autoarfima(data$VNI,ar.max = 2, ma.max = 2, criterion = "AIC", method = "full")
## $fit
##
## *----------------------------------*
## * ARFIMA Model Fit *
## *----------------------------------*
## Mean Model : ARFIMA(1,0,1)
## Distribution : norm
##
## Optimal Parameters
## ------------------------------------
## Estimate Std. Error t value Pr(>|t|)
## ar1 0.501620 0.167038 3.0030 0.002673
## ma1 -0.428330 0.174099 -2.4603 0.013884
## sigma 0.011802 0.000146 80.6027 0.000000
##
## Robust Standard Errors:
## Estimate Std. Error t value Pr(>|t|)
## ar1 0.501620 0.223486 2.2445 0.024799
## ma1 -0.428330 0.234928 -1.8232 0.068267
## sigma 0.011802 0.000431 27.3533 0.000000
##
## LogLikelihood : 9807.326
##
## Information Criteria
## ------------------------------------
##
## Akaike -6.0390
## Bayes -6.0334
## Shibata -6.0390
## Hannan-Quinn -6.0370
##
## Weighted Ljung-Box Test on Standardized Residuals
## ------------------------------------
## statistic p-value
## Lag[1] 0.00691 0.9338
## Lag[2*(p+q)+(p+q)-1][5] 0.21709 1.0000
## Lag[4*(p+q)+(p+q)-1][9] 2.21499 0.9735
##
## H0 : No serial correlation
##
## Weighted Ljung-Box Test on Standardized Squared Residuals
## ------------------------------------
## statistic p-value
## Lag[1] 125.7 0
## Lag[2*(p+q)+(p+q)-1][2] 205.1 0
## Lag[4*(p+q)+(p+q)-1][5] 353.1 0
##
##
## ARCH LM Tests
## ------------------------------------
## Statistic DoF P-Value
## ARCH Lag[2] 238.0 2 0
## ARCH Lag[5] 298.7 5 0
## ARCH Lag[10] 341.7 10 0
##
## Nyblom stability test
## ------------------------------------
## Joint Statistic: 1.5834
## Individual Statistics:
## ar1 0.4366
## ma1 0.4476
## sigma 1.0116
##
## Asymptotic Critical Values (10% 5% 1%)
## Joint Statistic: 0.846 1.01 1.35
## Individual Statistic: 0.35 0.47 0.75
##
##
## Elapsed time : 0.0407021
##
##
## $rank.matrix
## ar1 ar2 ma1 ma2 im arf AIC converged
## 1 1 0 1 0 0 0 -6.039006 1
## 2 1 1 0 0 0 0 -6.038796 1
## 3 1 0 0 1 0 0 -6.038751 1
## 4 1 0 1 0 1 0 -6.038751 1
## 5 0 1 1 0 0 0 -6.038745 1
## 6 0 0 1 1 0 0 -6.038680 1
## 7 1 1 0 0 1 0 -6.038555 1
## 8 1 0 0 1 1 0 -6.038513 1
## 9 0 1 1 0 1 0 -6.038507 1
## 10 0 0 1 1 1 0 -6.038444 1
## 11 1 0 1 1 0 0 -6.038377 1
## 12 0 1 1 1 0 0 -6.038376 1
## 13 1 1 0 1 0 0 -6.038372 1
## 14 1 1 1 0 0 0 -6.038362 1
## 15 1 0 0 0 0 0 -6.038138 1
## 16 1 0 1 1 1 0 -6.038106 1
## 17 1 1 1 0 1 0 -6.038106 1
## 18 1 1 0 1 1 0 -6.038104 1
## 19 0 1 1 1 1 0 -6.038093 1
## 20 1 0 0 0 1 0 -6.037921 1
## 21 1 1 1 1 0 0 -6.037762 1
## 22 0 0 1 0 0 0 -6.037732 1
## 23 0 0 1 0 1 0 -6.037523 1
## 24 1 1 1 1 1 0 -6.037490 1
## 25 0 1 0 0 0 0 -6.034190 1
## 26 0 0 0 1 0 0 -6.034136 1
## 27 0 1 0 0 1 0 -6.034000 1
## 28 0 0 0 1 1 0 -6.033949 1
## 29 0 1 0 1 0 0 -6.033793 1
## 30 0 1 0 1 1 0 -6.033511 1
## 31 0 0 0 0 1 0 -6.032901 1
autoarfima(data$SSEC,ar.max = 2, ma.max = 2, criterion = "AIC", method = "full")
## $fit
##
## *----------------------------------*
## * ARFIMA Model Fit *
## *----------------------------------*
## Mean Model : ARFIMA(2,0,2)
## Distribution : norm
##
## Optimal Parameters
## ------------------------------------
## Estimate Std. Error t value Pr(>|t|)
## ar1 0.055330 0.010194 5.4277 0.0e+00
## ar2 -0.972436 0.002295 -423.7588 0.0e+00
## ma1 -0.053427 0.013354 -4.0008 6.3e-05
## ma2 0.948445 0.005113 185.5076 0.0e+00
## sigma 0.012889 0.000160 80.5927 0.0e+00
##
## Robust Standard Errors:
## Estimate Std. Error t value Pr(>|t|)
## ar1 0.055330 0.013421 4.1227 0.000037
## ar2 -0.972436 0.009306 -104.4906 0.000000
## ma1 -0.053427 0.014313 -3.7328 0.000189
## ma2 0.948445 0.005183 182.9968 0.000000
## sigma 0.012889 0.000614 20.9895 0.000000
##
## LogLikelihood : 9521.575
##
## Information Criteria
## ------------------------------------
##
## Akaike -5.8618
## Bayes -5.8524
## Shibata -5.8618
