DETEKSI OUTLIER PADA MODEL EXPONENTIAL GENERALIZED AUTOREGRESSIVE CONDITIONAL HETEROSCEDASTIC DENGAN UJI RASIO LIKELIHOOD Repository - UNAIR REPOSITORY

  Lampiran 1-1

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 32 272.065 64 298.71 96 292.504

  Lampiran 1-2

  

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

117 284.666 151 307.96 118 283.633 152 312.43 119 283.748 153 315.482 120 280.604 154 317.469 121 281.11 155 320.951 122 289.743 156 320.444 123 294.239 157 320.865 124 297.208 158 318.02 125 297.361 159 314.317 126 297.83 160 314.701 127 299.751 161 318.453 128 297.609 162 316.37 129 298.61 163 317.609 130 298.729 164 320.608

Sumber : www.yahoofinance.com

• 0.004614
• 0.0075015
• 0.0077836
• 0.0010125
• 0.0049487
• 0.0007506
• 0.0037648
• 0.0130693
• 0.0044913
• 0.006885
• 0.0060321
• 0.0002515
• 0.0106171

• 0.013973
• 0.0157546
• 0.0210511
• 0.0112701
• 0.0009136

• 0.0179066
• 0.0080901
• 0.0064771
• 0.0032124
• 0.0007552
• 0.0214683
• 0.0035131
• 0.0041396
• 0.0200298
• 0.0038312
• 0.0717356
• 0.0228489
• 0.000328
• 0.0458657
• 0.00821
• 0.0665593
• 0.0196231
• 0.0049098
• 0.0021219
• 0.0015968
• 0.0005068
• 0.0325539
• 0.0161253
• 0.0053877
• 0.0018853
• 0.0282196

  23

  61

  26

  95

  60 0.0122856

  25 0.0129421

  94

  59 0.0002066

  24 0.001821

  93

  58 0.0051448

  92 0.0243383

  88 0.0085102

  96 0.0145671

  22 0.0017142

  91 0.0028079

  56

  21 0.0085048

  90

  55

  20 0.0021375

  89

  54 0.0213767

  19 0.0038813

  57 0.0039542

  62 0.0068467

  27 0.0078083

  32 0.000625

  70 0.0029578

  35

  104

  69 0.0066626

  34 0.003796

  103 0.0028433

  68 0.0102433

  33 0.0050594

  102 0.0204748

  67

  101

  97

  66 0.0056333

  31

  100

  65 0.0074045

  30 0.0004706

  99 0.0277364

  64 0.0155194

  29

  98 0.0122246

  63

  28 0.0043157

  53 0.0286866

  87 0.0044284

  18

  74

  8

  77 0.0159345

  42 0.0098796

  7 0.0142256

  76 0.0101865

  41 0.0093123

  6 0.0319974

  75

  40

  5

  39 0.0195308

  52 0.0299737

  4

  73 0.0085995

  38

  3 0.0259706

  72 0.0303933

  37

  2 0.0120351

  71 0.0240496

  36

  1

  Lampiran 2-1 Lampiran 2 – Data Return Saham LQ45 Periode Januari 2006 – September 2006 No RETURN No RETURN No RETURN

  43 0.009747

  78

  9

  83

  17 0.0216626

  86 0.0185665

  51

  16 0.0065041

  85 0.0158003

  50 0.0008771

  15

  84

  49

  14

  48 0.0076096

  44

  13 0.0347975

  82 0.0170077

  47 0.0052654

  12

  81

  46

  11

  80 0.0104649

  45

  10

  79

  105

• 0.0108054
• 0.0262839

No RETURN No RETURN No RETURN 106

  176 0.0093605

  Lampiran 2-2

  141 0.0127599

• 0.0417793
• 0.006027
• 0.0019299
• 0.0325037
• 0.002442
• 0.0033535
• 0.0120714
• 0.0075867

