PLUS Prosedur Pendeteksian
Outlier
Model
EGARCH (1,1) dengan Menggunakan Uji Rasio
Likelihood
det.outlier<-function(data) {
cat("\n===========================================================\n") cat("\n Program Deteksi outlier pada model EGARCH dengan metode LR \n")
cat("\n Oleh ")
cat("\n Moh.Taufik ") cat("\n 080710450 \n") cat("\n===========================================================\n") n<-nrow(data)
cat("\n Inputkan Nilai Parameter :\n") alfa0<-as.numeric(readline("alfa0 = ")) alfa1<-as.numeric(readline("alfa1 = ")) gamma1<-as.numeric(readline("gamma1 = ")) beta1<-as.numeric(readline("beta1 = ")) h0star<-1
hstar<-rep(0,n) for(t in 1:n) {
if(t==1) {
hstar[t]<-exp(alfa0+alfa1*((mean(data[,3]))/sqrt(h0star))+gamma1*(((abs(mean(data[, 3])))/sqrt(h0star))-sqrt(2/3.14))+beta1*(log(h0star)))
} else {
hstar[t]<-exp(alfa0+alfa1*((data[t-1,3])/sqrt(hstar[t-
1]))+gamma1*(((abs(data[t-1,3]))/sqrt(hstar[t-1]))-sqrt(2/3.14))+beta1*(log(hstar[t-1]))) }
}
cat("nilai hstar adalah : \n") print(hstar)
s<-rep(0,n) for(t in 1:n) {
s[t]<-(abs(data[t,3]/hstar[t])) }
S<-max(s) Time<-1:n
GabTimes<-cbind(Time,s)
S.titik<-GabTimes[GabTimes[,2]==S,1] gama<-data[S.titik,4]-data[S.titik,5] cat("Nilai S adalah : \n")
print(S)
cat("Nilai titik ke-S adalah : \n") print(S.titik)
cat("Nilai gama adalah : \n") print(gama)
for(t in 1:n) {
if(t==1) {
h[t]<-exp(alfa0+alfa1*(mean(data[,2])/sqrt(h0))+gamma1*(((abs(mean(data[,2])))/ sqrt(h0))-sqrt(2/3.14))+beta1*(log(h0)))
} else {
h[t]<-exp(alfa0+alfa1*((data[t-1,2])/sqrt(h[t- 1]))+gamma1*(((abs(data[t-1,2]))/sqrt(h[t-1]))-sqrt(2/3.14))+beta1*(log(h[t-1])))
} }
cat("nilai h adalah : \n") print(h)
GabTimesResidARIMA<-cbind(Time,s,data[,2])
residMaxARIMA<-GabTimesResidARIMA[GabTimesResidARIMA[,2]==S,3] cat("nilai residMaxARIMA adalah : \n")
print(residMaxARIMA)
ToTopi<-(alfa1)*(2*gama*residMaxARIMA+(gama)^2) cat("nilai ToTopi adalah : \n")
print(ToTopi) hm0<-1
hm<-rep(0,n) for(t in 1:n) {
if(t==1) {
hm[t]<-exp(alfa0+alfa1*((gama+residMaxARIMA)/sqrt(hm0))+gamma1*(((abs(gama+resid MaxARIMA))/sqrt(hm0))-sqrt(2/3.14))+(beta1*log(hm0))+ToTopi)
} else {
hm[t]<-exp(alfa0+alfa1*((gama+residMaxARIMA)/sqrt(hm[t-
1]))+gamma1*(((abs(gama+residMaxARIMA))/sqrt(hm[t-1]))-sqrt(2/3.14))+(beta1*log(hm[t-1]))+ToTopi) }
}
cat("nilai hm adalah : \n") print(hm)
LMTopi<-(1/2)*sum(log(hm))-(1/2)*sum((data[,2])^2/(hm)) cat("nilai LMTopi adalah : \n")
print(LMTopi)
LBTopi<-(1/2)*sum(log(h))-(1/2)*sum((data[,2])^2/(h)) cat("nilai LBTopi adalah : \n")
print(LBTopi)
LT1<-2*(LMTopi-LBTopi) cat("nilai LT1 adalah : \n") print(LT1)
if(LT1<216.37) {
cat("Karena nilai (LT1 < 216.37) maka tidak ada outlier terdeteksi pada data...\n")
else {
cat("Karena nilai (LT1 > 216.37) maka ada outlier terdeteksi pada data\n")
cat("Lanjutkan Kelangkah Selanjutnya...") }