## Hannan-Quinn -5.8584
##
## Weighted Ljung-Box Test on Standardized Residuals
## ------------------------------------
## statistic p-value
## Lag[1] 2.652 1.034e-01
## Lag[2*(p+q)+(p+q)-1][11] 9.321 9.584e-07
## Lag[4*(p+q)+(p+q)-1][19] 15.542 1.912e-02
##
## H0 : No serial correlation
##
## Weighted Ljung-Box Test on Standardized Squared Residuals
## ------------------------------------
## statistic p-value
## Lag[1] 123.5 0
## Lag[2*(p+q)+(p+q)-1][2] 195.7 0
## Lag[4*(p+q)+(p+q)-1][5] 382.2 0
##
##
## ARCH LM Tests
## ------------------------------------
## Statistic DoF P-Value
## ARCH Lag[2] 223.9 2 0
## ARCH Lag[5] 335.6 5 0
## ARCH Lag[10] 367.5 10 0
##
## Nyblom stability test
## ------------------------------------
## Joint Statistic: 3.1208
## Individual Statistics:
## ar1 0.09109
## ar2 0.19221
## ma1 0.12047
## ma2 0.21339
## sigma 2.79648
##
## Asymptotic Critical Values (10% 5% 1%)
## Joint Statistic: 1.28 1.47 1.88
## Individual Statistic: 0.35 0.47 0.75
##
##
## Elapsed time : 0.09556103
##
##
## $rank.matrix
## ar1 ar2 ma1 ma2 im arf AIC converged
## 1 1 1 1 1 0 0 -5.861765 1
## 2 1 1 1 1 1 0 -5.861153 1
## 3 1 1 0 1 0 0 -5.860945 1
## 4 0 1 1 1 0 0 -5.860351 1
## 5 1 1 0 1 1 0 -5.860333 1
## 6 0 1 1 1 1 0 -5.859739 1
## 7 0 1 0 1 0 0 -5.859656 1
## 8 0 1 0 1 1 0 -5.859044 1
## 9 1 0 1 0 0 0 -5.855938 1
## 10 1 0 1 0 1 0 -5.855326 1
## 11 0 1 1 0 0 0 -5.854481 1
## 12 1 1 0 0 0 0 -5.854460 1
## 13 0 0 1 1 0 0 -5.854454 1
## 14 0 0 1 0 0 0 -5.854276 1
## 15 1 0 0 0 0 0 -5.854221 1
## 16 0 1 0 0 0 0 -5.854136 1
## 17 0 0 0 1 0 0 -5.854091 1
## 18 1 0 0 1 0 0 -5.853994 1
## 19 1 1 1 0 0 0 -5.853904 1
## 20 0 1 1 0 1 0 -5.853869 1
## 21 1 1 0 0 1 0 -5.853848 1
## 22 0 0 1 1 1 0 -5.853841 1
## 23 1 0 1 1 0 0 -5.853832 1
## 24 1 0 0 1 1 0 -5.853821 1
## 25 0 0 1 0 1 0 -5.853663 1
## 26 1 0 0 0 1 0 -5.853608 1
## 27 0 1 0 0 1 0 -5.853524 1
## 28 0 0 0 1 1 0 -5.853479 1
## 29 0 0 0 0 1 0 -5.853338 1
## 30 1 1 1 0 1 0 -5.853286 1
## 31 1 0 1 1 1 0 -5.853245 1
CÁC DẠNG MÔ HÌNH CHO CHUỖI VNI
GJR-GARCH(11)VNI
vni.garch11n.spec <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(1, 1)), mean.model = list(armaOrder = c(2, 2), include.mean = TRUE), distribution.model = "norm")
vni.garch11n.fit <- ugarchfit(spec = vni.garch11n.spec, data = data$VNI)
vni.garch11t.spec <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(1, 1)), mean.model = list(armaOrder = c(2, 2), include.mean = TRUE), distribution.model = "std")
vni.garch11t.fit <- ugarchfit(spec = vni.garch11t.spec, data = data$VNI)
vni.garch11st.spec <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(1, 1)), mean.model = list(armaOrder = c(2, 2), include.mean = TRUE), distribution.model = "sstd")
vni.garch11st.fit <- ugarchfit(spec = vni.garch11st.spec, data = data$VNI)
vni.garch11g.spec <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(1, 1)), mean.model = list(armaOrder = c(2, 2), include.mean = TRUE), distribution.model = "ged")
vni.garch11g.fit <- ugarchfit(spec = vni.garch11g.spec, data = data$VNI)
vni.garch11sg.spec <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(1, 1)), mean.model = list(armaOrder = c(2, 2), include.mean = TRUE), distribution.model = "sged")
vni.garch11sg.fit <- ugarchfit(spec = vni.garch11sg.spec, data = data$VNI)
GJR-GARCH(12)VNI
vni.garch12n.spec <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(1, 2)), mean.model = list(armaOrder = c(2, 2), include.mean = TRUE), distribution.model = "norm")
vni.garch12n.fit <- ugarchfit(spec = vni.garch12n.spec, data = data$VNI)
vni.garch12t.spec <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(1, 2)), mean.model = list(armaOrder = c(2, 2), include.mean = TRUE), distribution.model = "std")
vni.garch12t.fit <- ugarchfit(spec = vni.garch12t.spec, data = data$VNI)