  107 0.0296777

• 0.001223
• 0.0058785
• 0.0010495
• 0.0227932
• 0.0127057
• 0.00366
• 0.0111634
• 0.0015903
• 0.0089218
• 0.0117027
• 0.0065531
• 0.0071649
• 0.0099918
• 0.0007346
• 0.0252693
• 0.0180904
• 0.0034595
• 0.0029485
• 0.0043128
• 0.0152178
• 0.0133302
• 0.001477
• 0.0091161

  162

  165 0.0191841

  130 0.0004018

  164 0.0094012

  129 0.0033545

  163 0.0039118

  128

  127 0.0064259

  166

  161 0.0118457

  126 0.0015793

  160 0.0012082

  125 0.0005046

  159

  124 0.0100432

  131

  132

  123 0.0154118

  137

  175 0.0063922

  140 0.0045203

  174 0.0048211

  139 0.0030134

  173 0.0090245

  138

  172 0.0123928

  171

  167 0.0018967

  136 0.0316612

  170

  135

  169

  134 0.0009882

  168

  133

  158

  157 0.001341

  142 0.0045107

  145 0.018195

  147 0.0085494

  112 0.0499691

  181

  146

  111 0.0063884

  180

  110

  113 0.0026925

  179 0.0012862

  144 0.0177964

  109

  178 0.0198906

  143 0.0119411

  108

  177

  182 0.0128813

  148 0.010561

  122 0.0302379

  118

  156

  155 0.010902

  120

  154 0.006288

  119 0.000423

  153 0.0097148

  152 0.0144105

  183 0.0037817

  117

  151

  116 0.009059

  150 0.0149335

  184 115

  149

  114

  121 0.0018159

  Lampiran 3-1 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

R-squared 0.045193 Mean dependent var 0.001306

Adjusted R-squared 0.039799 S.D. dependent var 0.015994

S.E. of regression 0.015672 Akaike info criterion -5.462724

Sum squared resid 0.043475 Schwarz criterion -5.427110

  Lampiran 3-2

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

R-squared 0.093992 Mean dependent var 0.001347

Adjusted R-squared 0.088694 S.D. dependent var 0.015922

S.E. of regression 0.015199 Akaike info criterion -5.523625

  Lampiran 3-3

Sum squared resid 0.039505 Schwarz criterion -5.487171

Log likelihood 479.7935 Durbin-Watson stat 1.874573

  AR(5) 0.185825 0.073200 2.538583 0.0120 MA(11) 0.366218 0.069158 5.295396 0.0000

R-squared 0.119560 Mean dependent var 0.001306

Adjusted R-squared 0.114586 S.D. dependent var 0.015994

S.E. of regression 0.015050 Akaike info criterion -5.543811

Sum squared resid 0.040089 Schwarz criterion -5.508198

Log likelihood 498.1711 Durbin-Watson stat 1.793344

  Lampiran 4-1

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 .|. | .|. | 3 -0.052 -0.046 2.1112 0.146 .|. | .|. | 4 -0.001 0.007 2.1113 0.348 .|. | .|. | 5 -0.008 -0.012 2.1240 0.547

• |. | *|. | 6 -0.078 -0.079 3.2605 0.515
• |. | *|. | 7 -0.075 -0.061 4.3063 0.506
• |. | *|. | 8 -0.079 -0.073 5.4816 0.484
• |. | *|. | 9 -0.085 -0.086 6.8646 0.443 .|. | .|. | 10 0.027 0.030 7.0068 0.536
• |. | *|. | 11 -0.072 -0.095 8.0072 0.533 .|. | .|. | 12 0.014 0.013 8.0426 0.625 .|. | .|. | 13 0.020 0.003 8.1212 0.702

Lampiran 5 - Uji Heteroskedastisitas Model ARIMA ([5], [11]) dengan

Correlogram of Residuals Squared

  0.8

  Gambar plot ACF residual kuadrat ARMA ([5],[11])

  

Atau gambar diatas dapat diperjelas melalui plot ACF dan PACF dengan bantuan

paket program MINITAB 14.

