ARMA (p,q)
Suatu model yang terdiri atas gabungan proses regresi diri ordo p dan rataan bergerak ordo q
ARIMA
Kependekan dari Autoregresif (AR), Integrated (I), dan Moving Average (MA). Suatu deret waktu {Yt} disebut mengikuti model ARIMA jika deret beda ke-d, Wt=Δd
Yt adalah proses ARMA yang stasioner
ARCH/GARCH (Auto Regressive Conditional Heteroscedasticity/General Auto Regressive Conditional Heteroscedasticity)
Suatu model yang menganggap variance yang tidak konstan (heteroskedastisitas) bukan sebagai suatu masalah tetapi justru dapat digunakan untuk modeling dan peramalan (forcasting)
ARCH
Suatu error process yang dapat digunakan untuk memodelkan periode volatilitas dalam kerangka univariate dan juga conditional short run variance (“volatilitas”) dari series yang merupakan fungsi dari nilai masa lalu galat kuadrat. Artinya, efek dari suatu shock baru εt, tergantung pada ukuran dari shock masa lalunya—shock yang besar pada periode t akan meningkatkan pengaruh (terhadap y) shock pada periode t+1, t+2 dst.
Autoregressive AR (y)
Suatu model yang menggambarkan suatu peubah terikat dipengaruhi oleh peubah terikat itu sendiri pada periode-periode/waktu-waktu sebelumnya.
Autoregressive AR (p)
Regresi antara Y pada periode t dengan Y pada periode-periode t-1, t-2, t-3...t-p
Beta
Risiko pasar atau risiko yang disebabkan oleh pergerakan pasar agregat, dimana saham bergerak tergantung dari pergerakan pasar
GARCH
Model yang merupakan pengembangan terhadap model ARCH yang memungkinkan conditional variance menjadi ARMA proses
Heteroskedasticity
Suatu kondisi apabila kesalahan tidak memiliki sebuah ragam konstan terhadap selang nilai
Faktor Acak (Irregular, tidak teratur)
Suatu kondisi dalam time series, dimana terjadi gerakan yang berbeda tetapi dalam waktu yang singkat, dengan pola yang tidak diketahui dan tidak dapat diperkirakan
Koefisien Autokorelasi
Angka yang menunjukkan tingkat asosiasi/keeratan hubungan antara nilai-nilai dari peubah yang sama dengan periode waktu (time lags) yang berbeda
Moving Average (MA) Model
Suatu model yang meramalkan nilai Yt berdasarkan kombinasi linier nilai galat masa lalu dalam jumlah terbatas
Risiko Sistematik
Risiko yang tidak dapat didiversifikasi (dihindarkan), disebut juga dengan risiko pasar
Proses Stokastik
Sekuens peubah random {Y1, Y2, ..., Yt}, missal Yt adalah pengamatan pada waktu t dan Yt adalah peubah random (peubah acak)
Stasioner
Suatu kondisi data time series jika rata-rata, variance, dan covariance dari peubah-peubah tersebut seluruhnya tidak dipengaruhi oleh waktu
Tren
Kecenderungan jangka panjang peubah time series yang secara grafis digambarkan sebagai garis/kurva yang halus yang menunjukkan kecenderungan umum (naik atau turun).
Unit root test
Tes formal untuk menguji kestasioneran data White noise
Lampiran 1 Hasil penelitian terdahulu yang relevan
Tahun Peneliti Judul Metode Hasil
2013 Efri Junaidi Analisis Volatilitas Harga Minyak Sawit dan Harga Minyak Goreng
ARCH-GARCH
Volatilitas harga minyak sawit dipengaruhi oleh
volatilitas pada dua periode sebelumnya, sedangkan volatilitas harga minyak
goreng dipengaruhi oleh volatilitas dan varian pada satu periode sebelumnya.
Volatilitas harga minyak sawit lebih tinggi dibandingkan volatilitas harga minyak goreng. 2012 Khoiru Liummah Ayu Nastiti, Agus Suharsono Analisis Analisis Volatilitas SahamPerusahaanG o PublicdenganMetod e ARCH-GARCH Analisis ARCH-GARCH
variabel beta saham dan varian Hasilnya return saham ANTM, BBCA dan SMGRmemiliki sifat heteroskedasticity sedangkansaham ASII dan UNTR telahbersifat homoskedasticity. Model volatilitas yang diperoleh yaitu sahamANTM memiliki model GARCH (1,1) dan saham SMGR memiliki modelARCH (1). Berdasarkan plot
conditional variance (volatilitas) didapatkan
bahwa saham SMGR memiliki potensi risiko lebih tinggi dari padasaham ANTM. 2010 Chang Su Application of EGARCH Model to Estimate FinancialVolatility of Daily Returns:The empirical case of China
EGARCH Model EGARCH cocok dengan data sampel yang lebih baik daripada model GARCH dalam pemodelan volatilitas return saham Cina. Hasil penelitian juga menunjukkan bahwa volatilitas jangka panjang lebih stabil selama periode krisis. Berita buruk menghasilkan efek yang lebih kuat dari kabar baik bagi pasar saham Cina selama krisis
2010 Jing Wu Threshold GARCH
Model: Theory and Application
Threshold GARCH
Estimator maximum likelihood
adalah baik dan konsisten untuk ukuran sampel sederhana ketika kondisi stasioneritas terpenuhi.
Dengan menggunakan indeks volatilitas sebagai variabel
threshold, padadata 20 saham dari Major Market Index (MMI),ditemukan bahwa model
threshold dengan pemicu eksogen
Chicago Board Options Exchange
(CBOE) Volatility Index (VIX)dapat dimodelkan dengan baik.
Lanjutan Lampiran 1
Tahun Peneliti Judul Metode Hasil
2009 Moses Alfian Simanjuntak Penanganan Masalah Heterskedastisitas dengan Model ARCH-GARCH dan Model Black-Sholes ARCH-GARCH dan Black-Scholes
Dari data 5 perusahaan, didapat bahwa adannya kecenderungan
menghasilkan kondisi heteroskedasitas,sehingga model
deret waktu membutuhkan persamaan ARCH-GARCH
Model deret waktu lebih baik dibandingkan model Black-Scholes karena memiliki rataan MSE dan simpangan baku MSE yang lebih kecil. Model Black-Scholes lebih baik dibandingkan model deret waktu dalam hal penyebaran data MSE yang kekar (robust)
2009 Sumaryanto Analisis Volatility Harga Eceran Beberapa Komoditas Pangan Utama Dengan Metode Arcg/Garch ARCH-GARCH
Ragam Harga Eceran Terdeflasi untuk komoditas gula pasir, cabai merah, beras, terigu dan bawang merah bersifat heteroskedasitas sehingga model peramalan yang lebih sesuai adalah ARCH/GARCH.
