MODEL ARCH/GARCH

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MODEL ARCH/GARCH
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PENDAHULUAN

• OLS ? Heteroskedastisitas ? Cross Section ? Time
  series?
• Ingat saat mempelajari stasioneritas
• Heteroskedastisitas masih memberikan estimator
  OLS yang tidak bias dan konsisten, tetapi
  estimator tersebut sudah tidak tidak efisien,
  yaitu varians dari estimator tidak minimum.
  Akibatnya Uji t, interval kepercayaan, dan
  berbagai ukuran lainnya, menjadi tidak tepat.
  Oleh karena itu, masalah ini harus diatasi dalam
  mengestimasi dengan metode OLS.
• Pada bagian ini kita akan berbicara mengenai
  suatu model yang tidak memandang
  heteroskedastisitas sebagai permasalahan, tetapi
  justru memanfaatkan kondisi tersebut untuk
  membuat model.

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AutoRegressive Conditional Heteroscedasticity
(ARCH) dan Generalized AutoRegressive Conditional
Heteroscedasticity (GARCH).

• Model ? memanfaatkan heteroskedastisitas dalam
  error dengan tepat, maka akan diperoleh estimator
  yang lebih efisien.
• Regresi ? heteroskedastisitas ? varian error
  berubah-ubah mengikuti satu atau beberapa
  variabel bebas.
• Misal
• yt b0 b1 x1t b2 x2t et
• dengan var (et) k x1t2 ? heteroskedastis
• Untuk mengatasi model ditransformasikan menjadi
• yt/x1t b0/x1t b1 b2 x2t /x1t et
• dengan et et / x1t
• Akibat dari transformasi ini,
• var(et) k x1t2/ x1t2 k ? homoskedastis.

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Akan tetapi, adakalanya, varian dari error tidak
tergantung pada variabel bebas-nya melainkan
varian tersebut berubah-ubah seiring dengan
perubahan waktu ? Time series

• Data dengan karakteristik seperti ini biasanya
  terjadi pada return dari pasar modal, inflasi,
  atau interest rate.
• Sebaran datanya ada suatu periode volatilitas
  sangat tinggi dan ada periode lain volatilitasnya
  sangat rendah. Pola volatilitas ?
  heteroskedastisitas, karena terdapat varian error
  yang besarnya tergantung pada volatilitas error
  di masa lalu.
• Data yang mempunyai sifat heteroskedastisitas
  seperti ini dapat dimodel dengan Autoregresive
  Conditional Heteroscedasticity (ARCH) yang
  dikenalkan oleh Robert Engle.

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ARCH

• Perhatikan model regresi berganda dibawah ini
• yt b0 b1 x1t b2 x2t et
• ?t2 atau varian et heteroskedastisitas, dan
  mengikuti persamaan berikut
• ?t2 ?0 ?1 e2t-1 ?t2 var (et)
• Perhatikan bahwa var (et) dijelaskan oleh dua
  komponen
• komponen konstanta ?0
• komponen variabel ?1 e2t-1 yang disebut
  komponen ARCH
• Pada model ini, et heteroskedastis, conditional
  pada et-1. Dengan menambahkan informasi
  conditional ini estimator dari b0, b1 dan b2
  menjadi lebih efisien.

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Model ARCH diatas, dimana var(et) tergantung
hanya pada volatilitas satu periode lalu ?Model
ARCH (1).

• Model umum ? var(et) tergantung pada volatilitas
  p periode lalu, disebut model ARCH (p), yang
  dituliskan dengan

Bagaimana cara mengestimasi b0, b1 dan b2 serta
?0 dan ?1 ? Teknik yang digunakan ? teknik
maximum likelihood.
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GARCH

• Model ARCH(p) ?jumlah p yang besar ? parameter
  yang harus diestimasi banyak ?presisi estimator
  berkurang. Hal semacam ini sering dijumpai pada
  analisis data harian.
• Untuk mengatasi permasalahan tersebut ? var (et)
  dapat dijadikan model berikut
• ?t2 ?0 ?1 e2t-1 ?1 ?2t-1 ? GARCH (1,1)
• var(et) selain diduga tergantung pada e2 juga
  tergantung pada ?2 pada masa lalu.
• Secara umum ? GARCH(p,q)

