library(readxl)
library(rugarch)
## Warning: package 'rugarch' was built under R version 4.3.1
## Loading required package: parallel
##
## Attaching package: 'rugarch'
## The following object is masked from 'package:stats':
##
## sigma
data <- read_excel('C:/Users/Thanh Lan/Documents/Zalo Received Files/data.xlsx')
SGX <- ts(data$SGX)
MÔ HÌNH ARMA
MÔ HÌNH PHÂN PHỐI BIÊN
GJR-GARCH(11)
PHÂN PHỐI CHUẨN
sgx11n.spec <- ugarchspec(variance.model = list(model = 'gjrGARCH', garchOrder = c(1,1)), mean.model = list(armaOrder = c(2,2), include.mean = TRUE), distribution.model = 'norm')
sgx11n <- ugarchfit(spec = sgx11n.spec, SGX)
print(sgx11n)
##
## *---------------------------------*
## * GARCH Model Fit *
## *---------------------------------*
##
## Conditional Variance Dynamics
## -----------------------------------
## GARCH Model : gjrGARCH(1,1)
## Mean Model : ARFIMA(2,0,2)
## Distribution : norm
##
## Optimal Parameters
## ------------------------------------
## Estimate Std. Error t value Pr(>|t|)
## mu 7.457124 0.185189 40.26758 0.000000
## ar1 0.440084 0.011552 38.09691 0.000000
## ar2 0.558340 0.011543 48.36988 0.000000
## ma1 -0.233099 0.027542 -8.46338 0.000000
## ma2 -0.635324 0.026471 -24.00063 0.000000
## omega 0.007404 0.003168 2.33721 0.019428
## alpha1 0.135357 0.032939 4.10928 0.000040
## beta1 0.867843 0.022025 39.40305 0.000000
## gamma1 -0.008400 0.038224 -0.21976 0.826058
##
## Robust Standard Errors:
## Estimate Std. Error t value Pr(>|t|)
## mu 7.457124 0.069296 107.61301 0.000000
## ar1 0.440084 0.001471 299.14694 0.000000
## ar2 0.558340 0.001552 359.72600 0.000000
## ma1 -0.233099 0.024780 -9.40670 0.000000
## ma2 -0.635324 0.024422 -26.01407 0.000000
## omega 0.007404 0.004052 1.82728 0.067657
## alpha1 0.135357 0.042251 3.20368 0.001357
## beta1 0.867843 0.027378 31.69870 0.000000
## gamma1 -0.008400 0.041963 -0.20018 0.841341
##
## LogLikelihood : -1257.906
##
## Information Criteria
## ------------------------------------
##
## Akaike 2.5262
## Bayes 2.5703
## Shibata 2.5261
## Hannan-Quinn 2.5430
##
## Weighted Ljung-Box Test on Standardized Residuals
## ------------------------------------
## statistic p-value
## Lag[1] 1.025 3.114e-01
## Lag[2*(p+q)+(p+q)-1][11] 28.135 0.000e+00
## Lag[4*(p+q)+(p+q)-1][19] 37.801 2.749e-13
## d.o.f=4
## H0 : No serial correlation
##
## Weighted Ljung-Box Test on Standardized Squared Residuals
## ------------------------------------
## statistic p-value
## Lag[1] 3.678 0.05514
## Lag[2*(p+q)+(p+q)-1][5] 9.154 0.01513
## Lag[4*(p+q)+(p+q)-1][9] 12.452 0.01430
## d.o.f=2
##
## Weighted ARCH LM Tests
## ------------------------------------
## Statistic Shape Scale P-Value
## ARCH Lag[3] 0.8285 0.500 2.000 0.36270
## ARCH Lag[5] 7.5656 1.440 1.667 0.02552
## ARCH Lag[7] 8.6271 2.315 1.543 0.03798
##
## Nyblom stability test
## ------------------------------------
## Joint Statistic: 6.769
## Individual Statistics:
## mu 0.01906
## ar1 0.33764
## ar2 0.31787
## ma1 4.06402
## ma2 4.32469
## omega 0.29187
## alpha1 0.16606
## beta1 0.41067
## gamma1 0.22492
##
## Asymptotic Critical Values (10% 5% 1%)
## Joint Statistic: 2.1 2.32 2.82
## Individual Statistic: 0.35 0.47 0.75
##
## Sign Bias Test
## ------------------------------------
## t-value prob sig
## Sign Bias 1.9343 0.0533531 *
## Negative Sign Bias 3.6276 0.0003005 ***
## Positive Sign Bias 0.3483 0.7276795
## Joint Effect 13.2898 0.0040500 ***
##
##
## Adjusted Pearson Goodness-of-Fit Test:
## ------------------------------------
## group statistic p-value(g-1)
## 1 20 53.89 3.433e-05
## 2 30 69.01 4.132e-05
## 3 40 80.51 1.039e-04
## 4 50 88.08 5.191e-04
##
##
## Elapsed time : 0.4990029
PHÂN PHỐI STUDENT