2006 Anton Analisis
ModelVolatilitas
Return Saham (Studi Kasus pada Saham LQ 45 di Bursa Efek Jakarta)
ARCH- GARCH-EGARCH
Hasil penelitian menunjukkanbahwa
return saham di Indonesia memilikipermasalahan time varying volatility, tetapi tidakterjadi leverage effect pada volatilitasreturn saham, serta return saham tidak dipengaruhioleh volume perdagangan.Ternyata pasar modal
Indonesiatermasuk pasar bentuk lemah
Lampiran 2 Data return saham harian yang bersifat white noise (random)
1. Return Saham Harian BMRI
Lanjutan Lampiran 2
3. Return Saham Harian BBKP
Lanjutan Lampiran 2
Lampiran 3 Uji stasioner return mingguan dengan unit root dengan ADF&PP
1. BMRI
Null Hypothesis: RETURN_BMRI has a unit root Exogenous: Constant
Lag Length: 25 (Automatic - based on SIC, maxlag=25)
t-Statistic Prob.* Augmented Dickey-Fuller test statistic -7.797714 0.0000 Test critical values: 1% level -3.433299
5% level -2.862729
10% level -2.567449
*MacKinnon (1996) one-sided p-values.
Null Hypothesis: RETURN_BMRI has a unit root Exogenous: Constant
Bandwidth: 80 (Newey-West automatic) using Bartlett kernel
Adj. t-Stat Prob.* Phillips-Perron test statistic -10.76431 0.0000 Test critical values: 1% level -3.433262
5% level -2.862712
10% level -2.567440
*MacKinnon (1996) one-sided p-values. 2. BBNI
Null Hypothesis: RETURN_BBNI has a unit root Exogenous: None
Bandwidth: 61 (Newey-West automatic) using Bartlett kernel
Adj. t-Stat Prob.* Phillips-Perron test statistic -14.55046 0.0000 Test critical values: 1% level -2.566062
5% level -1.940974
10% level -1.616598
*MacKinnon (1996) one-sided p-values.
Null Hypothesis: RETURN_BBNI has a unit root Exogenous: None
Lag Length: 25 (Automatic - based on SIC, maxlag=25)
t-Statistic Prob.* Augmented Dickey-Fuller test statistic -6.452857 0.0000 Test critical values: 1% level -2.566075
5% level -1.940976
10% level -1.616597
Lanjutan Lampiran 3
3. BBKP
Null Hypothesis: RETURN_BUKOPIN has a unit root Exogenous: None
Lag Length: 25 (Automatic - based on SIC, maxlag=25)
t-Statistic Prob.* Augmented Dickey-Fuller test statistic -7.663629 0.0000 Test critical values: 1% level -2.566062
5% level -1.940974
10% level -1.616598
*MacKinnon (1996) one-sided p-values.
Null Hypothesis: RETURN_BUKOPIN has a unit root Exogenous: None
Bandwidth: 54 (Newey-West automatic) using Bartlett kernel
Adj. t-Stat Prob.* Phillips-Perron test statistic -15.06611 0.0000 Test critical values: 1% level -2.566049
5% level -1.940973
10% level -1.616599
*MacKinnon (1996) one-sided p-values. 4. BNII
Null Hypothesis: RETURN_BNII has a unit root Exogenous: None
Bandwidth: 102 (Newey-West automatic) using Bartlett kernel
Adj. t-Stat Prob.* Phillips-Perron test statistic -14.57598 0.0000 Test critical values: 1% level -2.566062
5% level -1.940974
10% level -1.616598
*MacKinnon (1996) one-sided p-values.
Null Hypothesis: RETURN_BNII has a unit root Exogenous: None
Lag Length: 20 (Automatic - based on SIC, maxlag=25)
t-Statistic Prob.* Augmented Dickey-Fuller test statistic -7.718940 0.0000 Test critical values: 1% level -2.566073
5% level -1.940976
10% level -1.616597
Lanjutan Lampiran 3
5. BNLI
Null Hypothesis: RETURN_PERMATA has a unit root Exogenous: None
Bandwidth: 14 (Newey-West automatic) using Bartlett kernel
Adj. t-Stat Prob.* Phillips-Perron test statistic -16.60473 0.0000 Test critical values: 1% level -2.566062
5% level -1.940974
10% level -1.616598
*MacKinnon (1996) one-sided p-values.
Null Hypothesis: RETURN_PERMATA has a unit root Exogenous: None
Lag Length: 25 (Automatic - based on SIC, maxlag=25)
t-Statistic Prob.* Augmented Dickey-Fuller test statistic -7.565155 0.0000 Test critical values: 1% level -2.566075
5% level -1.940976
10% level -1.616597
Lampiran 4 Model ARMA terbaik dan heterokedastisity test 1. BMRI
Dependent Variable: RETURN_BMRI Method: Least Squares
Date: 09/15/14 Time: 08:37
Sample (adjusted): 8/08/2006 8/29/2014 Included observations: 2104 after adjustments Convergence achieved after 10 iterations MA Backcast: 8/02/2006 8/07/2006
Variable Coefficient Std. Error t-Statistic Prob. C 0.005675 0.002977 1.906242 0.0568
MA(1) 1.016403 0.010920 93.07942 0.0000 MA(2) 0.978747 0.015340 63.80196 0.0000 MA(3) 0.888282 0.015333 57.93182 0.0000 MA(4) 0.864163 0.010911 79.20092 0.0000 R-squared 0.782774 Mean dependent var 0.005897 Adjusted R-squared 0.782360 S.D. dependent var 0.061663 S.E. of regression 0.028767 Akaike info criterion -4.256796 Sum squared resid 1.737017 Schwarz criterion -4.243366 Log likelihood 4483.150 Hannan-Quinn criter. -4.251877 F-statistic 1890.931 Durbin-Watson stat 1.916748
Prob(F-statistic) 0.000000
Inverted MA Roots .28+.91i .28-.91i -.79-.58i -.79+.58i
Heteroskedasticity Test: ARCH
F-statistic 151.2743 Prob. F(1,2101) 0.0000 Obs*R-squared 141.2483 Prob. Chi-Square(1) 0.0000
Test Equation:
Dependent Variable: RESID^2 Method: Least Squares Date: 09/18/14 Time: 07:01
Sample (adjusted): 8/09/2006 8/29/2014 Included observations: 2103 after adjustments
Variable Coefficient Std. Error t-Statistic Prob. C 0.000611 6.19E-05 9.873400 0.0000
RESID^2(-1) 0.259165 0.021071 12.29936 0.0000 R-squared 0.067165 Mean dependent var 0.000825 Adjusted R-squared 0.066721 S.D. dependent var 0.002821 S.E. of regression 0.002725 Akaike info criterion -8.971464 Sum squared resid 0.015606 Schwarz criterion -8.966089 Log likelihood 9435.494 Hannan-Quinn criter. -8.969495 F-statistic 151.2743 Durbin-Watson stat 2.006023
Lanjutan Lampiran 4
2. BBNI
Dependent Variable: RETURN_BBNI Method: Least Squares
Date: 09/11/14 Time: 10:45
Sample (adjusted): 8/08/2006 8/29/2014 Included observations: 2104 after adjustments Convergence achieved after 18 iterations MA Backcast: 8/02/2006 8/07/2006
Variable Coefficient Std. Error t-Statistic Prob.