L0Topi<-LBTopi
cat("nilai L0Topi adalah : \n") print(L0Topi)
GabTimesResidEGARCH<-cbind(Time,s,data[,3])
cat("nilai Gab Times, s, ResidEGARCH adalah : \n") print(GabTimesResidEGARCH)
residMaxEGARCH<-GabTimesResidEGARCH[GabTimesResidEGARCH[,2]==S,3] cat("nilai resid Max EGARCH adalah : \n")
print(residMaxEGARCH) gamaM<-residMaxEGARCH
cat("nilai gamaM adalah : \n") print(gamaM)
if((gamaM)^2-(ToTopi/(alfa1))>0) {
if(gamaM>=0) {
gama1<-gamaM-sqrt((gamaM)^2-(ToTopi/(alfa1))) }
else {
gama1<-gamaM+sqrt((gamaM)^2-(ToTopi/(alfa1))) }
} else {
gama1<-0 }
L1Topi<-(1/2)*sum(log(hstar))-(1/2)*sum((data[,2])^2/(hstar)) cat("nilai L1Topi adalah : \n")
print(L1Topi)
cat("nilai gama1 adalah : ") print(gama1)
if(L0Topi>=L1Topi) {
gama2<-gamaM L2Topi<-L0Topi }
else {
gama2<-gama1 L2Topi<-L1Topi }
cat("\n")
cat("nilai gama2 adalah : ") print(gama2)
LT2<-2*(LMTopi-L2Topi) cat("nilai LT2 adalah : ") print(LT2)
if(LT2<=5.99) {
cat("Karena LT2 <= 5.99 ")
} else {
cat("Karena LT2 > 5.99 ")
cat("Maka -> TERDETEKSI OUTLIER tipe AVO\n") }
}
Lampiran 14 – Program S-PLUS Penghapusan
Outlier
Model EGARCH (1,1)
dengan Menggunakan
Hampel
Identifier
#PROGRAM HAMPEL IDENTIFIER Hampel <- function(X,n) {
A <- matrix(0,n,4)
dimnames(A) <- list(rep(“ “,n), c("Time", "Zt", "HampelJarak", "Outlier"))
A[,1] <- seq(1,n) A[,2] <- round(X,5)
med <- median(A[,2]) med2 <- abs(A[,2]-med) MAD <- median(med2) S <- 1.4826*MAD D <- A[,2]-med
A[,3] <- round(abs(D/S),5)
x <- 0
for(i in 1:n) {
if(A[i,3] > 3) {
A[i,4] <- 1 x <- x+1 }
else
A[i,4] <- 0 }
return(x,A) }
#PROGRAM PENGHAPUSAN OUTLIERS Outremove <- function(A,n,terhapus) {
cat("\n Proses Penghapusan Outliers :") cat("\n i Outlier \t Dihapus \t Diganti") Zt <- A[,2]
Ot <- A[,4] K <- rep(0,n)
t <- rep(0,n) for(i in 1:n) {
K <- Zt
if(Ot[i] == 1) {
K[i] <- mean(Zt) t[i] <- mean(K) }
}
Min <- abs(mean(Zt)-t[1]) for(i in 1:n)
{
if(abs(mean(Zt)-t[i]) < Min) Min <- abs(mean(Zt)-t[i]) }
for(i in 1:n) {
if(abs(mean(Zt)-t[i]) == Min) {
cat("\n",i,"\t",sum(A[,4]),"\t",Zt[i],"\t",round(mean(Zt))) Zt[i] <- round(mean(Zt))
terhapus <- terhapus+1 break
} }
#IDENTIFIKASI HAMPEL V <- Hampel(Zt,n) A <- V$A
x <- V$x Zt <- A[,2] Ot <- A[,4] cat(“\n”) print(A)
#BERHENTI JIKA OUTLIER SAMA DENGAN 0 if(x == 0)
{
cat("\n") break }
}
return(Zt,x,terhapus) }
#PROGRAM UTAMA
outlier <- function(data) {
cat("\n===================================================\n") cat("\n PENGHAPUSAN OUTLIER DENGAN HAMPEL IDENTIFIER \n") cat("\n Oleh: ")
cat("\n MOH.TAUFIK ") cat("\n 080710450 ")
#IDENTIFIKASI HAMPEL AWAL
cat("\n PROGRAM HAMPEL IDENTIFIER")
cat("\n Proses deteksi outlier, sebagai berikut : \n")
Zt <- data[,4] n <- length(Zt) S <- Hampel(Zt,n) x <- S$x
A <- S$A
print(A)
cat("\n Jumlah Outlier = ",x) cat("\n Keterangan :")