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Var(et) tergantung pada juga pada salah satu
regressor

• Kadangkala besaran varian error diduga tidak
  hanya tergantung pada e2 dan ?2 pada masa lalu,
  tetapi juga pada salah satu regresor. Perhatikan
  kembali model regresi
• yt b0 b1 x1t b2 x2t et
• Bila diduga varian error persamaan tersebut juga
  tergantung pada variabel x2t maka persamaan
  varian error-nya menjadi
• ?t2 ?0 ?1 e2t-1 ?1 ?2t-1 ?1 x2t
• Akan tetapi dalam implementasinya kita perlu
  lebih hati-hati terutama bila ada nilai x2t yang
  berharga negatif.

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Bentuk-bentuk Lain Model ARCH dan GARCH

• Apakah yang membedakan model ARCH dan GARCH?
• Pola atau bentuk atau model dari varian
  eror-nya.
• Berbagai bentuk ARCH dan GARCH, antara lain
• ARCH in mean (M-ARCH)
• Threshold ARCH (TARCH)
• Eksponential ARCH/GARCH (E-(G)ARCH)
• Simple asymmetric ARCH (SAARCH)
• Power ARCH (PARCH)

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Model ARCH M (ARCH - in - mean) memunculkan
?t2 sebagai variabel bebas. yt b0 b1 x1t
b2 x2t b3 ?t2 et

• Var (et) ?t2 dapat dinyatakan dalam bentuk
  GARCH (p,q), atau dengan memasukkan salah satu
  regressor.
• Model ini tidak hanya dapat dimasukkan ?t2 dalam
  model regresinya, tetapi juga standar
  deviasi-nya (?t).
• Apa yang membedakan Model ARCH M dengan Model
  GARCH?

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Var (et) dapat tergantung pada regressor?bisa
dalam bentuk dummy ? Model Threshold ARCH (TARCH)

• Perhatikan kembali model persamaan
• ?t2 ?0 ?1 e2t-1 ?1 ?2t-1 ?1 x2t
• varian error ? tergantung pada variabel x2t. Bila
  x2t merupakan variabel dummy pada waktu lalu
  dengan lag 1, atau dinotasikan dengan dt-1, maka
  persamaan tersebut menjadi
• ?t2 ?0 ?1 e2t-1 ?1 ?2t-1 ?1 dt-1
• secara umum dituliskan dengan

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Pengaruh Nilai Tukar Dolar dan Suku Bunga SBI
Terhadap IHSG

• IHSG b0 b1 Kurs_us b2 SBI

Dependent Variable IHSG Dependent Variable IHSG Dependent Variable IHSG Dependent Variable IHSG Dependent Variable IHSG
Method Least Squares Method Least Squares Method Least Squares Method Least Squares Method Least Squares
Date 09/22/04 Time 1647 Date 09/22/04 Time 1647 Date 09/22/04 Time 1647 Date 09/22/04 Time 1647 Date 09/22/04 Time 1647
Sample(adjusted) 1/01/2003 1/07/2004 Sample(adjusted) 1/01/2003 1/07/2004 Sample(adjusted) 1/01/2003 1/07/2004 Sample(adjusted) 1/01/2003 1/07/2004 Sample(adjusted) 1/01/2003 1/07/2004
Included observations 54 after adjusting endpoints Included observations 54 after adjusting endpoints Included observations 54 after adjusting endpoints Included observations 54 after adjusting endpoints Included observations 54 after adjusting endpoints
Variable Coefficient Std. Error t-Statistic Prob.
C 910.0360 344.8347 2.639050 0.0110
KURS_US 0.032385 0.046042 0.703377 0.4850
SBI -66.12620 6.927675 -9.545222 0.0000
R-squared 0.797108 Mean dependent var Mean dependent var 529.1296
Adjusted R-squared 0.789152 S.D. dependent var S.D. dependent var 110.0131
S.E. of regression 50.51604 Akaike info criterion Akaike info criterion 10.73641
Sum squared resid 130145.4 Schwarz criterion Schwarz criterion 10.84691
Log likelihood -286.8831 F-statistic F-statistic 100.1829
Durbin-Watson stat 0.108459 Prob(F-statistic) Prob(F-statistic) 0.000000

• Bagaimana hasilnya?