MA(1) 0.951552 0.008162 116.5867 0.0000
MA(2) 0.946957 0.009332 101.4720 0.0000
MA(3) 0.926893 0.009337 99.27452 0.0000
MA(4) 0.926161 0.008149 113.6528 0.0000
R-squared 0.785320 Mean dependent var 0.005709 Adjusted R-squared 0.785013 S.D. dependent var 0.064559 S.E. of regression 0.029934 Akaike info criterion -4.177763 Sum squared resid 1.881657 Schwarz criterion -4.167019 Log likelihood 4399.007 Hannan-Quinn criter. -4.173828 Durbin-Watson stat 1.918385
Inverted MA Roots .31+.93i .31-.93i -.79-.58i -.79+.58i
Heteroskedasticity Test: ARCH
F-statistic 64.81444 Prob. F(1,2101) 0.0000 Obs*R-squared 62.93465 Prob. Chi-Square(1) 0.0000
Test Equation:
Dependent Variable: RESID^2 Method: Least Squares Date: 09/18/14 Time: 07:04
Sample (adjusted): 8/09/2006 8/29/2014 Included observations: 2103 after adjustments
Variable Coefficient Std. Error t-Statistic Prob.
C 0.000740 7.31E-05 10.11790 0.0000
RESID^2(-1) 0.172990 0.021488 8.050742 0.0000 R-squared 0.029926 Mean dependent var 0.000895
Adjusted R-squared 0.029464 S.D. dependent var 0.003285 S.E. of regression 0.003236 Akaike info criterion -8.628090 Sum squared resid 0.021999 Schwarz criterion -8.622716 Log likelihood 9074.437 Hannan-Quinn criter. -8.626122 F-statistic 64.81444 Durbin-Watson stat 2.036344
Lanjutan Lampiran 4
3. BBKP
Dependent Variable: RETURN_BUKOPIN Method: Least Squares
Date: 09/12/14 Time: 05:15
Sample (adjusted): 8/09/2006 8/29/2014 Included observations: 2103 after adjustments Convergence achieved after 25 iterations MA Backcast: 8/02/2006 8/08/2006
Variable Coefficient Std. Error t-Statistic Prob. AR(1) -0.556920 0.145987 -3.814869 0.0001 MA(1) 1.421321 0.154652 9.190423 0.0000 MA(2) 1.391240 0.147597 9.425964 0.0000 MA(3) 1.367770 0.148050 9.238565 0.0000 MA(4) 1.334067 0.144754 9.216073 0.0000 MA(5) 0.413644 0.141805 2.916998 0.0036 R-squared 0.757035 Mean dependent var 0.002896 Adjusted R-squared 0.756455 S.D. dependent var 0.056277 S.E. of regression 0.027773 Akaike info criterion -4.326663 Sum squared resid 1.617487 Schwarz criterion -4.310540 Log likelihood 4555.486 Hannan-Quinn criter. -4.320758 Durbin-Watson stat 1.984780
Inverted AR Roots -.56
Inverted MA Roots .30-.93i .30+.93i -.46 -.79-.57i
-.79+.57i
Heteroskedasticity Test: ARCH
F-statistic 24.58517 Prob. F(1,2100) 0.0000 Obs*R-squared 24.32382 Prob. Chi-Square(1) 0.0000
Test Equation:
Dependent Variable: RESID^2 Method: Least Squares Date: 09/18/14 Time: 07:04
Sample (adjusted): 8/10/2006 8/29/2014 Included observations: 2102 after adjustments
Variable Coefficient Std. Error t-Statistic Prob. C 0.000687 6.39E-05 10.75077 0.0000
RESID^2(-1) 0.107572 0.021695 4.958343 0.0000 R-squared 0.011572 Mean dependent var 0.000769 Adjusted R-squared 0.011101 S.D. dependent var 0.002842 S.E. of regression 0.002827 Akaike info criterion -8.898559 Sum squared resid 0.016778 Schwarz criterion -8.893182 Log likelihood 9354.385 Hannan-Quinn criter. -8.896590 F-statistic 24.58517 Durbin-Watson stat 2.032704
Lanjutan Lampiran 4
4. BNII
Dependent Variable: RETURN_BNII Method: Least Squares
Date: 09/12/14 Time: 06:16
Sample (adjusted): 8/08/2006 8/29/2014 Included observations: 2104 after adjustments Convergence achieved after 14 iterations MA Backcast: 8/02/2006 8/07/2006
Variable Coefficient Std. Error t-Statistic Prob.
MA(1) 0.992043 0.010395 95.43885 0.0000
MA(2) 0.966839 0.013122 73.68313 0.0000
MA(3) 0.921298 0.013125 70.19154 0.0000
MA(4) 0.878877 0.010397 84.53237 0.0000
R-squared 0.756570 Mean dependent var 0.003090 Adjusted R-squared 0.756222 S.D. dependent var 0.065472 S.E. of regression 0.032326 Akaike info criterion -4.023975 Sum squared resid 2.194471 Schwarz criterion -4.013231 Log likelihood 4237.222 Hannan-Quinn criter. -4.020040 Durbin-Watson stat 2.079803
Inverted MA Roots .29+.92i .29-.92i -.79-.57i -.79+.57i
Heteroskedasticity Test: ARCH
F-statistic 50.65725 Prob. F(1,2101) 0.0000 Obs*R-squared 49.51169 Prob. Chi-Square(1) 0.0000
Test Equation:
Dependent Variable: RESID^2 Method: Least Squares Date: 09/18/14 Time: 07:05
Sample (adjusted): 8/09/2006 8/29/2014 Included observations: 2103 after adjustments
Variable Coefficient Std. Error t-Statistic Prob.