cat("\n - terjadi outlier jika HampelJarak > 3")
cat("\n - dengan ditandai -> outlier = 1 dan tidak = 0 \n")
terhapus <- 0
#PROSES PENGHAPUSAN OUTLIER if(x > 0)
{
G <- Outremove(A,n,terhapus) Zt <- G$Zt
x <- G$x
terhapus <- G$terhapus }
#OUTPUT DATA SETELAH PENGHAPUSAN OUTLIERS if(terhapus > 0)
{
cat("\n Output data : ") cat("\n no Zt")
for(i in 1:n)
cat("\n",i," ",Zt[i]) }
Lampiran 15 – Hasil
Output
Program S-PLUS Prosedur Pendeteksian
Outlier
Model EGARCH (1,1) dengan menggunakan Uji Rasio
Likelihood
===========================================================
Program Deteksi outlier pada model EGARCH dengan metode LR
Oleh
Moh.Taufik
080710450
===========================================================
Inputkan Nilai Parameter :
alfa0 = -2.429009
alfa1 = -0.23695
gamma1 = 0.453673
beta1 = 0.754068
nilai hstar adalah :
[171] 0.00011930527 0.00016135358 0.00009989879 0.00007238087 0.00005212767
[176] 0.00004252812 0.00003679491 0.00005899864 0.00006546343 0.00004555631
[181] 0.00004773916 0.00005449022 0.00006281627 0.00004647100
Nilai S adalah :
[1] 725.6687
Nilai titik ke-S adalah :
Time
52
Nilai gama adalah :
[1] 0.024622
nilai h adalah :
nilai residMaxARIMA adalah :
0.024622
nilai ToTopi adalah :
-0.0004309478
nilai hm adalah :
[96] 0.0002197194 0.0002197194 0.0002197194 0.0002197194 0.0002197194
[101] 0.0002197194 0.0002197194 0.0002197194 0.0002197194 0.0002197194
[106] 0.0002197194 0.0002197194 0.0002197194 0.0002197194 0.0002197194
[111] 0.0002197194 0.0002197194 0.0002197194 0.0002197194 0.0002197194
[116] 0.0002197194 0.0002197194 0.0002197194 0.0002197194 0.0002197194
[121] 0.0002197194 0.0002197194 0.0002197194 0.0002197194 0.0002197194
[126] 0.0002197194 0.0002197194 0.0002197194 0.0002197194 0.0002197194
[131] 0.0002197194 0.0002197194 0.0002197194 0.0002197194 0.0002197194
[136] 0.0002197194 0.0002197194 0.0002197194 0.0002197194 0.0002197194
[141] 0.0002197194 0.0002197194 0.0002197194 0.0002197194 0.0002197194
[146] 0.0002197194 0.0002197194 0.0002197194 0.0002197194 0.0002197194
[151] 0.0002197194 0.0002197194 0.0002197194 0.0002197194 0.0002197194
[156] 0.0002197194 0.0002197194 0.0002197194 0.0002197194 0.0002197194
[161] 0.0002197194 0.0002197194 0.0002197194 0.0002197194 0.0002197194
[166] 0.0002197194 0.0002197194 0.0002197194 0.0002197194 0.0002197194
[171] 0.0002197194 0.0002197194 0.0002197194 0.0002197194 0.0002197194
[176] 0.0002197194 0.0002197194 0.0002197194 0.0002197194 0.0002197194
[181] 0.0002197194 0.0002197194 0.0002197194 0.0002197194
nilai LMTopi adalah :
[1] -858.0486
nilai LBTopi adalah :
[1] -1056.247
Karena nilai (LT1 > 216.37) maka ada outlier terdeteksi pada data
Lanjutkan Kelangkah Selanjutnya...nilai L0Topi adalah :
[1] -1056.247
nilai Gab Times, s, ResidEGARCH adalah :
Time s
[1,] 1 0.0000000 0.0000000
