Berikut adalah series data IHK bulanan Januari 2010- Desember 2013. Tentukan model ARCH/GARCH yang sesuai dengan data berikut:
|
Periode
|
IHK
|
Periode
|
IHK
|
Periode
|
IHK
|
|
q12011
|
126.3
|
q12012
|
130.9
|
q12013
|
136.88
|
|
q22011
|
126.5
|
q22012
|
130.96
|
q22013
|
137.91
|
|
q32011
|
126.1
|
q32012
|
131.05
|
q32013
|
138.78
|
|
q42011
|
125.7
|
q42012
|
131.32
|
q42013
|
138.64
|
|
q52011
|
125.8
|
q52012
|
131.41
|
q52013
|
138.6
|
|
q62011
|
126.5
|
q62012
|
132.23
|
q62013
|
140.03
|
|
q72011
|
127.4
|
q72012
|
133.16
|
q72013
|
144.63
|
|
q82011
|
128.5
|
q82012
|
134.43
|
q82013
|
146.25
|
|
q92011
|
128.9
|
q92012
|
134.45
|
q92013
|
145.74
|
|
q102011
|
128.7
|
q102012
|
134.67
|
q102013
|
145.87
|
|
q112011
|
129.2
|
q112012
|
134.76
|
q112013
|
146.04
|
|
q122011
|
129.9
|
q122012
|
135.49
|
q122013
|
146.84
|
Sebelum
membentuk model ARCH/GARCH dilakukan uji stationeritas/ unit root test
terhadp datanya (untuk teknik uji stationeritas dapat dilihat pada
postingan uji unit root test menggunakan eviews)
|
Null Hypothesis: IHK has a unit root
|
||||
|
Exogenous: Constant, Linear Trend
|
||||
|
Lag Length: 2 (Automatic based on SIC, MAXLAG=9)
|
||||
|
t-Statistic |
Prob.* |
|||
|
Augmented Dickey-Fuller test statistic
|
-1.426581 |
0.8340 |
||
|
Test critical values:
|
1% level |
-4.262735 |
||
|
5% level |
-3.552973 |
|||
|
10% level |
-3.209642 |
|||
|
*MacKinnon (1996) one-sided p-values.
|
||||
Terlihat pada level data IHK belum stationer pada level karena p (0.834) >alpha(0.05)
Sehingga datanya dicoba untuk ditranformasi dengan menggunakan log sehingga didapat variabel baru lihk
Caranya ketik pada kotak syntax paling atas: genr lihk=log(ihk)
|
Null Hypothesis: LIHK has a unit root
|
||||
|
Exogenous: Constant, Linear Trend
|
||||
|
Lag Length: 2 (Automatic based on SIC, MAXLAG=9)
|
||||
|
t-Statistic |
Prob.* |
|||
|
Augmented Dickey-Fuller test statistic
|
-1.596716 |
0.7726 |
||
|
Test critical values:
|
1% level |
-4.262735 |
||
|
5% level |
-3.552973 |
|||
|
10% level |
-3.209642 |
|||
|
*MacKinnon (1996) one-sided p-values.
|
||||
Terlihat
pada level data LIHK belum stationer pada level karena p (0.772)
>alpha(0.05), sehingga dilakukan uji stationeritas menggunakan
difference I
Terlihat
pada diffeence l data LIHK sudah stationer pada level karena p (0.002)
<alpha(0.05), sehingga data yang kita gunakan untuk model adalah
DLINK atau yang lebih sering disebut dengan inflasi
Caranay ketik pada kotak syntax paling atas: genr dlihk=d(lihk)
Selanjutny dilakukan model rata-rata/mean ARIMA (menentukan model ARIMA dapat dibaca pada postingan sebelumnya: Model ARIMA dengan Eviews )
Model ARI(1) atau ARIMA(1,1,0)
|
Dependent Variable: DLIHK
|
||||
|
Method: Least Squares
|
||||
|
Date: 09/01/14 Time: 10:14
|
||||
|
Sample (adjusted): 3 36
|
||||
|
Included observations: 34 after adjustments
|
||||
|
Convergence achieved after 3 iterations
|
||||
|
Variable |
Coefficient
|
Std. Error
|
t-Statistic
|
Prob.