vni.garch12st.spec <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(1, 2)), mean.model = list(armaOrder = c(2, 2), include.mean = TRUE), distribution.model = "sstd")
vni.garch12st.fit <- ugarchfit(spec = vni.garch12st.spec, data = data$VNI)
vni.garch12g.spec <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(1, 2)), mean.model = list(armaOrder = c(2, 2), include.mean = TRUE), distribution.model = "ged")
vni.garch12g.fit <- ugarchfit(spec = vni.garch12g.spec, data = data$VNI)
vni.garch12sg.spec <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(1, 2)), mean.model = list(armaOrder = c(2, 2), include.mean = TRUE), distribution.model = "sged")
vni.garch12sg.fit <- ugarchfit(spec = vni.garch12sg.spec, data = data$VNI)
GJR-GARCH(21)VNI
vni.garch21n.spec <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(2, 1)), mean.model = list(armaOrder = c(2, 2), include.mean = TRUE), distribution.model = "norm")
vni.garch21n.fit <- ugarchfit(spec = vni.garch21n.spec, data = data$VNI)
vni.garch21t.spec <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(2, 1)), mean.model = list(armaOrder = c(2, 2), include.mean = TRUE), distribution.model = "std")
vni.garch21t.fit <- ugarchfit(spec = vni.garch21t.spec, data = data$VNI)
vni.garch21st.spec <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(2, 1)), mean.model = list(armaOrder = c(2, 2), include.mean = TRUE), distribution.model = "sstd")
vni.garch21st.fit <- ugarchfit(spec = vni.garch21st.spec, data = data$VNI)
vni.garch21g.spec <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(2, 1)), mean.model = list(armaOrder = c(2, 2), include.mean = TRUE), distribution.model = "ged")
vni.garch21g.fit <- ugarchfit(spec = vni.garch21g.spec, data = data$VNI)
vni.garch21sg.spec <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(2, 1)), mean.model = list(armaOrder = c(2, 2), include.mean = TRUE), distribution.model = "sged")
vni.garch21sg.fit <- ugarchfit(spec = vni.garch21sg.spec, data = data$VNI)
GJR-GARCH(22)VNI
vni.garch22n.spec <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(2, 2)), mean.model = list(armaOrder = c(2, 2), include.mean = TRUE), distribution.model = "norm")
vni.garch22n.fit <- ugarchfit(spec = vni.garch22n.spec, data = data$VNI)
vni.garch22t.spec <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(2, 2)), mean.model = list(armaOrder = c(2, 2), include.mean = TRUE), distribution.model = "std")
vni.garch22t.fit <- ugarchfit(spec = vni.garch22t.spec, data = data$VNI)
vni.garch22st.spec <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(2, 2)), mean.model = list(armaOrder = c(2, 2), include.mean = TRUE), distribution.model = "sstd")
vni.garch22st.fit <- ugarchfit(spec = vni.garch22st.spec, data = data$VNI)
vni.garch22g.spec <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(2, 2)), mean.model = list(armaOrder = c(2, 2), include.mean = TRUE), distribution.model = "ged")
vni.garch22g.fit <- ugarchfit(spec = vni.garch22g.spec, data = data$VNI)
vni.garch22sg.spec <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(2, 2)), mean.model = list(armaOrder = c(2, 2), include.mean = TRUE), distribution.model = "sged")
vni.garch22sg.fit <- ugarchfit(spec = vni.garch22sg.spec, data = data$VNI)
CÁC DẠNG MÔ HÌNH CHO CHUỖI SSEC
GJR-GARCH(11)SSEC
ssec.garch11n.spec <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(1, 1)), mean.model = list(armaOrder = c(2, 2), include.mean = TRUE), distribution.model = "norm")
ssec.garch11n.fit <- ugarchfit(spec = ssec.garch11n.spec, data = data$SSEC)
ssec.garch11t.spec <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(1, 1)), mean.model = list(armaOrder = c(2, 2), include.mean = TRUE), distribution.model = "std")
ssec.garch11t.fit <- ugarchfit(spec = ssec.garch11t.spec, data = data$SSEC)