  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

  Autocorrelation Function for residual kuadrat (with 5% significance limits for the autocorrelations)

  0.0

  0.2

  0.4

  0.6

  1.0

  Lampiran 4-2 Lag A u to c o rr e la ti o n

• 0.2
• 0.4
• 0.6
• 0.8
• 1.0

  1

  5

  10

  15

  

20

  25

  30

  35

  40

  45

  Lampiran 4-3 Partial Autocorrelation Function for residual kuadrat

  (with 5% significance limits for the partial autocorrelations)

  1.0

  0.8 n

  0.6 o ti

  0.4 la e

  0.2 rr o c

  0.0 to u

• 0.2

  A l ia

• 0.4

  rt a P

• 0.6
• 0.8
• 1.0

  1

  5

  10

  15

  20

  25

  30

  35

  40

  45 Lag Gambar plot PACF residual kuadrat ARMA ([5],[11])

  Dari plot ACF dan PACF diatas terlihat bahwa ada lag yang keluar dari batas margin error (batas merah). Hal itu menunjukkan adanya kasus Hetreoskedastisitas.

  Autocorrelation Partial Correlation AC PAC Q-Stat Prob .|* | .|* | 1 0.184 0.184 6.1721 .|. | .|. | 2 -0.018 -0.054 6.2333

  Lampiran 4-4

Lampiran 6 - Uji White Noise Model EGARCH(1,1) dengan Correlogram of

Residuals

MODEL EGARCH(1,1)

• |. | *|. | 3 -0.074 -0.063 7.2536 0.007 .|. | .|. | 4 -0.007 0.019 7.2625 0.026 .|. | .|. | 5 0.031 0.025 7.4389 0.059
• |. | *|. | 6 -0.067 -0.086 8.2723 0.082
• |. | *|. | 7 -0.096 -0.068 9.9933 0.075
• |. | .|. | 8 -0.074 -0.045 11.041 0.087
• |. | *|. | 9 -0.068 -0.064 11.912 0.103 .|. | .|. | 10 0.009 0.017 11.926 0.155 .|. | .|. | 11 -0.032 -0.046 12.120 0.207 .|. | .|. | 12 -0.016 -0.011 12.167 0.274 .|. | .|. | 13 -0.018 -0.023 12.234 0.346

• 0.0108054
• 0.0018853
• 0.0010125
• 0.004614
• 0.0007506
• 0.0075015
• 0.0077836
• 0.0044913
• 0.0037648
• 0.0060321

• 0.013973
• 0.0049487
• 0.0210511
• 0.0130693
• 0.0179066
• 0.0002515
• 0.0157546
• 0.0064771
• 0.0112701
• 0.006885
• 0.0214683
• 0.0106171
• 0.0032124
• 0.0009136
• 0.0041396
• 0.0035131
• 0.0080901
• 0.0007552
• 0.000328
• 0.0038312
• 0.0228489
• 0.0200298
• 0.0196231
• 0.0005068
• 0.0049098
• 0.00821
• 0.0161253
• 0.0015968