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Uji Heteroskedastisitas
White Heteroskedasticity Test White Heteroskedasticity Test White Heteroskedasticity Test White Heteroskedasticity Test White Heteroskedasticity Test
F-statistic 2.911382 Probability Probability 0.022478
ObsR-squared 12.56573 Probability Probability 0.027807

Test Equation Test Equation Test Equation Test Equation Test Equation
Dependent Variable RESID2 Dependent Variable RESID2 Dependent Variable RESID2 Dependent Variable RESID2 Dependent Variable RESID2
Method Least Squares Method Least Squares Method Least Squares Method Least Squares Method Least Squares
Date 09/22/04 Time 1649 Date 09/22/04 Time 1649 Date 09/22/04 Time 1649 Date 09/22/04 Time 1649 Date 09/22/04 Time 1649
Sample 1/01/2003 1/07/2004 Sample 1/01/2003 1/07/2004 Sample 1/01/2003 1/07/2004 Sample 1/01/2003 1/07/2004 Sample 1/01/2003 1/07/2004
Included observations 54 Included observations 54 Included observations 54 Included observations 54 Included observations 54
Variable Coefficient Std. Error t-Statistic Prob.
C 396521.0 1055530. 0.375661 0.7088
KURS_US -0.699613 276.8569 -0.002527 0.9980
KURS_US2 -0.005077 0.019030 -0.266780 0.7908
KURS_USSBI 8.513615 6.769105 1.257717 0.2146
SBI -74867.90 46013.11 -1.627099 0.1103
SBI2 16.30629 687.2254 0.023728 0.9812
R-squared 0.232699 Mean dependent var Mean dependent var 2410.099
Adjusted R-squared 0.152771 S.D. dependent var S.D. dependent var 4035.066
S.E. of regression 3714.077 Akaike info criterion Akaike info criterion 19.38209
Sum squared resid 6.62E08 Schwarz criterion Schwarz criterion 19.60309
Log likelihood -517.3164 F-statistic F-statistic 2.911382
Durbin-Watson stat 0.259531 Prob(F-statistic) Prob(F-statistic) 0.022478
Bagaimana Hasilnya?
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Hasil Transformasi
Dependent Variable IHSG Dependent Variable IHSG Dependent Variable IHSG Dependent Variable IHSG Dependent Variable IHSG
Method Least Squares Method Least Squares Method Least Squares Method Least Squares Method Least Squares
Date 09/22/04 Time 1652 Date 09/22/04 Time 1652 Date 09/22/04 Time 1652 Date 09/22/04 Time 1652 Date 09/22/04 Time 1652
Sample(adjusted) 1/01/2003 1/07/2004 Sample(adjusted) 1/01/2003 1/07/2004 Sample(adjusted) 1/01/2003 1/07/2004 Sample(adjusted) 1/01/2003 1/07/2004 Sample(adjusted) 1/01/2003 1/07/2004
Included observations 54 after adjusting endpoints Included observations 54 after adjusting endpoints Included observations 54 after adjusting endpoints Included observations 54 after adjusting endpoints Included observations 54 after adjusting endpoints
Weighting series SBI Weighting series SBI Weighting series SBI Weighting series SBI Weighting series SBI
Variable Coefficient Std. Error t-Statistic Prob.
C 1011.332 310.9866 3.252010 0.0020
KURS_US 0.012528 0.041858 0.299304 0.7659
SBI -59.35252 6.392304 -9.284997 0.0000
Weighted Statistics
R-squared -0.117235 Mean dependent var Mean dependent var 513.9303
Adjusted R-squared -0.161048 S.D. dependent var S.D. dependent var 43.33402
S.E. of regression 46.69326 Akaike info criterion Akaike info criterion 10.57903
Sum squared resid 111193.3 Schwarz criterion Schwarz criterion 10.68953
Log likelihood -282.6338 F-statistic F-statistic 112.9801
Durbin-Watson stat 0.112449 Prob(F-statistic) Prob(F-statistic) 0.000000
Unweighted Statistics
R-squared 0.792057 Mean dependent var Mean dependent var 529.1296
Adjusted R-squared 0.783903 S.D. dependent var S.D. dependent var 110.0131
S.E. of regression 51.14099 Sum squared resid Sum squared resid 133385.5