ssec.garch11st.spec <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(1, 1)), mean.model = list(armaOrder = c(2, 2), include.mean = TRUE), distribution.model = "sstd")
ssec.garch11st.fit <- ugarchfit(spec = ssec.garch11st.spec, data = data$SSEC)
ssec.garch11g.spec <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(1, 1)), mean.model = list(armaOrder = c(2, 2), include.mean = TRUE), distribution.model = "ged")
ssec.garch11g.fit <- ugarchfit(spec = ssec.garch11g.spec, data = data$SSEC)
ssec.garch11sg.spec <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(1, 1)), mean.model = list(armaOrder = c(2, 2), include.mean = TRUE), distribution.model = "sged")
ssec.garch11sg.fit <- ugarchfit(spec = ssec.garch11sg.spec, data = data$SSEC)
GJR-GARCH(12)SSEC
ssec.garch12n.spec <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(1, 2)), mean.model = list(armaOrder = c(2, 2), include.mean = TRUE), distribution.model = "norm")
ssec.garch12n.fit <- ugarchfit(spec = ssec.garch12n.spec, data = data$SSEC)
ssec.garch12t.spec <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(1, 2)), mean.model = list(armaOrder = c(2, 2), include.mean = TRUE), distribution.model = "std")
ssec.garch12t.fit <- ugarchfit(spec = ssec.garch12t.spec, data = data$SSEC)
ssec.garch12st.spec <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(1, 2)),mean.model = list(armaOrder = c(2, 2), include.mean = TRUE), distribution.model = "sstd")
ssec.garch12st.fit <- ugarchfit(spec = ssec.garch12st.spec, data = data$SSEC)
ssec.garch12g.spec <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(1, 2)), mean.model = list(armaOrder = c(2, 2), include.mean = TRUE), distribution.model = "ged")
ssec.garch12g.fit <- ugarchfit(spec = ssec.garch12g.spec, data = data$SSEC)
ssec.garch12sg.spec <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(1, 2)), mean.model = list(armaOrder = c(2, 2), include.mean = TRUE), distribution.model = "sged")
ssec.garch12sg.fit <- ugarchfit(spec = ssec.garch12sg.spec, data = data$SSEC)
GJR-GARCH(21)SSEC
ssec.garch21n.spec <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(2, 1)), mean.model = list(armaOrder = c(2, 2), include.mean = TRUE), distribution.model = "norm")
ssec.garch21n.fit <- ugarchfit(spec = ssec.garch21n.spec, data = data$SSEC)
ssec.garch21t.spec <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(2, 1)), mean.model = list(armaOrder = c(2, 2), include.mean = TRUE), distribution.model = "std")
ssec.garch21t.fit <- ugarchfit(spec = ssec.garch21t.spec, data = data$SSEC)
ssec.garch21st.spec <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(2, 1)), mean.model = list(armaOrder = c(2, 2), include.mean = TRUE), distribution.model = "sstd")
ssec.garch21st.fit <- ugarchfit(spec = ssec.garch21st.spec, data = data$SSEC)
ssec.garch21g.spec <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(2, 1)), mean.model = list(armaOrder = c(2, 2), include.mean = TRUE), distribution.model = "ged")
ssec.garch21g.fit <- ugarchfit(spec = ssec.garch21g.spec, data = data$SSEC)
ssec.garch21sg.spec <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(2, 1)), mean.model = list(armaOrder = c(2, 2), include.mean = TRUE), distribution.model = "sged")
ssec.garch21sg.fit <- ugarchfit(spec = ssec.garch21sg.spec, data = data$SSEC)
GJR-GARCH(22)SSEC
ssec.garch22n.spec <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(2, 2)), mean.model = list(armaOrder = c(2, 2), include.mean = TRUE), distribution.model = "norm")
ssec.garch22n.fit <- ugarchfit(spec = ssec.garch22n.spec, data = data$SSEC)
ssec.garch22t.spec <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(2, 2)), mean.model = list(armaOrder = c(2, 2), include.mean = TRUE), distribution.model = "std")
ssec.garch22t.fit <- ugarchfit(spec = ssec.garch22t.spec, data = data$SSEC)