sgx11std.spec <- ugarchspec(variance.model = list(model = 'gjrGARCH', garchOrder = c(1,1)), mean.model = list(armaOrder = c(2,2), include.mean = TRUE), distribution.model = 'std')
sgx11std <- ugarchfit(sgx11std.spec, SGX)
print(sgx11std)
##
## *---------------------------------*
## * GARCH Model Fit *
## *---------------------------------*
##
## Conditional Variance Dynamics
## -----------------------------------
## GARCH Model : gjrGARCH(1,1)
## Mean Model : ARFIMA(2,0,2)
## Distribution : std
##
## Optimal Parameters
## ------------------------------------
## Estimate Std. Error t value Pr(>|t|)
## mu 7.451364 0.183870 40.52509 0.000000
## ar1 0.441812 0.011375 38.83917 0.000000
## ar2 0.556660 0.011367 48.97258 0.000000
## ma1 -0.233484 0.027451 -8.50540 0.000000
## ma2 -0.635709 0.026522 -23.96906 0.000000
## omega 0.007053 0.003330 2.11827 0.034152
## alpha1 0.131562 0.033004 3.98631 0.000067
## beta1 0.870018 0.022605 38.48859 0.000000
## gamma1 -0.005160 0.038297 -0.13475 0.892812
## shape 99.980863 199.691326 0.50068 0.616598
##
## Robust Standard Errors:
## Estimate Std. Error t value Pr(>|t|)
## mu 7.451364 0.069266 107.57599 0.000000
## ar1 0.441812 0.001439 307.08868 0.000000
## ar2 0.556660 0.001506 369.54145 0.000000
## ma1 -0.233484 0.025120 -9.29480 0.000000
## ma2 -0.635709 0.024717 -25.71906 0.000000
## omega 0.007053 0.003810 1.85107 0.064159
## alpha1 0.131562 0.041622 3.16086 0.001573
## beta1 0.870018 0.027061 32.14969 0.000000
## gamma1 -0.005160 0.042095 -0.12259 0.902432
## shape 99.980863 197.361751 0.50659 0.612445
##
## LogLikelihood : -1257.873
##
## Information Criteria
## ------------------------------------
##
## Akaike 2.5282
## Bayes 2.5771
## Shibata 2.5280
## Hannan-Quinn 2.5468
##
## Weighted Ljung-Box Test on Standardized Residuals
## ------------------------------------
## statistic p-value
## Lag[1] 1.061 3.031e-01
## Lag[2*(p+q)+(p+q)-1][11] 27.772 0.000e+00
## Lag[4*(p+q)+(p+q)-1][19] 37.468 4.281e-13
## d.o.f=4
## H0 : No serial correlation
##
## Weighted Ljung-Box Test on Standardized Squared Residuals
## ------------------------------------
## statistic p-value
## Lag[1] 3.434 0.06385
## Lag[2*(p+q)+(p+q)-1][5] 8.922 0.01732
## Lag[4*(p+q)+(p+q)-1][9] 12.239 0.01600
## d.o.f=2
##
## Weighted ARCH LM Tests
## ------------------------------------
## Statistic Shape Scale P-Value
## ARCH Lag[3] 0.845 0.500 2.000 0.35796
## ARCH Lag[5] 7.615 1.440 1.667 0.02483
## ARCH Lag[7] 8.681 2.315 1.543 0.03693
##
## Nyblom stability test
## ------------------------------------
## Joint Statistic: 7.1407
## Individual Statistics:
## mu 0.01732
## ar1 0.34177
## ar2 0.32256
## ma1 3.98568
## ma2 4.30415
## omega 0.28756
## alpha1 0.15437
## beta1 0.39795
## gamma1 0.21056
## shape 0.86463
##
## Asymptotic Critical Values (10% 5% 1%)
## Joint Statistic: 2.29 2.54 3.05
## Individual Statistic: 0.35 0.47 0.75
##
## Sign Bias Test
## ------------------------------------
## t-value prob sig
## Sign Bias 1.9399 0.0526792 *
## Negative Sign Bias 3.6320 0.0002956 ***
## Positive Sign Bias 0.3108 0.7560199
## Joint Effect 13.2927 0.0040445 ***
##
##
## Adjusted Pearson Goodness-of-Fit Test:
## ------------------------------------
## group statistic p-value(g-1)
## 1 20 52.53 5.503e-05
## 2 30 68.42 4.979e-05
## 3 40 80.03 1.187e-04
## 4 50 84.39 1.254e-03
##
##
## Elapsed time : 0.7286642
PHÂN PHỐI ĐỐI XỨNG (sstd)