|
|
C |
0.004464
|
0.001646
|
2.712055
|
0.0107
|
|
AR(1) |
0.365124
|
0.164044
|
2.225773
|
0.0332
|
|
R-squared
|
0.134060
|
Mean dependent var
|
0.004395
|
|
|
Adjusted R-squared
|
0.106999
|
S.D. dependent var
|
0.006446
|
|
|
S.E. of regression
|
0.006091
|
Akaike info criterion
|
-7.306993
|
|
|
Sum squared resid
|
0.001187
|
Schwarz criterion
|
-7.217207
|
|
|
Log likelihood
|
126.2189
|
Hannan-Quinn criter.
|
-7.276373
|
|
|
F-statistic
|
4.954066
|
Durbin-Watson stat
|
1.639355
|
|
|
Prob(F-statistic)
|
0.033198
|
|||
Asumsi Heterokedastisitas
|
Heteroskedasticity Test: White
|
||||
|
F-statistic
|
1.616781
|
Prob. F(2,31)
|
0.2148
|
|
|
Obs*R-squared
|
3.211500
|
Prob. Chi-Square(2)
|
0.2007
|
|
|
Scaled explained SS
|
14.45066
|
Prob. Chi-Square(2)
|
0.0007
|
|
Model MA(1) atau IMA(0,1,1)
|
Dependent Variable: DLIHK
|
||||
|
Method: Least Squares
|
||||
|
Date: 09/01/14 Time: 10:16
|
||||
|
Sample (adjusted): 2 36
|
||||
|
Included observations: 35 after adjustments
|
||||
|
Convergence achieved after 6 iterations
|
||||
|
MA Backcast: 1
|
||||
|
Variable |
Coefficient
|
Std. Error
|
t-Statistic
|
Prob.
|
|
C |
0.004350
|
0.001503
|
2.893816
|
0.0067
|
|
MA(1) |
0.594722
|
0.140068
|
4.245957
|
0.0002
|
|
R-squared
|
0.248195
|
Mean dependent var
|
0.004308
|
|
|
Adjusted R-squared
|
0.225413
|
S.D. dependent var
|
0.006371
|
|
|
S.E. of regression
|
0.005607
|
Akaike info criterion
|
-7.474113
|
|
|
Sum squared resid
|
0.001038
|
Schwarz criterion
|
-7.385236
|
|
|
Log likelihood
|
132.7970
|
Hannan-Quinn criter.
|
-7.443432
|
|
|
F-statistic
|
10.89435
|
Durbin-Watson stat
|
2.022980
|
|
|
Prob(F-statistic)
|
0.002322
|
|||
|
Inverted MA Roots
|
-.59
|
|||
|
Heteroskedasticity Test: White
|
||||
|
F-statistic
|
0.220973
|
Prob. F(5,29)
|
0.9506
|
|
|
Obs*R-squared
|
1.284517
|
Prob. Chi-Square(5)
|
0.9365
|
|
|
Scaled explained SS
|
5.957673
|
Prob. Chi-Square(5)
|
0.3104
|
|
Model ARIMA (1,1,1)
|
Dependent Variable: DLIHK
|
||||
|
Method: Least Squares
|
||||
|
Date: 09/01/14 Time: 10:18
|
||||
|
Sample (adjusted): 3 36
|
||||
|
Included observations: 34 after adjustments
|
||||
|
Convergence achieved after 16 iterations
|
||||
|
MA Backcast: 2
|
||||
|
Variable |
Coefficient
|
Std. Error
|
t-Statistic
|
Prob.
|
|
C |
0.003824
|
0.001243
|
3.076090
|
0.0044
|
|
AR(1) |
-0.430175
|
0.174823
|
-2.460640
|
0.0196
|
|
MA(1) |
0.997478
|
0.046431
|
21.48304
|
0.0000
|
|
R-squared
|
0.295458
|
Mean dependent var
|
0.004395
|
|
|
Adjusted R-squared
|
0.250004
|
S.D. dependent var
|
0.006446
|
|
|
S.E. of regression
|
0.005582
|
Akaike info criterion
|
-7.454437
|
|
|
Sum squared resid
|
0.000966
|
Schwarz criterion
|
-7.319758
|
|
|
Log likelihood
|
129.7254
|
Hannan-Quinn criter.