ssec.garch22st.spec <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(2, 2)), mean.model = list(armaOrder = c(2, 2), include.mean = TRUE), distribution.model = "sstd")
ssec.garch22st.fit <- ugarchfit(spec = ssec.garch22st.spec, data = data$SSEC)
ssec.garch22g.spec <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(2, 2)), mean.model = list(armaOrder = c(2, 2), include.mean = TRUE), distribution.model = "ged")
ssec.garch22g.fit <- ugarchfit(spec = ssec.garch22g.spec, data = data$SSEC)
ssec.garch22sg.spec <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(2, 2)), mean.model = list(armaOrder = c(2, 2), include.mean = TRUE), distribution.model = "sged")
ssec.garch22sg.fit <- ugarchfit(spec = ssec.garch22sg.spec, data = data$SSEC)
LỰA CHỌN MÔ HÌNH GJR-GARCH
VNI
vni.model.list <- list(garch11n = vni.garch11n.fit, garch11t = vni.garch11t.fit, garch11st = vni.garch11st.fit, garch11g = vni.garch11g.fit, garch11sg = vni.garch11sg.fit, garch12n = vni.garch12n.fit, garch12t = vni.garch12t.fit, garch12st = vni.garch12st.fit, garch12g = vni.garch12g.fit, garch12sg = vni.garch12sg.fit, garch21n = vni.garch21n.fit, garch21t = vni.garch21t.fit, garch21st = vni.garch21st.fit, garch21g = vni.garch21g.fit, garch21sg = vni.garch21sg.fit, garch22n = vni.garch22n.fit, garch22t = vni.garch22t.fit, garch22st = vni.garch22st.fit, garch22g =vni.garch22g.fit, garch22sg = vni.garch22sg.fit)
vni.info.mat <- sapply(vni.model.list, infocriteria)
rownames(vni.info.mat) <- rownames(infocriteria(vni.garch11n.fit))
vni.info.mat
## garch11n garch11t garch11st garch11g garch11sg garch12n
## Akaike -6.287760 -6.322286 -6.323867 -6.325813 -6.327080 -6.286958
## Bayes -6.270892 -6.303545 -6.303251 -6.307071 -6.306464 -6.268216
## Shibata -6.287775 -6.322305 -6.323890 -6.325832 -6.327103 -6.286977
## Hannan-Quinn -6.281717 -6.315572 -6.316481 -6.319099 -6.319695 -6.280244
## garch12t garch12st garch12g garch12sg garch21n garch21t
## Akaike -6.321670 -6.323251 -6.325197 -6.326464 -6.286453 -6.321109
## Bayes -6.301054 -6.300761 -6.304581 -6.303974 -6.265836 -6.298619
## Shibata -6.321693 -6.323278 -6.325220 -6.326492 -6.286475 -6.321136
## Hannan-Quinn -6.314285 -6.315194 -6.317811 -6.318407 -6.279067 -6.313052
## garch21st garch21g garch21sg garch22n garch22t garch22st
## Akaike -6.322664 -6.324633 -6.325877 -6.285905 -6.320563 -6.322093
## Bayes -6.298300 -6.302143 -6.301512 -6.263414 -6.296198 -6.295854
## Shibata -6.322696 -6.324660 -6.325908 -6.285932 -6.320595 -6.322130
## Hannan-Quinn -6.313935 -6.316576 -6.317148 -6.277847 -6.311834 -6.312693
## garch22g garch22sg
## Akaike -6.324065 -6.325293
## Bayes -6.299701 -6.299054
## Shibata -6.324097 -6.325330
## Hannan-Quinn -6.315337 -6.315893
vni.inds <- which(vni.info.mat == min(vni.info.mat), arr.ind=TRUE)
model.vni <- colnames(vni.info.mat)[vni.inds[,2]]
model.vni
## [1] "garch11sg"
SSEC
ssec.model.list <- list(garch11n = ssec.garch11n.fit, garch11t = ssec.garch11t.fit, garch11st = ssec.garch11st.fit, garch11g = ssec.garch11g.fit, garch11sg = ssec.garch11sg.fit, garch12n = ssec.garch12n.fit, garch12t = ssec.garch12t.fit, garch12st = ssec.garch12st.fit, garch12g = ssec.garch12g.fit, garch12sg = ssec.garch12sg.fit, garch21n = ssec.garch21n.fit, garch21t = ssec.garch21t.fit, garch21st = ssec.garch21st.fit, garch21g = ssec.garch21g.fit, garch21sg = ssec.garch21sg.fit, garch22n = ssec.garch22n.fit, garch22t = ssec.garch22t.fit, garch22st = ssec.garch22st.fit, garch22g =ssec.garch22g.fit, garch22sg = ssec.garch22sg.fit)
ssec.info.mat <- sapply(ssec.model.list, infocriteria)
rownames(ssec.info.mat) <- rownames(infocriteria(ssec.garch11n.fit))
ssec.info.mat