Durbin-Watson stat 0.100055
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GARCH(1,1)
Bagaimana Modelnya?Bagaimana cara menuliskan
modelnya?
Dependent Variable IHSG Dependent Variable IHSG Dependent Variable IHSG Dependent Variable IHSG Dependent Variable IHSG
Method ML - ARCH Method ML - ARCH Method ML - ARCH Method ML - ARCH Method ML - ARCH
Date 09/22/04 Time 1709 Date 09/22/04 Time 1709 Date 09/22/04 Time 1709 Date 09/22/04 Time 1709 Date 09/22/04 Time 1709
Sample(adjusted) 1/01/2003 1/07/2004 Sample(adjusted) 1/01/2003 1/07/2004 Sample(adjusted) 1/01/2003 1/07/2004 Sample(adjusted) 1/01/2003 1/07/2004 Sample(adjusted) 1/01/2003 1/07/2004
Included observations 54 after adjusting endpoints Included observations 54 after adjusting endpoints Included observations 54 after adjusting endpoints Included observations 54 after adjusting endpoints Included observations 54 after adjusting endpoints
Convergence achieved after 41 iterations Convergence achieved after 41 iterations Convergence achieved after 41 iterations Convergence achieved after 41 iterations Convergence achieved after 41 iterations
Coefficient Std. Error z-Statistic Prob.
C 909.3049 133.5022 6.811161 0.0000
KURS_US 0.015623 0.020986 0.744466 0.4566
SBI -52.63821 5.866526 -8.972636 0.0000
Variance Equation Variance Equation Variance Equation Variance Equation
C 1566.652 1113.885 1.406476 0.1596
ARCH(1) 1.255666 1.101884 1.139562 0.2545
GARCH(1) -0.712948 0.448501 -1.589624 0.1119
R-squared 0.760577 Mean dependent var Mean dependent var 529.1296
Adjusted R-squared 0.735637 S.D. dependent var S.D. dependent var 110.0131
S.E. of regression 56.56458 Akaike info criterion Akaike info criterion 10.14233
Sum squared resid 153578.5 Schwarz criterion Schwarz criterion 10.36333
Log likelihood -267.8430 F-statistic F-statistic 30.49643
Durbin-Watson stat 0.085450 Prob(F-statistic) Prob(F-statistic) 0.000000
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ARCH-M ? GARCH(1,1)
Baikkah Modelnya? Perlu diperhatikan tanda
variabel Kurs_US yang masih positif
Dependent Variable IHSG Dependent Variable IHSG Dependent Variable IHSG Dependent Variable IHSG Dependent Variable IHSG
Method ML - ARCH Method ML - ARCH Method ML - ARCH Method ML - ARCH Method ML - ARCH
Date 09/22/04 Time 1708 Date 09/22/04 Time 1708 Date 09/22/04 Time 1708 Date 09/22/04 Time 1708 Date 09/22/04 Time 1708
Sample(adjusted) 1/01/2003 1/07/2004 Sample(adjusted) 1/01/2003 1/07/2004 Sample(adjusted) 1/01/2003 1/07/2004 Sample(adjusted) 1/01/2003 1/07/2004 Sample(adjusted) 1/01/2003 1/07/2004
Included observations 54 after adjusting endpoints Included observations 54 after adjusting endpoints Included observations 54 after adjusting endpoints Included observations 54 after adjusting endpoints Included observations 54 after adjusting endpoints
Convergence achieved after 106 iterations Convergence achieved after 106 iterations Convergence achieved after 106 iterations Convergence achieved after 106 iterations Convergence achieved after 106 iterations
Bollerslev-Wooldrige robust standard errors covariance Bollerslev-Wooldrige robust standard errors covariance Bollerslev-Wooldrige robust standard errors covariance Bollerslev-Wooldrige robust standard errors covariance Bollerslev-Wooldrige robust standard errors covariance
Coefficient Std. Error z-Statistic Prob.
SQR(GARCH) 0.317312 0.235984 1.344635 0.1787
C 968.5116 26.36188 36.73910 0.0000
KURS_US 0.019832 0.001591 12.46713 0.0000
SBI -63.56387 3.166960 -20.07094 0.0000
Variance Equation Variance Equation Variance Equation Variance Equation
C 1535.364 441.9163 3.474331 0.0005