|
-7.408507
|
|
|
F-statistic
|
6.500103
|
Durbin-Watson stat
|
1.853674
|
|
|
Prob(F-statistic)
|
0.004391
|
|||
|
Inverted AR Roots
|
-.43
|
|||
|
Inverted MA Roots
|
-1.00
|
|||
|
Heteroskedasticity Test: White
|
||||
|
F-statistic
|
4.012121
|
Prob. F(8,25)
|
0.0035
|
|
|
Obs*R-squared
|
19.11304
|
Prob. Chi-Square(8)
|
0.0143
|
|
|
Scaled explained SS
|
67.77232
|
Prob. Chi-Square(8)
|
0.0000
|
|
Kesimpulan ketiga model
|
Model
|
Model
|
R square
Adj.
|
AIK
|
SC
|
Asumsi
heterokedastis
|
|
ARI(1)
|
significan
|
0.10
|
-7.306
|
-7.217
|
Memenuhi
|
|
IMA(1)
|
significan
|
0.22
|
-7.473
|
-7.385
|
Memenuhi
|
|
ARIMA(1,1,1)
|
significan
|
0.25
|
-7.454
|
-7.319
|
Tidak memenuhi
|
Terlihat dari kesimpulan di atas jika
kita ingin menggunakan model ARIMA maka sebaiknya kita menggunakn model
ARI(1) tetapi karena r-squarenya kecil dan kita ingin mengunakan model
GARCH maka model mena/rata-rata yang kita pilih adalah model ARIMA
(1,1,1) dengan R-square terbesar dan masih mengalami heterokedastisitas.
Karena datanya stationer pada difference I, maka model yang digunakan model GARCH(1,1,0), GARCH(0,1,1) atau GARCH(1,1,1)
Maka klik menu estimate
Pada estimate setting →pada methode pilih ARCH (Autoregresif Conditional Heterokedascity)
Pada mean equation ketik: dlihk c ar(1) ma(1)
Pada variance dan distribution specification:
Model: GARCH/TARCH
Untul model ARCH(1) atau GARCH(1,0,0)
Order:
ARCH: ketik 1
Theshold Order : 0
GARCH: ketik 0
Untul model GARCH(1) atau GARCH(0,0,1)
Order:
ARCH: ketik 0
Theshold Order : 0
GARCH: ketik 1
Untul model GARCH(1,1,0)
Order:
ARCH: ketik 1
Theshold Order : 1
GARCH: ketik 0
Untul model GARCH(0,1,1)
Order:
ARCH: ketik 0
Theshold Order : 1
GARCH: ketik 1
Untul model GARCH(1,1,1)
Order:
ARCH: ketik 1
Theshold Order : 1
GARCH: ketik 1
Model GARCH (1,1,0)
|
Dependent Variable: DLIHK
|
||||
|
Method: ML - ARCH (Marquardt) - Normal distribution
|
||||
|
Date: 09/01/14 Time: 10:50
|
||||
|
Sample (adjusted): 3 36
|
||||
|
Included observations: 34 after adjustments
|
||||
|
Convergence achieved after 72 iterations
|
||||
|
MA Backcast: 2
|
||||
|
Presample variance: backcast (parameter = 0.7)
|
||||
|
GARCH = C(4) + C(5)*RESID(-1)^2 + C(6)*RESID(-1)^2*(RESID(-1)<0)
|
||||
|
Variable |
Coefficient
|
Std. Error
|
z-Statistic
|
Prob.