## garch11n garch11t garch11st garch11g garch11sg garch12n
## Akaike -6.145434 -6.209460 -6.210553 -6.218478 -6.216318 -6.142700
## Bayes -6.128566 -6.190718 -6.189937 -6.199736 -6.195702 -6.123958
## Shibata -6.145449 -6.209479 -6.210576 -6.218497 -6.216341 -6.142719
## Hannan-Quinn -6.139391 -6.202746 -6.203167 -6.211763 -6.208933 -6.135985
## garch12t garch12st garch12g garch12sg garch21n garch21t
## Akaike -6.208844 -6.209937 -6.217862 -6.217515 -6.144596 -6.211585
## Bayes -6.188228 -6.187447 -6.197246 -6.195024 -6.123980 -6.189094
## Shibata -6.208867 -6.209964 -6.217885 -6.217542 -6.144618 -6.211612
## Hannan-Quinn -6.201458 -6.201880 -6.210476 -6.209457 -6.137210 -6.203527
## garch21st garch21g garch21sg garch22n garch22t garch22st
## Akaike -6.209703 -6.216970 -6.219737 -6.146805 -6.209285 -6.209087
## Bayes -6.185338 -6.194480 -6.195372 -6.124315 -6.184921 -6.182848
## Shibata -6.209735 -6.216997 -6.219769 -6.146832 -6.209317 -6.209124
## Hannan-Quinn -6.200974 -6.208913 -6.211008 -6.138748 -6.200556 -6.199687
## garch22g garch22sg
## Akaike -6.216963 -6.216852
## Bayes -6.192599 -6.190614
## Shibata -6.216995 -6.216889
## Hannan-Quinn -6.208235 -6.207452
ssec.inds <- which(ssec.info.mat == min(ssec.info.mat), arr.ind=TRUE)
model.ssec <- colnames(ssec.info.mat)[ssec.inds[,2]]
model.ssec
## [1] "garch21sg"
THAM SỐ ƯỚC LƯỢNG MÔ HÌNH BIÊN PHÙ HỢP NHẤT
vni.garch11sg.fit
##
## *---------------------------------*
## * GARCH Model Fit *
## *---------------------------------*
##
## Conditional Variance Dynamics
## -----------------------------------
## GARCH Model : gjrGARCH(1,1)
## Mean Model : ARFIMA(2,0,2)
## Distribution : sged
##
## Optimal Parameters
## ------------------------------------
## Estimate Std. Error t value Pr(>|t|)
## mu -0.001023 0.000204 -5.0065 0.000001
## ar1 0.604507 0.038619 15.6529 0.000000
## ar2 0.171267 0.074060 2.3125 0.020748
## ma1 -0.524645 0.040383 -12.9919 0.000000
## ma2 -0.206374 0.079652 -2.5909 0.009571
## omega 0.000003 0.000002 1.9858 0.047058
## alpha1 0.054830 0.014738 3.7203 0.000199
## beta1 0.843936 0.019409 43.4820 0.000000
## gamma1 0.195020 0.030296 6.4372 0.000000
## skew 1.053377 0.022758 46.2858 0.000000
## shape 1.363629 0.047625 28.6328 0.000000
##
## Robust Standard Errors:
## Estimate Std. Error t value Pr(>|t|)
## mu -0.001023 0.000193 -5.2933 0.000000
## ar1 0.604507 0.013839 43.6816 0.000000
## ar2 0.171267 0.047944 3.5722 0.000354
## ma1 -0.524645 0.016129 -32.5283 0.000000
## ma2 -0.206374 0.050241 -4.1077 0.000040
## omega 0.000003 0.000005 0.6808 0.495995
## alpha1 0.054830 0.020751 2.6423 0.008234
## beta1 0.843936 0.043171 19.5485 0.000000
## gamma1 0.195020 0.040883 4.7702 0.000002
## skew 1.053377 0.023557 44.7159 0.000000
## shape 1.363629 0.051565 26.4449 0.000000
##
## LogLikelihood : 10283.01
##
## Information Criteria
## ------------------------------------
##
## Akaike -6.3271
## Bayes -6.3065
## Shibata -6.3271
## Hannan-Quinn -6.3197
##
## Weighted Ljung-Box Test on Standardized Residuals
## ------------------------------------
## statistic p-value
## Lag[1] 3.451 6.320e-02
## Lag[2*(p+q)+(p+q)-1][11] 11.315 6.791e-13
## Lag[4*(p+q)+(p+q)-1][19] 17.567 3.645e-03
## d.o.f=4
## H0 : No serial correlation
##
## Weighted Ljung-Box Test on Standardized Squared Residuals
## ------------------------------------
## statistic p-value
## Lag[1] 0.07107 0.7898
## Lag[2*(p+q)+(p+q)-1][5] 3.35014 0.3468
## Lag[4*(p+q)+(p+q)-1][9] 4.94499 0.4375
## d.o.f=2
##
## Weighted ARCH LM Tests
## ------------------------------------
## Statistic Shape Scale P-Value
## ARCH Lag[3] 0.9745 0.500 2.000 0.3235
## ARCH Lag[5] 1.5892 1.440 1.667 0.5692
## ARCH Lag[7] 2.3292 2.315 1.543 0.6479
##
## Nyblom stability test
## ------------------------------------
## Joint Statistic: 15.3688
## Individual Statistics:
## mu 0.59749
## ar1 0.45104
## ar2 0.09977
## ma1 0.50633
## ma2 0.09922
## omega 4.46470
## alpha1 0.80600
## beta1 0.66558
## gamma1 0.18355
## skew 0.24638
## shape 1.17729
##
## Asymptotic Critical Values (10% 5% 1%)
## Joint Statistic: 2.49 2.75 3.27
## Individual Statistic: 0.35 0.47 0.75
##
## Sign Bias Test
## ------------------------------------
## t-value prob sig
## Sign Bias 0.8371 0.4026
## Negative Sign Bias 1.1230 0.2615
## Positive Sign Bias 0.6554 0.5123
## Joint Effect 1.7046 0.6359
##
##
## Adjusted Pearson Goodness-of-Fit Test:
## ------------------------------------
## group statistic p-value(g-1)
## 1 20 16.28 0.6387
## 2 30 25.49 0.6523
## 3 40 36.51 0.5840
## 4 50 49.29 0.4616
##
##
## Elapsed time : 3.5702
ssec.garch21sg.fit