C 0.000883 0.000138 6.405083 0.0000
RESID^2(-1) 0.153439 0.021558 7.117390 0.0000 R-squared 0.023543 Mean dependent var 0.001043
Adjusted R-squared 0.023079 S.D. dependent var 0.006312 S.E. of regression 0.006238 Akaike info criterion -7.315261 Sum squared resid 0.081764 Schwarz criterion -7.309887 Log likelihood 7693.997 Hannan-Quinn criter. -7.313293 F-statistic 50.65725 Durbin-Watson stat 2.027377
Lanjutan Lampiran 4
5. BNLI
Dependent Variable: RETURN_PERMATA Method: Least Squares
Date: 09/09/14 Time: 08:11
Sample (adjusted): 8/08/2006 8/29/2014 Included observations: 2104 after adjustments Convergence achieved after 11 iterations MA Backcast: 8/01/2006 8/07/2006
Variable Coefficient Std. Error t-Statistic Prob. MA(1) 0.852857 0.021622 39.44450 0.0000
MA(2) 0.843675 0.022967 36.73355 0.0000 MA(3) 0.798937 0.023714 33.68981 0.0000 MA(4) 0.775510 0.022968 33.76545 0.0000 MA(5) -0.135166 0.021621 -6.251628 0.0000 R-squared 0.725661 Mean dependent var 0.002853 Adjusted R-squared 0.725138 S.D. dependent var 0.051501 S.E. of regression 0.027000 Akaike info criterion -4.383561 Sum squared resid 1.530210 Schwarz criterion -4.370130 Log likelihood 4616.506 Hannan-Quinn criter. -4.378642 Durbin-Watson stat 1.994067
Inverted MA Roots .29-.93i .29+.93i .15 -.79-.58i
-.79+.58i
Heteroskedasticity Test: ARCH
F-statistic 232.5617 Prob. F(1,2101) 0.0000 Obs*R-squared 209.5840 Prob. Chi-Square(1) 0.0000
Test Equation:
Dependent Variable: RESID^2 Method: Least Squares Date: 09/18/14 Time: 07:06
Sample (adjusted): 8/09/2006 8/29/2014 Included observations: 2103 after adjustments
Variable Coefficient Std. Error t-Statistic Prob. C 0.000498 6.86E-05 7.253737 0.0000
RESID^2(-1) 0.315690 0.020701 15.24997 0.0000 R-squared 0.099660 Mean dependent var 0.000728 Adjusted R-squared 0.099231 S.D. dependent var 0.003236 S.E. of regression 0.003071 Akaike info criterion -8.732737 Sum squared resid 0.019813 Schwarz criterion -8.727363 Log likelihood 9184.473 Hannan-Quinn criter. -8.730769 F-statistic 232.5617 Durbin-Watson stat 2.075201
Lampiran 5 Model ARCH-GARCH terpilih dengan dummy
1. BMRI
Dependent Variable: RETURN_BMRI Method: ML - ARCH
Date: 09/17/14 Time: 12:01
Sample (adjusted): 8/08/2006 8/29/2014 Included observations: 2104 after adjustments Convergence achieved after 21 iterations MA Backcast: 8/02/2006 8/07/2006
Presample variance: backcast (parameter = 0.7)
GARCH = C(7) + C(8)*RESID(-1)^2 + C(9)*RESID(-1)^2*(RESID(-1)<0) + C(10)*GARCH(-1) + C(11)*DUMMY_BMRI
Variable Coefficient Std. Error z-Statistic Prob.
C 0.003308 0.002380 1.389849 0.1646 DUMMY_BMRI 0.003690 0.002040 1.808599 0.0705 MA(1) 0.979023 0.009740 100.5166 0.0000 MA(2) 0.945760 0.012065 78.39085 0.0000 MA(3) 0.908634 0.012947 70.18277 0.0000 MA(4) 0.896087 0.009832 91.14406 0.0000 Variance Equation C 1.92E-05 3.26E-06 5.887401 0.0000 RESID(-1)^2 0.055299 0.010536 5.248736 0.0000 RESID(-1)^2*(RESID(-1)<0) 0.073534 0.017498 4.202331 0.0000 GARCH(-1) 0.877496 0.011583 75.75540 0.0000
DUMMY_BMRI 2.02E-05 5.56E-06 3.622711 0.0003 R-squared 0.778673 Mean dependent var 0.005897
Adjusted R-squared 0.778145 S.D. dependent var 0.061663 S.E. of regression 0.029044 Akaike info criterion -4.550529 Sum squared resid 1.769809 Schwarz criterion -4.520982 Log likelihood 4798.157 Hannan-Quinn criter. -4.539708 Durbin-Watson stat 1.838234
Lanjutan Lampiran 5
2. BBNI
Dependent Variable: RETURN_BBNI Method: ML - ARCH
Date: 09/17/14 Time: 09:35
Sample (adjusted): 8/08/2006 8/29/2014 Included observations: 2104 after adjustments Convergence achieved after 33 iterations MA Backcast: 8/02/2006 8/07/2006
Presample variance: backcast (parameter = 0.7)
GARCH = C(6) + C(7)*RESID(-1)^2 + C(8)*RESID(-2)^2 + C(9)*GARCH(-1) + C(10)*DUMMY_BBNI
Variable Coefficient Std. Error z-Statistic Prob. DUMMY_BBNI 0.001889 0.002559 0.738319 0.4603 MA(1) 0.966250 0.008597 112.3913 0.0000 MA(2) 0.960037 0.009475 101.3273 0.0000 MA(3) 0.933843 0.008888 105.0658 0.0000 MA(4) 0.923547 0.006780 136.2143 0.0000 Variance Equation C 7.53E-06 1.31E-06 5.765319 0.0000 RESID(-1)^2 0.179329 0.022721 7.892703 0.0000 RESID(-2)^2 -0.107378 0.023661 -4.538231 0.0000 GARCH(-1) 0.916306 0.007073 129.5462 0.0000 DUMMY_BBNI 6.62E-06 1.81E-06 3.659768 0.0003 R-squared 0.785079 Mean dependent var 0.005709 Adjusted R-squared 0.784670 S.D. dependent var 0.064559 S.E. of regression 0.029958 Akaike info criterion -4.547238 Sum squared resid 1.883766 Schwarz criterion -4.520376 Log likelihood 4793.694 Hannan-Quinn criter. -4.537400 Durbin-Watson stat 1.949896
Lanjutan Lampiran 5
3. BBKP
Dependent Variable: RETURN_BUKOPIN Method: ML - ARCH
Date: 09/17/14 Time: 07:34
Sample (adjusted): 8/09/2006 8/29/2014 Included observations: 2103 after adjustments Convergence achieved after 64 iterations MA Backcast: 8/02/2006 8/08/2006
Presample variance: backcast (parameter = 0.7)
GARCH = C(8) + C(9)*RESID(-1)^2 + C(10)*RESID(-1)^2*(RESID(-1)<0) + C(11)*RESID(-2)^2 + C(12)*GARCH(-1) + C(13)*DUMMY_BBKP
Variable Coefficient Std. Error z-Statistic Prob.