|
|
C |
0.004478
|
0.001072
|
4.175983
|
0.0000
|
|
AR(1) |
0.017174
|
0.205620
|
0.083521
|
0.9334
|
|
MA(1) |
0.714078
|
0.110471
|
6.463937
|
0.0000
|
|
Variance Equation |
||||
|
C |
9.65E-06
|
3.92E-06
|
2.462620
|
0.0138
|
|
RESID(-1)^2 |
1.732166
|
0.693158
|
2.498947
|
0.0125
|
|
RESID(-1)^2*(RESID(-1)<0) |
-1.816201
|
0.724633
|
-2.506373
|
0.0122
|
|
R-squared
|
0.230534
|
Mean dependent var
|
0.004395
|
|
|
Adjusted R-squared
|
0.093129
|
S.D. dependent var
|
0.006446
|
|
|
S.E. of regression
|
0.006138
|
Akaike info criterion
|
-7.912814
|
|
|
Sum squared resid
|
0.001055
|
Schwarz criterion
|
-7.643457
|
|
|
Log likelihood
|
140.5178
|
Hannan-Quinn criter.
|
-7.820956
|
|
|
F-statistic
|
1.677772
|
Durbin-Watson stat
|
2.322140
|
|
|
Prob(F-statistic)
|
0.172696
|
|||
|
Inverted AR Roots
|
.02
|
|||
|
Inverted MA Roots
|
-.71
|
|||
Untuk Uji Normalitas
Klik Menu Residual Test →Histogram Normality test
Untuk Uji heterokedastisitas
Klik Menu Residual Test→ARCH LM test→White
|
Heteroskedasticity Test: White
|
||||
|
F-statistic
|
1.99E+09
|
Prob. F(26,7)
|
0.0000
|
|
|
Obs*R-squared
|
34.00000
|
Prob. Chi-Square(26)
|
0.1350
|
|
|
Scaled explained SS
|
2.74E+10
|
Prob. Chi-Square(26)
|
0.0000
|
|
Model GARCH (0,1,1)
|
Dependent Variable: DLIHK
|
||||
|
Method: ML - ARCH (Marquardt) - Normal distribution
|
||||
|
Date: 09/01/14 Time: 10:55
|
||||
|
Sample (adjusted): 3 36
|
||||
|
Included observations: 34 after adjustments
|
||||
|
Convergence achieved after 13 iterations
|
||||
|
MA Backcast: 2
|
||||
|
Presample variance: backcast (parameter = 0.7)
|
||||
|
GARCH = C(4) + C(5)*RESID(-1)^2*(RESID(-1)<0) + C(6)*GARCH(-1)
|
||||
|
Variable |
Coefficient
|
Std. Error
|
z-Statistic
|
Prob.
|
|
C |
0.004043
|
0.001013
|
3.990541
|
0.0001
|
|
AR(1) |
-0.010516
|
0.112723
|
-0.093294
|
0.9257
|
|
MA(1) |
0.744300
|
0.071223
|
10.45024
|
0.0000
|
|
Variance Equation |
||||
|
C |
1.94E-06
|
1.15E-06
|
1.679453
|
0.0931
|
|
RESID(-1)^2*(RESID(-1)<0) |
-0.333119
|
0.210668
|
-1.581252
|
0.1138
|
|
GARCH(-1) |
1.056712
|
0.038531
|
27.42507
|
0.0000
|
|
R-squared
|
0.227199
|
Mean dependent var
|
0.004395
|
|
|
Adjusted R-squared
|
0.089199
|
S.D. dependent var
|
0.006446
|
|
|
S.E. of regression
|
0.006151
|
Akaike info criterion
|
-7.624984
|
|
|
Sum squared resid
|
0.001060
|
Schwarz criterion
|
-7.355626
|
|
|
Log likelihood
|
135.6247
|
Hannan-Quinn criter.