ARCH(1) 0.980778 0.110584 8.869042 0.0000
GARCH(1) -0.511250 0.104594 -4.887940 0.0000
R-squared 0.807864 Mean dependent var Mean dependent var 529.1296
Adjusted R-squared 0.783336 S.D. dependent var S.D. dependent var 110.0131
S.E. of regression 51.20806 Akaike info criterion Akaike info criterion 10.24593
Sum squared resid 123246.5 Schwarz criterion Schwarz criterion 10.50376
Log likelihood -269.6400 F-statistic F-statistic 32.93631
Durbin-Watson stat 0.109820 Prob(F-statistic) Prob(F-statistic) 0.000000
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MODEL TARCH
Dependent Variable IHSG Dependent Variable IHSG Dependent Variable IHSG Dependent Variable IHSG Dependent Variable IHSG
Method ML - ARCH Method ML - ARCH Method ML - ARCH Method ML - ARCH Method ML - ARCH
Date 09/22/04 Time 1826 Date 09/22/04 Time 1826 Date 09/22/04 Time 1826 Date 09/22/04 Time 1826 Date 09/22/04 Time 1826
Sample(adjusted) 1/01/2003 1/07/2004 Sample(adjusted) 1/01/2003 1/07/2004 Sample(adjusted) 1/01/2003 1/07/2004 Sample(adjusted) 1/01/2003 1/07/2004 Sample(adjusted) 1/01/2003 1/07/2004
Included observations 54 after adjusting endpoints Included observations 54 after adjusting endpoints Included observations 54 after adjusting endpoints Included observations 54 after adjusting endpoints Included observations 54 after adjusting endpoints
Convergence not achieved after 500 iterations Convergence not achieved after 500 iterations Convergence not achieved after 500 iterations Convergence not achieved after 500 iterations Convergence not achieved after 500 iterations
Bollerslev-Wooldrige robust standard errors covariance Bollerslev-Wooldrige robust standard errors covariance Bollerslev-Wooldrige robust standard errors covariance Bollerslev-Wooldrige robust standard errors covariance Bollerslev-Wooldrige robust standard errors covariance
Coefficient Std. Error z-Statistic Prob.
SQR(GARCH) 2.717333 0.213715 12.71475 0.0000
C 968.2053 12.36291 78.31531 0.0000
KURS_US -0.007922 0.000812 -9.757067 0.0000
SBI -45.06920 2.362412 -19.07762 0.0000
Variance Equation Variance Equation Variance Equation Variance Equation
C 1535.339 43.41265 35.36617 0.0000
ARCH(1) 0.414933 0.154315 2.688876 0.0072
(RESIDlt0)ARCH(1) -0.871533 0.240693 -3.620927 0.0003
GARCH(1) 0.802888 0.114755 6.996533 0.0000
KURS_US -0.165367 0.005035 -32.84081 0.0000
R-squared 0.949284 Mean dependent var Mean dependent var 529.1296
Adjusted R-squared 0.940268 S.D. dependent var S.D. dependent var 110.0131
S.E. of regression 26.88728 Akaike info criterion Akaike info criterion 9.167134
Sum squared resid 32531.66 Schwarz criterion Schwarz criterion 9.498631
Log likelihood -238.5126 F-statistic F-statistic 105.2877
Durbin-Watson stat 0.684882 Prob(F-statistic) Prob(F-statistic) 0.000000
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Model sangat baik.Bagaimana otokorelasinya?Bagai
mana Kenormalan data?
Hasilnyameragukan?
Otokorelasi tidak tepat lagi diukur dengan
DWGunakan Korelogram atau Uji Unit Root
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Bagaimana hasilnya?
ADF Test Statistic -3.160046 1 Critical Value 1 Critical Value -4.1420
5 Critical Value 5 Critical Value -3.4969
10 Critical Value 10 Critical Value -3.1772
MacKinnon critical values for rejection of hypothesis of a unit root. MacKinnon critical values for rejection of hypothesis of a unit root. MacKinnon critical values for rejection of hypothesis of a unit root. MacKinnon critical values for rejection of hypothesis of a unit root. MacKinnon critical values for rejection of hypothesis of a unit root.