DUMMY_BBKP 0.001409 0.001882 0.748536 0.4541 AR(1) 0.997630 0.001751 569.6663 0.0000 MA(1) -0.032509 0.009568 -3.397532 0.0007 MA(2) 0.002845 0.008686 0.327584 0.7432 MA(3) -0.010414 0.008178 -1.273418 0.2029 MA(4) -0.050377 0.008418 -5.984411 0.0000 MA(5) -0.905754 0.008792 -103.0187 0.0000 Variance Equation C 2.91E-05 3.50E-06 8.307135 0.0000 RESID(-1)^2 0.233530 0.024094 9.692567 0.0000 RESID(-1)^2*(RESID(-1)<0) 0.048215 0.019169 2.515266 0.0119 RESID(-2)^2 -0.123146 0.021982 -5.602054 0.0000 GARCH(-1) 0.826691 0.011657 70.92081 0.0000
DUMMY_BBKP 1.43E-05 3.19E-06 4.474097 0.0000 R-squared 0.752516 Mean dependent var 0.002896
Adjusted R-squared 0.751807 S.D. dependent var 0.056277 S.E. of regression 0.028037 Akaike info criterion -4.554565 Sum squared resid 1.647571 Schwarz criterion -4.519631 Log likelihood 4802.125 Hannan-Quinn criter. -4.541771 Durbin-Watson stat 2.202722
Inverted AR Roots 1.00
Inverted MA Roots 1.00 .30-.94i .30+.94i -.78+.57i
Lanjutan Lampiran 5
4. BNII
Dependent Variable: RETURN_BNII Method: ML - ARCH
Date: 09/17/14 Time: 07:35
Sample (adjusted): 8/08/2006 8/29/2014 Included observations: 2104 after adjustments Convergence achieved after 41 iterations MA Backcast: 8/02/2006 8/07/2006
Presample variance: backcast (parameter = 0.7)
GARCH = C(6) + C(7)*RESID(-1)^2 + C(8)*GARCH(-1) + C(9)*DUMMY_BNII
Variable Coefficient Std. Error z-Statistic Prob. DUMMY_BNII -0.004959 0.002537 -1.954781 0.0506 MA(1) 0.975050 0.009752 99.98889 0.0000 MA(2) 0.952181 0.011957 79.63322 0.0000 MA(3) 0.928532 0.010049 92.39796 0.0000 MA(4) 0.869279 0.008724 99.64732 0.0000 Variance Equation C 3.75E-05 2.38E-06 15.78007 0.0000 RESID(-1)^2 0.273534 0.014709 18.59666 0.0000 GARCH(-1) 0.696703 0.012842 54.25144 0.0000 DUMMY_BNII 4.56E-05 5.15E-06 8.860747 0.0000 R-squared 0.755336 Mean dependent var 0.003090 Adjusted R-squared 0.754870 S.D. dependent var 0.065472 S.E. of regression 0.032416 Akaike info criterion -4.643228 Sum squared resid 2.205597 Schwarz criterion -4.619053 Log likelihood 4893.676 Hannan-Quinn criter. -4.634374 Durbin-Watson stat 2.046835
Lanjutan Lampiran 5
5. BNLI
Dependent Variable: RETURN_PERMATA Method: ML - ARCH
Date: 09/17/14 Time: 07:38
Sample (adjusted): 8/08/2006 8/29/2014 Included observations: 2104 after adjustments Convergence achieved after 81 iterations MA Backcast: 8/01/2006 8/07/2006
Presample variance: backcast (parameter = 0.7)
GARCH = C(7) + C(8)*RESID(-1)^2 + C(9)*RESID(-1)^2*(RESID(-1)<0) + C(10)*RESID(-2)^2 + C(11)*GARCH(-1) + C(12)*GARCH(-2) + C(13) *DUMMY_BNLI
Variable Coefficient Std. Error z-Statistic Prob.