  24 0.001821

  87 0.0044284

  55

  23

  86 0.0185665

  54 0.0213767

  22 0.0017142

  85 0.0158003

  53 0.0286866

  21 0.0085048

  84

  52 0.0299737

  20 0.0021375

  83

  51

  19 0.0038813

  82 0.0170077

  50 0.0008771

  18

  81

  49

  56

  25 0.0129421

  88 0.0085102

  61

  64 0.0155194

  32 0.000625

  95

  63

  31

  94

  62 0.0068467

  30 0.0004706

  93

  29

  57 0.0039542

  92 0.0243383

  60 0.0122856

  28 0.0043157

  91 0.0028079

  59 0.0002066

  27 0.0078083

  90

  58 0.0051448

  26

  89

  17 0.0216626

  48 0.0076096

  80 0.0104649

  36

  39 0.0195308

  7 0.0142256

  70 0.0029578

  38

  6 0.0319974

  69 0.0066626

  37

  5

  68 0.0102433

  4

  8

  67

  35

  3 0.0259706

  66 0.0056333

  34 0.003796

  2 0.0120351

  65 0.0074045

  33 0.0050594

  1

  Lampiran 5-1 Lampiran 7 – Data Return Saham LQ45 Setelah Penghapusan Outlier Periode Januari 2006 – September 2006 No RETURN No RETURN No RETURN

  71 0.0240496

  40

  16 0.0065041

  76 0.0101865

  79

  47 0.0052654

  15

  78

  46

  14

  77 0.0159345

  45

  13

  44

  72 0.0303933

  12

  75

  43 0.009747

  11

  74

  42 0.0098796

  10

  73 0.0085995

  41 0.0093123

  9

  96 0.0145671

• 0.0021219
• 0.0252693
• 0.0180904
• 0.0034595
• 0.0029485
• 0.0043128
• 0.0152178
• 0.0053877
• 0.0133302
• 0.001477
• 0.0091161
• 0.0282196

• 0.0262839

• 0.006027
• 0.0019299
• 0.002442
• 0.0033535
• 0.0120714
• 0.0075867
• 0.001223
• 0.0058785
• 0.0010495
• 0.0227932
• 0.0127057
• 0.00366
• 0.0111634
• 0.0015903
• 0.0089218
• 0.0117027
• 0.0065531
• 0.0071649

  120

  154 0.006288

  119 0.000423

  153 0.0097148

  118

  152 0.0144105

  117

  151

  150 0.0149335

  116 0.009059

  184 115

  149

  114

  183 0.0037817

  148 0.010561

  113 0.0026925

  182 0.0128813

  112 147 0.0085494

  155 0.010902

  156

  121 0.0018159

  127 0.0064259

  131

  165 0.0191841

  130 0.0004018

  164 0.0094012

  129 0.0033545

  163 0.0039118

  128

  162

  161 0.0118457

  122 0.0302379

  126 0.0015793

  160 0.0012082

  125 0.0005046

  159

  124 0.0100432

  158

  123 0.0154118

  157 0.001341

  181

  111 0.0063884

  146

  169

  137

  102 0.0204748

  171

  136 0.0316612

  101

  170

  100 135

  134 0.0009882

  103 0.0028433

  99 0.0277364

  168

  133

  98 0.0122246

  167 0.0018967

  132

  97

  Lampiran 5-2 No RETURN No RETURN No RETURN

  172 0.0123928

  138

  180

  173 0.0090245

  145 0.018195

  110

  179 0.0012862

  109 144 0.0177964

  178 0.0198906

  143 0.0119411

  108

  177

  142 0.0045107

  107 0.0296777

  176 0.0093605

  106 141 0.0127599

  175 0.0063922

  140 0.0045203

  105

  174 0.0048211

  139 0.0030134

  104

  166

• 0.0099918
• 0.0007346

  Lampiran 6-1

Lampiran 8 –Correlogram of Return Saham LQ45 Setelah Penghapusan Outlier

  Autocorrelation Partial Correlation AC PAC Q-Stat Prob .|* | .|* | 1 0.178 0.178 5.9493 0.015