Augmented Dickey-Fuller Test Equation Augmented Dickey-Fuller Test Equation Augmented Dickey-Fuller Test Equation Augmented Dickey-Fuller Test Equation Augmented Dickey-Fuller Test Equation
Dependent Variable D(RESID01) Dependent Variable D(RESID01) Dependent Variable D(RESID01) Dependent Variable D(RESID01) Dependent Variable D(RESID01)
Method Least Squares Method Least Squares Method Least Squares Method Least Squares Method Least Squares
Date 09/23/04 Time 1421 Date 09/23/04 Time 1421 Date 09/23/04 Time 1421 Date 09/23/04 Time 1421 Date 09/23/04 Time 1421
Sample(adjusted) 1/20/2003 1/12/2004 Sample(adjusted) 1/20/2003 1/12/2004 Sample(adjusted) 1/20/2003 1/12/2004 Sample(adjusted) 1/20/2003 1/12/2004 Sample(adjusted) 1/20/2003 1/12/2004
Included observations 52 after adjusting endpoints Included observations 52 after adjusting endpoints Included observations 52 after adjusting endpoints Included observations 52 after adjusting endpoints Included observations 52 after adjusting endpoints
Variable Coefficient Std. Error t-Statistic Prob.
RESID01(-1) -0.447804 0.141708 -3.160046 0.0027
D(RESID01(-1)) -0.043779 0.125145 -0.349828 0.7280
C -9.421583 5.179260 -1.819098 0.0751
_at_TREND(1/06/2003) 0.467350 0.184320 2.535538 0.0145
R-squared 0.252970 Mean dependent var Mean dependent var 0.708121
Adjusted R-squared 0.206280 S.D. dependent var S.D. dependent var 17.75114
S.E. of regression 15.81466 Akaike info criterion Akaike info criterion 8.433555
Sum squared resid 12004.96 Schwarz criterion Schwarz criterion 8.583651
Log likelihood -215.2724 F-statistic F-statistic 5.418141
Durbin-Watson stat 2.158713 Prob(F-statistic) Prob(F-statistic) 0.002720
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Masukan AR(1) untuk menghilangkan otokorelasi
Dependent Variable IHSG Dependent Variable IHSG Dependent Variable IHSG Dependent Variable IHSG Dependent Variable IHSG
Method ML - ARCH Method ML - ARCH Method ML - ARCH Method ML - ARCH Method ML - ARCH
Date 09/23/04 Time 1439 Date 09/23/04 Time 1439 Date 09/23/04 Time 1439 Date 09/23/04 Time 1439 Date 09/23/04 Time 1439
Sample(adjusted) 1/13/2003 1/12/2004 Sample(adjusted) 1/13/2003 1/12/2004 Sample(adjusted) 1/13/2003 1/12/2004 Sample(adjusted) 1/13/2003 1/12/2004 Sample(adjusted) 1/13/2003 1/12/2004
Included observations 53 after adjusting endpoints Included observations 53 after adjusting endpoints Included observations 53 after adjusting endpoints Included observations 53 after adjusting endpoints Included observations 53 after adjusting endpoints
Convergence achieved after 31 iterations Convergence achieved after 31 iterations Convergence achieved after 31 iterations Convergence achieved after 31 iterations Convergence achieved after 31 iterations
Bollerslev-Wooldrige robust standard errors covariance Bollerslev-Wooldrige robust standard errors covariance Bollerslev-Wooldrige robust standard errors covariance Bollerslev-Wooldrige robust standard errors covariance Bollerslev-Wooldrige robust standard errors covariance
Coefficient Std. Error z-Statistic Prob.
SQR(GARCH) -0.087837 0.088683 -0.990453 0.3220
C 1077.351 289.7946 3.717637 0.0002
KURS_US -0.004989 0.027774 -0.179646 0.8574
SBI -54.04489 23.10312 -2.339290 0.0193
AR(1) 0.972741 0.041699 23.32781 0.0000
Variance Equation Variance Equation Variance Equation Variance Equation
C 1541.928 123.4076 12.49459 0.0000
ARCH(1) 0.409331 0.111098 3.684419 0.0002
(RESIDlt0)ARCH(1) -0.329912 0.256587 -1.285773 0.1985
GARCH(1) -0.278948 0.103837 -2.686392 0.0072