##
## *---------------------------------*
## * GARCH Model Fit *
## *---------------------------------*
##
## Conditional Variance Dynamics
## -----------------------------------
## GARCH Model : gjrGARCH(2,1)
## Mean Model : ARFIMA(2,0,2)
## Distribution : sged
##
## Optimal Parameters
## ------------------------------------
## Estimate Std. Error t value Pr(>|t|)
## mu -0.000284 0.000224 -1.27048 0.203914
## ar1 -0.232564 0.000432 -537.91497 0.000000
## ar2 -0.999226 0.000594 -1680.86639 0.000000
## ma1 0.234416 0.000046 5117.57624 0.000000
## ma2 1.001321 0.000046 21704.13350 0.000000
## omega 0.000001 0.000000 7.27706 0.000000
## alpha1 0.000002 0.026877 0.00007 0.999944
## alpha2 0.029599 0.025129 1.17790 0.238838
## beta1 0.923878 0.006840 135.06498 0.000000
## gamma1 0.128054 0.046361 2.76214 0.005742
## gamma2 -0.039084 0.044670 -0.87496 0.381598
## skew 1.029892 0.019657 52.39304 0.000000
## shape 1.186529 0.041651 28.48771 0.000000
##
## Robust Standard Errors:
## Estimate Std. Error t value Pr(>|t|)
## mu -0.000284 0.000312 -9.1112e-01 0.362232
## ar1 -0.232564 0.000568 -4.0932e+02 0.000000
## ar2 -0.999226 0.000658 -1.5189e+03 0.000000
## ma1 0.234416 0.000059 3.9918e+03 0.000000
## ma2 1.001321 0.000115 8.6934e+03 0.000000
## omega 0.000001 0.000001 1.9925e+00 0.046313
## alpha1 0.000002 0.031795 5.9000e-05 0.999953
## alpha2 0.029599 0.033409 8.8597e-01 0.375634
## beta1 0.923878 0.016994 5.4365e+01 0.000000
## gamma1 0.128054 0.045722 2.8007e+00 0.005099
## gamma2 -0.039084 0.042323 -9.2347e-01 0.355763
## skew 1.029892 0.023528 4.3774e+01 0.000000
## shape 1.186529 0.045771 2.5923e+01 0.000000
##
## LogLikelihood : 10110.74
##
## Information Criteria
## ------------------------------------
##
## Akaike -6.2197
## Bayes -6.1954
## Shibata -6.2198
## Hannan-Quinn -6.2110
##
## Weighted Ljung-Box Test on Standardized Residuals
## ------------------------------------
## statistic p-value
## Lag[1] 1.862e-04 9.891e-01
## Lag[2*(p+q)+(p+q)-1][11] 1.054e+01 2.606e-10
## Lag[4*(p+q)+(p+q)-1][19] 1.691e+01 6.396e-03
## d.o.f=4
## H0 : No serial correlation
##
## Weighted Ljung-Box Test on Standardized Squared Residuals
## ------------------------------------
## statistic p-value
## Lag[1] 2.473 0.1158
## Lag[2*(p+q)+(p+q)-1][8] 6.627 0.1790
## Lag[4*(p+q)+(p+q)-1][14] 10.115 0.1912
## d.o.f=3
##
## Weighted ARCH LM Tests
## ------------------------------------
## Statistic Shape Scale P-Value
## ARCH Lag[4] 0.7016 0.500 2.000 0.4022
## ARCH Lag[6] 0.8495 1.461 1.711 0.7913
## ARCH Lag[8] 2.9676 2.368 1.583 0.5495
##
## Nyblom stability test
## ------------------------------------
## Joint Statistic: 200.8615
## Individual Statistics:
## mu 0.24011
## ar1 0.02560
## ar2 0.13236
## ma1 0.02827
## ma2 0.09385
## omega 37.69238
## alpha1 0.37661
## alpha2 0.25578
## beta1 0.35111
## gamma1 0.12540
## gamma2 0.14744
## skew 0.22948
## shape 0.21914
##
## Asymptotic Critical Values (10% 5% 1%)
## Joint Statistic: 2.89 3.15 3.69
## Individual Statistic: 0.35 0.47 0.75
##
## Sign Bias Test
## ------------------------------------
## t-value prob sig
## Sign Bias 2.7983 0.005168 ***
## Negative Sign Bias 1.6403 0.101046
## Positive Sign Bias 0.2665 0.789840
## Joint Effect 10.7860 0.012941 **
##
##
## Adjusted Pearson Goodness-of-Fit Test:
## ------------------------------------
## group statistic p-value(g-1)
## 1 20 17.31 0.5688
## 2 30 20.80 0.8663
## 3 40 34.86 0.6592
## 4 50 42.70 0.7251
##
##
## Elapsed time : 21.59815
KIỂM ĐỊNH SỰ PHÙ HỢP CỦA MÔ HÌNH BIÊN