|
-7.533125
|
|
|
F-statistic
|
1.646365
|
Durbin-Watson stat
|
2.336899
|
|
|
Prob(F-statistic)
|
0.180502
|
|||
|
Inverted AR Roots
|
-.01
|
|||
|
Inverted MA Roots
|
-.74
|
|||
Untuk Uji Normalitas
Klik Menu Residual Test →Histogram Normality test
Untuk Uji heterokedastisitas
Klik Menu Residual Test→ARCH LM test →White
|
Heteroskedasticity Test: White
|
||||
|
F-statistic
|
637.7209
|
Prob. F(11,22)
|
0.0000
|
|
|
Obs*R-squared
|
33.89370
|
Prob. Chi-Square(11)
|
0.0004
|
|
|
Scaled explained SS
|
1.42E+11
|
Prob. Chi-Square(11)
|
0.0000
|
|
Model GARCH (1,1,1)
|
Dependent Variable: DLIHK
|
||||
|
Method: ML - ARCH (Marquardt) - Normal distribution
|
||||
|
Date: 09/01/14 Time: 10:56
|
||||
|
Sample (adjusted): 3 36
|
||||
|
Included observations: 34 after adjustments
|
||||
|
Convergence achieved after 76 iterations
|
||||
|
MA Backcast: 2
|
||||
|
Presample variance: backcast (parameter = 0.7)
|
||||
|
GARCH = C(4) + C(5)*RESID(-1)^2 + C(6)*RESID(-1)^2*(RESID(-1)<0) +
|
||||
|
C(7)*GARCH(-1)
|
||||
|
Variable |
Coefficient
|
Std. Error
|
z-Statistic
|
Prob.
|
|
C |
0.004673
|
0.001379
|
3.387646
|
0.0007
|
|
AR(1) |
0.302141
|
0.301873
|
1.000889
|
0.3169
|
|
MA(1) |
0.309719
|
0.215668
|
1.436092
|
0.1510
|
|
Variance Equation |
||||
|
C |
1.20E-05
|
5.49E-06
|
2.178430
|
0.0294
|
|
RESID(-1)^2 |
0.889084
|
0.475492
|
1.869817
|
0.0615
|
|
RESID(-1)^2*(RESID(-1)<0) |
-1.165908
|
0.343128
|
-3.397883
|
0.0007
|
|
GARCH(-1) |
0.098022
|
0.268616
|
0.364916
|
0.7152
|
|
R-squared
|
0.205128
|
Mean dependent var
|
0.004395
|
|
|
Adjusted R-squared
|
0.028489
|
S.D. dependent var
|
0.006446
|
|
|
S.E. of regression
|
0.006353
|
Akaike info criterion
|
-7.820032
|
|
|
Sum squared resid
|
0.001090
|
Schwarz criterion
|
-7.505781
|
|
|
Log likelihood
|
139.9405
|
Hannan-Quinn criter.
|
-7.712863
|
|
|
F-statistic
|
1.161286
|
Durbin-Watson stat
|
1.976682
|
|
|
Prob(F-statistic)
|
0.355596
|
|||
|
Inverted AR Roots
|
.30
|
|||
|
Inverted MA Roots
|
-.31
|
|||
Untuk Uji Normalitas
Klik Menu Residual Test àHistogram Normality test
Untuk Uji heterokedastisitas
Klik Menu Residual Test →ARCH LM test →White
Tidak dapat diuji
Kesimpulan dari ketiga model tersebut adalah:
|
Model
|
Model
|
R-square
|
AIK
|
SC
|
Normalitas
|
heterokedastuitas
|
|
GARCH (1,1,0)
|
signifikan
|
0.09
|
-7.91
|
-7.64
|
terpenuhi
|
terpenuhi
|
|
GARCH (0,1,1)
|
signifikan
|
0.089
|
-7.62
|
-7.63
|
Tdk terpenuhi
|
Tdk terpenuhi
|
|
GARCH (1,1,1)
|
Tdk sign
|
0.02
|
-7.82
|
-6.50
|
terpenuhi
|
-
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Maka model yang akan digunakan adalah model ARCH(1,1) atau GARCh(1,1,0)
Selanjutny klik menu forecast dan ok
Terlihat nilai bias proportionnya kecil sekali berarti model yang digunakan baik untuk melakukan forecasting
Thanks ya, artikel sangat membantu dalam menyelesaikan tugas perkuliahan tentang Generalized AutoRegressive Conditional Heteroskedastisitas (GARCH). Kunjungi juga ya MAKALAH GARCH
BalasHapus