[2,] 2 0.0000000 0.0000000
[3,] 3 0.0000000 0.0000000
[4,] 4 0.0000000 0.0000000
[5,] 5 0.0000000 0.0000000
[6,] 6 313.5027697 0.0297590
[7,] 7 104.7882986 0.0115430
[8,] 8 80.7630583 -0.0065160
[9,] 9 61.9955211 -0.0051430
[10,] 10 163.7687041 -0.0124160
[11,] 11 174.1939731 -0.0223680
[12,] 12 63.6193982 -0.0177460
[13,] 13 120.6854258 0.0322010
[14,] 14 25.9193056 -0.0049220
[15,] 15 151.8743308 -0.0186300
[16,] 16 37.4774409 0.0082560
[17,] 17 121.2976177 0.0146700
[18,] 18 124.9514728 -0.0113800
[19,] 19 52.1143462 0.0065400
[39,] 39 191.4473811 0.0191350
[40,] 40 38.0902355 -0.0034070
[41,] 41 153.3188201 0.0106830
[42,] 42 259.9387094 0.0154380
[43,] 43 189.9240895 0.0116970
[44,] 44 56.5141068 -0.0032010
[45,] 45 310.0481228 -0.0160110
[46,] 46 58.3846983 -0.0097660
[47,] 47 43.1596604 0.0063330
[48,] 48 84.5991582 0.0074770
[49,] 49 3.4390197 -0.0002200
[50,] 50 73.4548151 -0.0031590
[51,] 51 29.0672937 -0.0012680
[52,] 52 725.6687066 0.0261950
[53,] 53 329.4006529 0.0232260
[54,] 54 220.2394085 0.0182130
[55,] 55 37.5111945 -0.0029650
[56,] 56 283.4184593 -0.0176610
[57,] 57 18.7406290 0.0036350
[58,] 58 1.2710631 0.0001310
[59,] 59 71.8644329 -0.0043570
[60,] 60 214.0709132 0.0127670
[61,] 61 25.8956751 -0.0014830
[62,] 62 152.9592184 0.0067980
[87,] 87 4.0869659 0.0003630
[88,] 88 114.3182155 0.0062300
[89,] 89 386.6641648 -0.0173600
[90,] 90 359.8288028 -0.0695830
[91,] 91 0.7565093 -0.0023290
[92,] 92 30.7286011 0.0247760
[93,] 93 143.9805453 -0.0496090
[94,] 94 1.0869643 -0.0010340
[95,] 95 176.6479104 -0.0584050
[96,] 96 7.1868405 0.0096190
[97,] 97 26.6794984 -0.0118040
[98,] 98 63.9523633 0.0170910
[99,] 99 172.0040149 0.0267570
[100,] 100 153.2668188 -0.0201210
[101,] 101 57.0612554 0.0139240
[102,] 102 152.3625244 0.0214040
[103,] 103 52.4331945 -0.0059220
[104,] 104 171.6011385 -0.0163340
[105,] 105 124.0206159 -0.0224420
[106,] 106 80.8745083 -0.0236590
[107,] 107 71.1820788 0.0245680
[108,] 108 6.5194225 0.0013060
[109,] 109 339.5933196 -0.0345740
[110,] 110 11.9398560 -0.0076240
[135,] 135 45.1744496 -0.0076760
[136,] 136 246.2495358 0.0325980
[137,] 137 9.0492357 0.0012210
[138,] 138 88.8972450 -0.0067370
[139,] 139 55.8019972 0.0045660
[140,] 140 57.9965539 0.0032870
[141,] 141 218.1555465 0.0092360
[142,] 142 182.2394428 0.0076620
[143,] 143 528.8632878 0.0210080
[144,] 144 413.0553118 0.0250590
[145,] 145 218.4998360 0.0177900
[146,] 146 143.7102941 -0.0111510
[147,] 147 14.7606702 -0.0017270
[148,] 148 119.8005407 0.0088990
[149,] 149 97.9448247 -0.0057860
[150,] 150 173.4044808 0.0115890
[151,] 151 378.9578648 -0.0224710
[152,] 152 35.8188636 0.0107100
[153,] 153 40.6098341 0.0062690
[154,] 154 6.7566014 0.0006180
[155,] 155 31.3741326 0.0017580
[156,] 156 110.9795975 -0.0044590