KURS_US -0.150344 0.011117 -13.52365 0.0000
R-squared 0.979293 Mean dependent var Mean dependent var 531.5717
Adjusted R-squared 0.974960 S.D. dependent var S.D. dependent var 109.5783
S.E. of regression 17.33986 Akaike info criterion Akaike info criterion 8.590234
Sum squared resid 12928.84 Schwarz criterion Schwarz criterion 8.961987
Log likelihood -217.6412 F-statistic F-statistic 225.9600
Durbin-Watson stat 1.325697 Prob(F-statistic) Prob(F-statistic) 0.000000
Inverted AR Roots .97 .97 .97 .97
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Hasilnya ? sudah tidak ada otokorelasi
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Uji Jarque-Bera ? Uji Normalitas
statistik Jarque-Bera, mempunyai probabilitas
0,000001. Keputusan tolak hipotesis (error
term mengikuti distribusi normal). Atau dengan
kata lain, error term kita belum berdistribusi
normal.
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Model GARCH(1,1) dengan memasukan SBI
Dependent Variable IHSG Dependent Variable IHSG Dependent Variable IHSG Dependent Variable IHSG Dependent Variable IHSG
Method ML - ARCH Method ML - ARCH Method ML - ARCH Method ML - ARCH Method ML - ARCH
Date 09/23/04 Time 1506 Date 09/23/04 Time 1506 Date 09/23/04 Time 1506 Date 09/23/04 Time 1506 Date 09/23/04 Time 1506
Sample(adjusted) 1/13/2003 1/12/2004 Sample(adjusted) 1/13/2003 1/12/2004 Sample(adjusted) 1/13/2003 1/12/2004 Sample(adjusted) 1/13/2003 1/12/2004 Sample(adjusted) 1/13/2003 1/12/2004
Included observations 53 after adjusting endpoints Included observations 53 after adjusting endpoints Included observations 53 after adjusting endpoints Included observations 53 after adjusting endpoints Included observations 53 after adjusting endpoints
Convergence achieved after 139 iterations Convergence achieved after 139 iterations Convergence achieved after 139 iterations Convergence achieved after 139 iterations Convergence achieved after 139 iterations
Bollerslev-Wooldrige robust standard errors covariance Bollerslev-Wooldrige robust standard errors covariance Bollerslev-Wooldrige robust standard errors covariance Bollerslev-Wooldrige robust standard errors covariance Bollerslev-Wooldrige robust standard errors covariance
Coefficient Std. Error z-Statistic Prob.
C 919.2472 272.1758 3.377402 0.0007
KURS_US -0.034497 0.013060 -2.641427 0.0083
SBI -14.15274 15.35689 -0.921589 0.3567
AR(1) 1.000000 0.031752 33.23277 0.0000
Variance Equation Variance Equation Variance Equation Variance Equation
C 1543.394 529.9268 2.912467 0.0036
ARCH(1) -0.101398 0.042591 -2.380753 0.0173
GARCH(1) -0.710293 0.167489 -4.240834 0.0000
SBI -110.3890 41.24571 -2.676376 0.0074
R-squared 0.982119 Mean dependent var Mean dependent var 531.5717
Adjusted R-squared 0.979337 S.D. dependent var S.D. dependent var 109.5783
S.E. of regression 15.75140 Akaike info criterion Akaike info criterion 8.373049
Sum squared resid 11164.80 Schwarz criterion Schwarz criterion 8.670451
Log likelihood -213.8858 F-statistic F-statistic 353.0854
Durbin-Watson stat 1.858701 Prob(F-statistic) Prob(F-statistic) 0.000000
Inverted AR Roots 1.06 1.06 1.06 1.06
Estimated AR process is nonstationary Estimated AR process is nonstationary Estimated AR process is nonstationary Estimated AR process is nonstationary
24
Otokorelasi?
25
Kenormalan?
Kenapa SBI tidak signifikan?
26
Penutup

• Membuat model ? Seni
• Dasar keseluruhan model yang dipelajari adalah
  regresi
• Ujian buka buku
• Jangan lupa paper
• Semoga berguna untuk menyusun tesis
• Wassalam