Trích xuất chuỗi phần dư u của chuỗi SSEC
ssec.res <- residuals(ssec.garch21sg.fit)/sigma(ssec.garch21sg.fit)
fitdist(distribution = "sged", ssec.res, control = list())
## $pars
## mu sigma skew shape
## 0.01288543 0.99956818 1.03815404 1.18790272
##
## $convergence
## [1] 0
##
## $values
## [1] 4607.775 4483.681 4483.681
##
## $lagrange
## [1] 0
##
## $hessian
## [,1] [,2] [,3] [,4]
## [1,] 4209.85344 -372.58321 -1881.09603 26.21724
## [2,] -372.58321 3813.08748 79.27614 554.48237
## [3,] -1881.09603 79.27614 3297.48627 -75.86870
## [4,] 26.21724 554.48237 -75.86870 675.50865
##
## $ineqx0
## NULL
##
## $nfuneval
## [1] 98
##
## $outer.iter
## [1] 2
##
## $elapsed
## Time difference of 0.377492 secs
##
## $vscale
## [1] 1 1 1 1 1
u <- pdist(distribution = "sged", q = ssec.res, mu = 0.01288543 , sigma = 0.99956818 , skew=1.03815404, shape= 1.18790272)
Trích xuất chuỗi phần dư v của chuỗi VNI
vni.res <- residuals(vni.garch11sg.fit)/sigma(vni.garch11sg.fit)
fitdist(distribution = "sged", vni.res, control = list())
## $pars
## mu sigma skew shape
## 0.02640162 1.00144379 1.06670509 1.36529700
##
## $convergence
## [1] 0
##
## $values
## [1] 4614.913 4547.547 4547.547
##
## $lagrange
## [1] 0
##
## $hessian
## [,1] [,2] [,3] [,4]
## [1,] 3618.2645 -328.64774 -794.86532 -18.95670
## [2,] -328.6477 4405.58532 -54.42895 362.63126
## [3,] -794.8653 -54.42895 2035.57203 -57.54076
## [4,] -18.9567 362.63126 -57.54076 477.28223
##
## $ineqx0
## NULL
##
## $nfuneval
## [1] 92
##
## $outer.iter
## [1] 2
##
## $elapsed
## Time difference of 0.3321469 secs
##
## $vscale
## [1] 1 1 1 1 1
v <- pdist("sged",vni.res, mu = 0.02640162, sigma = 1.00144379 , skew=1.06670509, shape = 1.36529700)
Các kiểm định sự phù hợp mô hình biên
Kiểm định Anderson-Darling (A-D)
ad.test(u, "punif")
##
## Anderson-Darling test of goodness-of-fit
## Null hypothesis: uniform distribution
## Parameters assumed to be fixed
##
## data: u
## An = 0.3015, p-value = 0.937
ad.test(v, "punif")
##
## Anderson-Darling test of goodness-of-fit
## Null hypothesis: uniform distribution
## Parameters assumed to be fixed
##
## data: v
## An = 0.44647, p-value = 0.8017
Kiểm định Cramer-von Mises (Cv-M)
cvm.test(u, "punif")
##
## Cramer-von Mises test of goodness-of-fit
## Null hypothesis: uniform distribution
## Parameters assumed to be fixed
##
## data: u
## omega2 = 0.038331, p-value = 0.9416
cvm.test(v, "punif")
##
## Cramer-von Mises test of goodness-of-fit
## Null hypothesis: uniform distribution
## Parameters assumed to be fixed
##
## data: v
## omega2 = 0.053155, p-value = 0.8569
Kiểm định Kolmogorov-Smornov (K-S).
ks.test(u, "punif")
##
## Asymptotic one-sample Kolmogorov-Smirnov test
##
## data: u
## D = 0.0094853, p-value = 0.932
## alternative hypothesis: two-sided
ks.test(v, "punif")
##
## Asymptotic one-sample Kolmogorov-Smirnov test
##
## data: v
## D = 0.011751, p-value = 0.761
## alternative hypothesis: two-sided
ƯỚC LƯỢNG THAM SỐ COUPULA
BiCopSelect(u, v, familyset= NA, selectioncrit="AIC",indeptest = FALSE, level = 0.05)
## Bivariate copula: Survival BB1 (par = 0.14, par2 = 1.04, tau = 0.1)
Stu <- BiCopEst(u, v, family = 7, method = "mle", se = T, max.df = 10)
summary(Stu)
## Family
## ------
## No: 7
## Name: BB1
##
## Parameter(s)
## ------------
## par: 0.05 (SE = 0.02)
## par2: 1.08 (SE = 0.02)
## Dependence measures
## -------------------
## Kendall's tau: 0.1 (empirical = 0.1, p value < 0.01)
## Upper TD: 0.1
## Lower TD: 0
##
## Fit statistics
## --------------
## logLik: 45.8
## AIC: -87.6
## BIC: -75.43