• |. | *|. | 2 -0.110 -0.146 8.2195 0.016
• |. | .|. | 3 -0.083 -0.037 9.5359 0.023 .|. | .|. | 4 0.012 0.021 9.5632 0.048 .|. | .|. | 5 0.002 -0.021 9.5639 0.089
• |. | *|. | 6 -0.105 -0.106 11.675 0.070
• |. | *|. | 7 -0.099 -0.061 13.565 0.059
• |. | *|. | 8 -0.066 -0.066 14.410 0.072
• |. | *|. | 9 -0.093 -0.110 16.096 0.065 .|. | .|. | 10 -0.025 -0.014 16.222 0.093 .|* | .|* | 11 0.133 0.117 19.734 0.049 .|. | *|. | 12 -0.030 -0.115 19.912 0.069 .|. | .|. | 13 -0.036 0.001 20.167 0.091 .|* | .|* | 14 0.131 0.138 23.620 0.051

  .|. | *|. | 15 0.030 -0.078 23.799 0.069 .|. | .|. | 16 -0.003 0.009 23.800 0.094

• |. | .|. | 17 -0.070 -0.038 24.805 0.099
• |. | *|. | 18 -0.060 -0.061 25.542 0.111 .|. | .|. | 19 0.047 0.052 26.001 0.130 .|* | .|* | 20 0.105 0.126 28.298 0.103 .|. | .|. | 21 0.008 -0.028 28.312 0.132 .|. | .|. | 22 0.002 0.019 28.312 0.166 .|. | .|. | 23 0.002 0.058 28.314 0.204

  .|. | *|. | 24 -0.030 -0.065 28.512 0.239

  Lampiran 6-2 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

  

AR(1) -0.100063 0.295829 -0.338247 0.7356

MA(1) 0.341741 0.279462 1.222855 0.2230

R-squared 0.011092 Mean dependent var 0.002602 Adjusted R-squared 0.005629 S.D. dependent var 0.011991 S.E. of regression 0.011958 Akaike info criterion -6.004014 Sum squared resid 0.025881 Schwarz criterion -5.968938

  Lampiran 6-3 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

R-squared -0.011124 Mean dependent var 0.002539 Adjusted R-squared -0.017037 S.D. dependent var 0.011702 S.E. of regression 0.011801 Akaike info criterion -6.029752 Sum squared resid 0.023815 Schwarz criterion -5.993298 Log likelihood 523.5736 Durbin-Watson stat 1.619146

  Lampiran 6-4

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

• |. | *|. | 2 -0.138 -0.138 3.5407 0.060
• |. | *|. | 3 -0.069 -0.072 4.4481 0.108 .|. | .|. | 4 0.031 0.011 4.6302 0.201 .|. | .|. | 5 0.026 0.007 4.7570 0.313
• |. | *|. | 6 -0.091 -0.092 6.3370 0.275
• |. | *|. | 7 -0.070 -0.067 7.2831 0.295 .|. | .|. | 8 -0.029 -0.056 7.4464 0.384
• |. | *|. | 9 -0.082 -0.120 8.7398 0.365 .|. | *|. | 10 -0.038 -0.067 9.0298 0.435 .|* | .|* | 11 0.155 0.127 13.731 0.186 .|. | *|. | 12 -0.054 -0.089 14.306 0.217
• |. | .|. | 13 -0.062 -0.050 15.076 0.237 .|* | .|* | 14 0.141 0.144 19.043 0.122 .|. | .|. | 15 0.005 -0.048 19.048 0.163 .|. | .|. | 16 0.008 0.005 19.061 0.211

  Autocorrelation Partial Correlation AC PAC Q-Stat Prob .|. | .|. | 1 0.005 0.005 0.0049

  Lampiran 6-5

LAMPIRAN 11 – Uji Heteroskedastisitas Model ARMA ([1],0) Setelah Penghapusan Outlier dengan Correlogram of Residuals Squared ARMA ([1], 0)