DUMMY_BNLI 0.006034 0.006337 0.952219 0.3410 MA(1) 0.872188 0.025832 33.76425 0.0000 MA(2) 0.858732 0.026045 32.97138 0.0000 MA(3) 0.830768 0.026618 31.21040 0.0000 MA(4) 0.809430 0.026685 30.33264 0.0000 MA(5) -0.117004 0.025136 -4.654857 0.0000 Variance Equation C 1.64E-06 3.39E-07 4.849903 0.0000 RESID(-1)^2 0.220758 0.023340 9.458508 0.0000 RESID(-1)^2*(RESID(-1)<0) 0.023477 0.003394 6.916552 0.0000 RESID(-2)^2 -0.219184 0.022690 -9.659724 0.0000 GARCH(-1) 1.364183 0.052979 25.74935 0.0000 GARCH(-2) -0.383082 0.050782 -7.543617 0.0000
DUMMY_BNLI 1.27E-05 2.97E-06 4.270585 0.0000 R-squared 0.725188 Mean dependent var 0.002853
Adjusted R-squared 0.724533 S.D. dependent var 0.051501 S.E. of regression 0.027030 Akaike info criterion -5.073101 Sum squared resid 1.532848 Schwarz criterion -5.038181 Log likelihood 5349.902 Hannan-Quinn criter. -5.060312 Durbin-Watson stat 2.036515
Inverted MA Roots .30-.93i .30+.93i .13 -.80-.58i
Lampiran 6 Signifikansi periode dummy vs standar deviasi
Lanjutan Lampiran 6
Lampiran 7 ARCH LM-Test dari model ARCH-GARCH terpilih 1. BMRI
Heteroskedasticity Test: ARCH
F-statistic 1.254065 Prob. F(1,2101) 0.2629 Obs*R-squared 1.254510 Prob. Chi-Square(1) 0.2627
Test Equation:
Dependent Variable: WGT_RESID^2 Method: Least Squares
Date: 09/18/14 Time: 07:22
Sample (adjusted): 8/09/2006 8/29/2014 Included observations: 2103 after adjustments
Variable Coefficient Std. Error t-Statistic Prob. C 0.975569 0.047604 20.49334 0.0000
WGT_RESID^2(-1) 0.024423 0.021810 1.119851 0.2629 R-squared 0.000597 Mean dependent var 1.000003 Adjusted R-squared 0.000121 S.D. dependent var 1.940368 S.E. of regression 1.940251 Akaike info criterion 4.164462 Sum squared resid 7909.369 Schwarz criterion 4.169837 Log likelihood -4376.932 Hannan-Quinn criter. 4.166431 F-statistic 1.254065 Durbin-Watson stat 1.999198
Prob(F-statistic) 0.262905
2. BBNI
Heteroskedasticity Test: ARCH
F-statistic 0.016299 Prob. F(1,2101) 0.8984 Obs*R-squared 0.016315 Prob. Chi-Square(1) 0.8984
Test Equation:
Dependent Variable: WGT_RESID^2 Method: Least Squares
Date: 09/18/14 Time: 07:27
Sample (adjusted): 8/09/2006 8/29/2014 Included observations: 2103 after adjustments
Variable Coefficient Std. Error t-Statistic Prob. C 1.006614 0.062038 16.22582 0.0000
WGT_RESID^2(-1) -0.002785 0.021816 -0.127668 0.8984 R-squared 0.000008 Mean dependent var 1.003819 Adjusted R-squared -0.000468 S.D. dependent var 2.661359 S.E. of regression 2.661982 Akaike info criterion 4.796969 Sum squared resid 14887.99 Schwarz criterion 4.802344 Log likelihood -5042.013 Hannan-Quinn criter. 4.798938 F-statistic 0.016299 Durbin-Watson stat 1.999986
Lanjutan Lampiran 7
3. BBKP
Heteroskedasticity Test: ARCH
F-statistic 0.168919 Prob. F(1,2100) 0.6811 Obs*R-squared 0.169067 Prob. Chi-Square(1) 0.6809
Test Equation:
Dependent Variable: WGT_RESID^2 Method: Least Squares
Date: 09/18/14 Time: 07:28
Sample (adjusted): 8/10/2006 8/29/2014 Included observations: 2102 after adjustments
Variable Coefficient Std. Error t-Statistic Prob.
C 1.009325 0.071170 14.18192 0.0000
WGT_RESID^2(-1) -0.008968 0.021821 -0.410998 0.6811 R-squared 0.000080 Mean dependent var 1.000355 Adjusted R-squared -0.000396 S.D. dependent var 3.105123 S.E. of regression 3.105738 Akaike info criterion 5.105331 Sum squared resid 20255.77 Schwarz criterion 5.110707 Log likelihood -5363.702 Hannan-Quinn criter. 5.107300 F-statistic 0.168919 Durbin-Watson stat 1.999542
Prob(F-statistic) 0.681116
4. BBNII
Heteroskedasticity Test: ARCH
F-statistic 0.429006 Prob. F(1,2101) 0.5125 Obs*R-squared 0.429326 Prob. Chi-Square(1) 0.5123
Test Equation:
Dependent Variable: WGT_RESID^2 Method: Least Squares
Date: 09/18/14 Time: 07:30
Sample (adjusted): 8/09/2006 8/29/2014 Included observations: 2103 after adjustments
Variable Coefficient Std. Error t-Statistic Prob.
C 0.985560 0.075601 13.03627 0.0000
WGT_RESID^2(-1) 0.014288 0.021814 0.654985 0.5125 R-squared 0.000204 Mean dependent var 0.999853 Adjusted R-squared -0.000272 S.D. dependent var 3.318961 S.E. of regression 3.319412 Akaike info criterion 5.238403 Sum squared resid 23149.85 Schwarz criterion 5.243777 Log likelihood -5506.180 Hannan-Quinn criter. 5.240371 F-statistic 0.429006 Durbin-Watson stat 1.999538
Lanjutan Lampiran 7
5. BBNLI
Heteroskedasticity Test: ARCH
F-statistic 0.056815 Prob. F(1,2101) 0.8116 Obs*R-squared 0.056868 Prob. Chi-Square(1) 0.8115
Test Equation:
Dependent Variable: WGT_RESID^2 Method: Least Squares
Date: 09/18/14 Time: 07:30
Sample (adjusted): 8/09/2006 8/29/2014 Included observations: 2103 after adjustments
Variable Coefficient Std. Error t-Statistic Prob. C 1.003829 0.070433 14.25228 0.0000