[157,] 157 64.7194404 0.0031260
[158,] 158 251.2815796 -0.0094570
[183,] 183 20.1380952 -0.0012650
[184,] 184 63.6310768 -0.0029570
nilai resid Max EGARCH adalah :
0.026195
nilai gamaM adalah :
0.026195
nilai L1Topi adalah :
[1] -1061.284
nilai gama1 adalah : [1] 0
nilai gama2 adalah :
0.026195
nilai LT2 adalah : [1] 394.39
Lampiran 16 – Hasil
Output
Program S-PLUS Penghapusan
Outlier
Model
EGARCH (1,1) dengan Menggunakan
Hampel Identifier
===================================================
PENGHAPUSAN OUTLIER DENGAN HAMPEL IDENTIFIER
Oleh:
MOH.TAUFIK
080710450
===================================================
PROGRAM HAMPEL IDENTIFIERProses deteksi outlier, sebagai berikut :
Time Zt HampelJarak Outlier
1 0.000000 0.152733 0
2 0.012035 0.888706 0
3 0.025971 2.094647 0
4 -0.001012 0.240305 0
5 -0.000751 0.217720 0
6 0.031997 2.616102 0
7 0.014226 1.078303 0
8 -0.004491 0.541358 0
9 -0.006032 0.674707 0
10 -0.013973 1.361875 0
11 -0.021051 1.974364 0
12 -0.017907 1.702301 0
13 0.034798 2.858484 0
14 -0.006477 0.713215 0
15 -0.021468 2.010449 0
16 0.006504 0.410086 0
17 0.021663 1.721857 0
18 -0.004140 0.510984 0
19 0.003881 0.183106 0
20 0.002138 0.032277 0
21 0.008505 0.583240 0
22 0.001714 0.004413 0
23 -0.000328 0.181116 0
24 0.001821 0.004846 0
25 0.012942 0.967193 0
26 -0.019623 1.850793 0
27 0.007808 0.522926 0
28 0.004316 0.220749 0
29 -0.000507 0.196606 0
30 0.000471 0.111975 0
31 -0.016125 1.548097 0
32 0.000625 0.098649 0
33 0.005059 0.285044 0
34 0.003796 0.175751 0
35 -0.010805 1.087735 0
36 -0.004614 0.552002 0
37 -0.007502 0.801912 0
38 -0.007784 0.826315 0
39 0.019531 1.537366 0
40 -0.003765 0.478534 0
41 0.009312 0.653074 0
127 0.006426
128 -0.007165
129 0.003354
130 0.000402
131 -0.009992
132 -0.025269
133 -0.01809
134 0.000988
135 -0.004313
136 0.031661
137 -0.001477
138 -0.009116
139 0.003013
140 0.00452
141 0.01276
142 0.004511
143 0.011941
144 0.017796
145 0.018195
146 -0.012071
147 0.008549
148 0.010561
149 -0.005878
150 0.014934
151 -0.022793
152 0.01441
153 0.009715
154 0.006288
155 0.010902
156 -0.00159
157 0.001341
158 -0.008922
159 -0.011703
160 0.001208
161 0.011846
162 -0.006553
163 0.003912
164 0.009401
165 0.019184
166 -0.000735
167 0.001897
168 -0.00346
169 -0.002948
170 -0.015218
171 -0.01333
172 0.012393
173 0.009024
174 0.004821
175 0.006392
176 0.00936
177 -0.006027
178 0.019891
179 0.001286
180 -0.003354
181 -0.007587
182 0.012881
183 0.003782
![Gambar plot ACF residual kuadrat ARMA ([5],[11])](https://thumb-ap.123doks.com/thumbv2/123dok/4014034.1957454/9.595.115.489.217.690/gambar-plot-acf-residual-kuadrat-arma.webp)
![Gambar plot PACF residual kuadrat ARMA ([5],[11])](https://thumb-ap.123doks.com/thumbv2/123dok/4014034.1957454/10.595.111.516.127.568/gambar-plot-pacf-residual-kuadrat-arma.webp)