• |. | *|. | 2 -0.093 -0.093 1.6126 0.204 .|* | .|* | 3 0.067 0.069 2.4579 0.293 .|. | .|. | 4 0.003 -0.006 2.4601 0.483 .|. | .|. | 5 0.009 0.022 2.4743 0.649
• |. | *|. | 6 -0.067 -0.073 3.3205 0.651
• |. | *|. | 7 -0.064 -0.060 4.1101 0.662 .|. | .|. | 8 -0.017 -0.031 4.1649 0.761 .|. | *|. | 9 -0.057 -0.060 4.7950 0.779 .|. | .|. | 10 0.014 0.019 4.8308 0.849 .|. | *|. | 11 -0.057 -0.065 5.4622 0.858
• |. | .|. | 12 -0.061 -0.053 6.1917 0.860 .|. | .|. | 13 -0.008 -0.032 6.2050 0.905 .|* | .|* | 14 0.079 0.073 7.4506 0.877 .|* | .|* | 15 0.173 0.171 13.495 0.488 .|. | .|. | 16 -0.041 -0.031 13.839 0.538

  Lampiran 6-6

LAMPIRAN 12 - Uji Normalitas Model EGARCH(1,1) dengan Histogram

  24 Series: Standardized Residuals Sample 2 184

  20 Observations 183

  16 Mean 0.205436 Median 0.171973 Maximum 3.731255

  12 Minimum -2.335133 Std. Dev. 1.004014

  8 Skewness 0.177054 Kurtosis 3.462131

  4 Jarque-Bera 2.584555 Probability 0.274645

• 2 -1

  1

  

2

  3 5 %

  α = H : Residual berdistribusi normal H

  : Residual tidak berdistribusi normal

  1 Keputusan : P-value > maka terima H sehingga residual EGARCH(1,1) berdistribusi α normal.

  Lampiran 7-1

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) h0<-1 h<-rep(0,n)

Lampiran 7-2

  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") break }

Lampiran 7-3

  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 ") cat("Maka -> TERDETEKSI OUTLIER tipe ALO\n")

  Lampiran 7-4 } 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) repeat {

Lampiran 7-5

  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 ")

cat("\n===================================================\n")

Lampiran 7-6

  #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]) } cat("\n\n") }

  Lampiran 7-7

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 :

[1] 0.06136700869 0.00747945790 0.00152968878 0.00046222014 0.00018746441

[6] 0.00009492420 0.00011015543 0.00008068045 0.00008295761 0.00007581424

[11] 0.00012840858 0.00027894008 0.00026681764 0.00018989706 0.00012266721

[16] 0.00022029252 0.00012094219 0.00009107536 0.00012549328 0.00007959627

[21] 0.00005757827 0.00005417222 0.00004452232 0.00003832166 0.00007212064

[26] 0.00006634241 0.00015409443 0.00008957454 0.00005460226 0.00004054837

[31] 0.00004096539 0.00016587209 0.00010545632 0.00006521200 0.00004543437

[36] 0.00007688509 0.00008495983 0.00006582991 0.00009994913 0.00008944550

[41] 0.00006967833 0.00005939092 0.00006158776 0.00005664073 0.00005164037

[46] 0.00016726985 0.00014673424 0.00008838149 0.00006397172 0.00004300603

  Lampiran 7-8

[51] 0.00004362291 0.00003609774 0.00007050988 0.00008269637 0.00007904307

[56] 0.00006231422 0.00019396361 0.00010306333 0.00006062804 0.00005963912

[61] 0.00005726825 0.00004444322 0.00003999228 0.00008844469 0.00006556376

[66] 0.00004368567 0.00003988857 0.00003239217 0.00003602700 0.00003271217

[71] 0.00002901509 0.00005115940 0.00009132421 0.00006244601 0.00005229369

[76] 0.00016625541 0.00009818512 0.00007336634 0.00009376337 0.00014107315

[81] 0.00009261529 0.00006946409 0.00005732304 0.00017761817 0.00009718336

[86] 0.00008125954 0.00008881895 0.00005449700 0.00004489684 0.00019337807

[91] 0.00307861403 0.00080628467 0.00034455349 0.00095127316 0.00033062944

[96] 0.00133841845 0.00044243710 0.00026724579 0.00015556032 0.00013128086