WGT_RESID^2(-1) 0.005200 0.021816 0.238360 0.8116 R-squared 0.000027 Mean dependent var 1.009077 Adjusted R-squared -0.000449 S.D. dependent var 3.067397 S.E. of regression 3.068085 Akaike info criterion 5.080935 Sum squared resid 19777.02 Schwarz criterion 5.086309 Log likelihood -5340.603 Hannan-Quinn criter. 5.082903 F-statistic 0.056815 Durbin-Watson stat 1.999864
Lampiran 8 Ringkasan hasil analisis
Parameter BMRI BBNI BBKP BNII BNLI
Nilai Prob Nilai Prob Nilai Prob Nilai Prob Nilai Prob ARIMA Konstanta (α0) 0.005675 0.0568 AR (1) -0.55692 0.0001 MA (1) 1.016403 0.0000 0.951552 0.0000 1.421321 0.0000 0.992043 0.0000 0.852857 0.0000 MA (2) 0.978747 0.0000 0.946957 0.0000 1.39124 0.0000 0.966839 0.0000 0.843675 0.0000 MA (3) 0.888282 0.0000 0.926893 0.0000 1.36777 0.0000 0.921298 0.0000 0.798937 0.0000 MA (4) 0.864163 0.0000 0.926161 0.0000 1.334067 0.0000 0.878877 0.0000 0.77551 0.0000 MA (5) 0.413644 0.0036 -0.135166 0.0000
Uji Efek ARCH 151.27430 0.0000 64.81444 0.0000 24.58517 0.0000 50.65725 0.0000 232.56170 0.0000 ARCH-GARCH
Konstanta (α0) 1.92E-05 0.0000 7.53E-06 0.0000 2.91E-05 0.0000 3.75E-05 0.0000 1.64E-06 0.0000
ARCH-1(α1) 0.055299 0.0000 0.179329 0.0000 0.23353 0.0000 0.273534 0.0000 0.220758 0.0000
ARCH-2 (α2) -0.107378 0.0000 -0.12314 0.0000 -0.219184 0.0000
Asimetric ( ) 0.073534 0.0000 0.048215 0.0119 0.023477 0.0119
GARCH-1 ( 1) 0.877496 0.0000 0.916306 0.0000 0.826691 0.0000 0.696703 0.0000 1,364,183 0.0000
GARCH-2 ( 1) -0.383082 0.0000
Dummy (Dt) 2.02E-05 0.0003 6.62E-06 0.0003 1.43E-05 0.0003 4.56E-05 0.0000 1.27E-05 0.0003
Evaluasi Model
Uji Jarque Bera 305.7786 0.0000 1,514.033 0.0000 3,553.352 0.0000 6,233.423 0.0000 3,318.415 0.0000
Uji Ljung-Box Tidak Signifikan Tidak Signifikan Tidak Signifikan Tidak Signifikan Tidak Signifikan
Uji ARCH-LM 0.876188 0.3494 1.054188 0.3047 0.0494 0.8241 1.905864 0.1676 0.017342 0.8952
Beta Sistematis 1.415899743 Risky 1.309671875 Risky 1.003369707 Normal 0.404564914 Riskless 0.547958216 Riskless
Lampiran 9 Hasil peramalan 1. Peramalan Statik BMRI
Harga BMRI 25 hari terakhir dan peramalan 25 hari kedepan
Nilai Aktual Peramalan
Tanggal Harga (Rp) Tanggal Harga (Rp)
7/28/2014 10650 09/01/2014 10.529 7/29/2014 10475 09/02/2014 10.537 7/30/2014 10500 09/03/2014 10.546 7/31/2014 10450 09/04/2014 10.555 08/01/2014 10250 09/05/2014 10.562 08/04/2014 10250 09/08/2014 10.570 08/05/2014 10250 09/09/2014 10.577 08/06/2014 10250 09/10/2014 10.584 08/07/2014 10250 09/11/2014 10.592 08/08/2014 10250 09/12/2014 10.599 08/11/2014 10275 9/15/2014 10.607 08/12/2014 10400 9/16/2014 10.614 8/13/2014 10275 9/17/2014 10.621 8/14/2014 10200 9/18/2014 10.629 8/15/2014 10200 9/19/2014 10.636 8/18/2014 10475 9/22/2014 10.644 8/19/2014 10500 9/23/2014 10.651 8/20/2014 10500 9/24/2014 10.658 8/21/2014 10475 9/25/2014 10.666 8/22/2014 10450 9/26/2014 10.673 8/25/2014 10475 9/29/2014 10.681 8/26/2014 10525 9/30/2014 10.688 8/27/2014 10550 10/01/2014 10.696 8/28/2014 10550 10/02/2014 10.703 8/29/2014 10525 10/03/2014 10.710 0 2,000 4,000 6,000 8,000 10,000 12,000 2006 2007 2008 2009 2010 2011 2012 2013 2014 BMRIF ± 2 S.E. Forecast: BMRIF Actual: BMRI Forecast sample: 8/08/2006 10/03/2014 Adjusted sample: 8/09/2006 10/03/2014 Included observations: 2127
Root Mean Squared Error 133.3859 Mean Absolute Error 89.80618 Mean Abs. Percent Error 1.776864 Theil Inequality Coeffic ient 0.010695 Bias Proportion 0.000011 Variance Proportion 0.000024 Covariance Proportion 0.999965 .000 .002 .004 .006 .008 2006 2007 2008 2009 2010 2011 2012 2013 2014
Lanjutan Lampiran 9
2. Peramalan Statik BBNI
Harga BBNI 25 hari terakhir dan peramalan 25 hari kedepan
Nilai Aktual Peramalan
Tanggal Harga (Rp) Tanggal Harga (Rp)
7/28/2014 5.150 09/01/2014 5.350 7/29/2014 4.985 09/02/2014 5.343 7/30/2014 4.975 09/03/2014 5.346 7/31/2014 5.000 09/04/2014 5.346 08/01/2014 5.100 09/05/2014 5.346 08/04/2014 5.100 09/08/2014 5.346 08/05/2014 5.100 09/09/2014 5.346 08/06/2014 5.100 09/10/2014 5.346 08/07/2014 5.100 09/11/2014 5.346 08/08/2014 5.100 09/12/2014 5.346 08/11/2014 5.125 9/15/2014 5.346 08/12/2014 5.150 9/16/2014 5.346 8/13/2014 4.995 9/17/2014 5.346 8/14/2014 5.075 9/18/2014 5.346 8/15/2014 5.075 9/19/2014 5.346 8/18/2014 5.100 9/22/2014 5.346 8/19/2014 5.125 9/23/2014 5.346 8/20/2014 5.150 9/24/2014 5.346 8/21/2014 5.175 9/25/2014 5.346 8/22/2014 5.175 9/26/2014 5.346 8/25/2014 5.250 9/29/2014 5.346 8/26/2014 5.300 9/30/2014 5.346 8/27/2014 5.300 10/01/2014 5.346 8/28/2014 5.400 10/02/2014 5.346 8/29/2014 5.350 10/03/2014 5.346 0 1,000 2,000 3,000 4,000 5,000 6,000 2006 2007 2008 2009 2010 2011 2012 2013 2014 BBNIF ± 2 S.E. Forecast: BBNIF Actual: BBNI Forecast sample: 8/08/2006 10/03/2014 Adjusted sample: 8/09/2006 10/03/2014 Included observations: 2111
Root Mean Squared Error 70.48084 Mean Absolute Error 44.48372 Mean Abs. Percent Error 1.713789 Theil Inequality Coefficient 0.010998 Bias Proportion 0.000937 Variance Proportion 0.000076 Covariance Proportion 0.998987 .0000 .0025 .0050 .0075 .0100 .0125 .0150 2006 2007 2008 2009 2010 2011 2012 2013 2014 Forecas t of Variance
Lanjutan Lampiran 9
3. Peramalan Statik BBKP
Harga BBKP 25 hari terakhir dan peramalan 25 hari kedepan
Nilai Aktual Peramalan
Tanggal Harga (Rp) Tanggal Harga (Rp)
7/28/2014 720 09/01/2014 739,591 7/29/2014 720 09/02/2014 740,063 7/30/2014 720 09/03/2014 739,870 7/31/2014 720 09/04/2014 739,875 08/01/2014 720 09/05/2014 739,896 08/04/2014 710 09/08/2014 739,914 08/05/2014 700 09/09/2014 739,931 08/06/2014 700 09/10/2014 739,946 08/07/2014 695 09/11/2014 739,959 08/08/2014 700 09/12/2014 739,971 08/11/2014 720 9/15/2014 739,982 08/12/2014 720 9/16/2014 739,991 8/13/2014 725 9/17/2014 740,000 8/14/2014 750 9/18/2014 740,007 8/15/2014 755 9/19/2014 740,014 8/18/2014 750 9/22/2014 740,020 8/19/2014 755 9/23/2014 740,026 8/20/2014 760 9/24/2014 740,031 8/21/2014 760 9/25/2014 740,035 8/22/2014 750 9/26/2014 740,039 8/25/2014 750 9/29/2014 740,042 8/26/2014 740 9/30/2014 740,046 8/27/2014 740 10/01/2014 740,048 8/28/2014 735 10/02/2014 740,051 8/29/2014 740 10/03/2014 740,053 0 200 400 600 800 1,000 1,200 2006 2007 2008 2009 2010 2011 2012 2013 2014 BUKOPINF ± 2 S.E. Forecast: BUKOPINF Actual: BUKOPIN Forecast sample: 8/08/2006 10/03/2014 Adjusted sample: 8/10/2006 10/03/2014 Included observations: 2126
Root Mean Squared Error 13.55045 Mean Absolute Error 8.627227 Mean Abs. Percent Error 1.597451 Theil Inequality Coefficient 0.011571 Bias Proportion 0.000097 Variance Proportion 0.000007 Covariance Proportion 0.999896 .000 .004 .008 .012 .016 2006 2007 2008 2009 2010 2011 2012 2013 2014 Forecast of Variance
Lanjutan Lampiran 9
4. Peramalan Statik BNII
Harga BNII 25 hari terakhir dan peramalan 25 hari kedepan
Nilai Aktual Peramalan
Tanggal Harga (Rp) Tanggal Harga (Rp)
7/28/2014 295 09/01/2014 291,7828 7/29/2014 295 09/02/2014 291,9740 7/30/2014 295 09/03/2014 292,2104 7/31/2014 295 09/04/2014 292,2823 08/01/2014 295 09/05/2014 292,2823 08/04/2014 295 09/08/2014 292,2823 08/05/2014 299 09/09/2014 292,2823 08/06/2014 295 09/10/2014 292,2823 08/07/2014 300 09/11/2014 292,2823 08/08/2014 290 09/12/2014 292,2823 08/11/2014 293 9/15/2014 292,2823 08/12/2014 299 9/16/2014 292,2823 8/13/2014 298 9/17/2014 292,2823 8/14/2014 298 9/18/2014 292,2823 8/15/2014 300 9/19/2014 292,2823 8/18/2014 300 9/22/2014 292,2823 8/19/2014 299 9/23/2014 292,2823 8/20/2014 299 9/24/2014 292,2823 8/21/2014 296 9/25/2014 292,2823 8/22/2014 295 9/26/2014 292,2823 8/25/2014 297 9/29/2014 292,2823 8/26/2014 299 9/30/2014 292,2823 8/27/2014 293 10/01/2014 292,2823 8/28/2014 296 10/02/2014 292,2823 8/29/2014 291 10/03/2014 292,2823 0 200 400 600 800 1,000 1,200 1,400 2006 2007 2008 2009 2010 2011 2012 2013 2014 BNIIF ± 2 S.E. Forecast: BNIIF Actual: BNII Forecast sample: 8/08/2006 10/03/2014 Adjusted sample: 8/09/2006 10/03/2014 Included observations: 2109
Root Mean Squared Error 12.75948
Mean Absolute Error 6.132757
Mean Abs. Percent Error 1.607219
Theil Inequality Coefficient 0.016377
Bias Proportion 0.000088 Variance Proportion 0.000169 Covariance Proportion 0.999743 .00 .01 .02 .03 .04 .05 .06 2006 2007 2008 2009 2010 2011 2012 2013 2014 Forecast of V ariance
Lanjutan Lampiran 9
5. Peramalan Statik BNLI
Harga BNLI 25 hari terakhir dan peramalan 25 hari kedepan
Nilai Aktual Peramalan
Tanggal Harga (Rp) Tanggal Harga (Rp)
7/28/2014 1380 09/01/2014 1.400,163 7/29/2014 1380 09/02/2014 1.400,603 7/30/2014 1380 09/03/2014 1.399,154 7/31/2014 1380 09/04/2014 1.399,409 08/01/2014 1380 09/05/2014 1.399,426 08/04/2014 1380 09/08/2014 1.399,426 08/05/2014 1365 09/09/2014 1.399,426 08/06/2014 1365 09/10/2014 1.399,426 08/07/2014 1370 09/11/2014 1.399,426 08/08/2014 1380 09/12/2014 1.399,426 08/11/2014 1380 9/15/2014 1.399,426 08/12/2014 1380 9/16/2014 1.399,426 8/13/2014 1380 9/17/2014 1.399,426 8/14/2014 1380 9/18/2014 1.399,426 8/15/2014 1380 9/19/2014 1.399,426 8/18/2014 1375 9/22/2014 1.399,426 8/19/2014 1370 9/23/2014 1.399,426 8/20/2014 1380 9/24/2014 1.399,426 8/21/2014 1380 9/25/2014 1.399,426 8/22/2014 1365 9/26/2014 1.399,426 8/25/2014 1370 9/29/2014 1.399,426 8/26/2014 1375 9/30/2014 1.399,426 8/27/2014 1385 10/01/2014 1.399,426 8/28/2014 1410 10/02/2014 1.399,426 8/29/2014 1400 10/03/2014 1.399,426 0 400 800 1,200 1,600 2,000 2,400 2006 2007 2008 2009 2010 2011 2012 2013 2014 PERMATA F ± 2 S.E. Forecast: PERMATAF Actual: PERMATA Forecast sample: 8/08/2006 10/03/2014 Adjusted sample: 8/09/2006 10/03/2014 Included observations: 2110
Root Mean Squared Error 24.57344 Mean Absolute Error 14.44498 Mean Abs. Percent Error 1.354668 Theil Inequality Coefficient 0.009918 Bias Proportion 0.000322 Variance Proportion 0.000000 Covariance Proportion 0.999678 .000 .005 .010 .015 .020 .025 2006 2007 2008 2009 2010 2011 2012 2013 2014 Forecast of Variance