sgx11sstd.spec <- ugarchspec(variance.model = list( model = 'gjrGARCH', garchOrder = c(1,1)), mean.model = list(armaOrder = c(2,2), include.mean = TRUE), distribution.model = 'sstd')
sgx11sstd <- ugarchfit(sgx11sstd.spec, SGX)
print(sgx11sstd)
##
## *---------------------------------*
## * GARCH Model Fit *
## *---------------------------------*
##
## Conditional Variance Dynamics
## -----------------------------------
## GARCH Model : gjrGARCH(1,1)
## Mean Model : ARFIMA(2,0,2)
## Distribution : sstd
##
## Optimal Parameters
## ------------------------------------
## Estimate Std. Error t value Pr(>|t|)
## mu 7.468130 0.185786 40.197421 0.000000
## ar1 0.440705 0.011187 39.392876 0.000000
## ar2 0.557776 0.011179 49.894418 0.000000
## ma1 -0.232592 0.027415 -8.484002 0.000000
## ma2 -0.635883 0.026589 -23.915420 0.000000
## omega 0.006533 0.003241 2.015661 0.043835
## alpha1 0.126720 0.032643 3.882031 0.000104
## beta1 0.873505 0.022536 38.760304 0.000000
## gamma1 -0.002429 0.037874 -0.064136 0.948862
## skew 1.033225 0.051112 20.215093 0.000000
## shape 59.999698 60.265545 0.995589 0.319450
##
## Robust Standard Errors:
## Estimate Std. Error t value Pr(>|t|)
## mu 7.468130 0.077612 96.224040 0.000000
## ar1 0.440705 0.001405 313.563723 0.000000
## ar2 0.557776 0.001485 375.640072 0.000000
## ma1 -0.232592 0.025464 -9.134101 0.000000
## ma2 -0.635883 0.025440 -24.995334 0.000000
## omega 0.006533 0.003980 1.641362 0.100722
## alpha1 0.126720 0.042141 3.007052 0.002638
## beta1 0.873505 0.028376 30.783530 0.000000
## gamma1 -0.002429 0.041875 -0.058008 0.953742
## skew 1.033225 0.065283 15.826941 0.000000
## shape 59.999698 50.543138 1.187099 0.235189
##
## LogLikelihood : -1257.72
##
## Information Criteria
## ------------------------------------
##
## Akaike 2.5299
## Bayes 2.5837
## Shibata 2.5296
## Hannan-Quinn 2.5503
##
## Weighted Ljung-Box Test on Standardized Residuals
## ------------------------------------
## statistic p-value
## Lag[1] 1.002 3.168e-01
## Lag[2*(p+q)+(p+q)-1][11] 27.642 0.000e+00
## Lag[4*(p+q)+(p+q)-1][19] 37.337 5.086e-13
## d.o.f=4
## H0 : No serial correlation
##
## Weighted Ljung-Box Test on Standardized Squared Residuals
## ------------------------------------
## statistic p-value
## Lag[1] 3.082 0.07916
## Lag[2*(p+q)+(p+q)-1][5] 8.614 0.02070
## Lag[4*(p+q)+(p+q)-1][9] 12.004 0.01811
## d.o.f=2
##
## Weighted ARCH LM Tests
## ------------------------------------
## Statistic Shape Scale P-Value
## ARCH Lag[3] 0.952 0.500 2.000 0.32921
## ARCH Lag[5] 7.837 1.440 1.667 0.02197
## ARCH Lag[7] 8.932 2.315 1.543 0.03239
##
## Nyblom stability test
## ------------------------------------
## Joint Statistic: 8.1908
## Individual Statistics:
## mu 0.01812
## ar1 0.37272
## ar2 0.35386
## ma1 3.93863
## ma2 4.31667
## omega 0.30684
## alpha1 0.16496
## beta1 0.42673
## gamma1 0.19967
## skew 0.36882
## shape 0.75242
##
## 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 1.9674 0.0494144 **
## Negative Sign Bias 3.6534 0.0002723 ***
## Positive Sign Bias 0.2614 0.7938676
## Joint Effect 13.4181 0.0038145 ***
##
##
## Adjusted Pearson Goodness-of-Fit Test:
## ------------------------------------
## group statistic p-value(g-1)
## 1 20 60.51 3.214e-06
## 2 30 67.58 6.454e-05
## 3 40 85.45 2.532e-05
## 4 50 94.96 9.104e-05
##
##
## Elapsed time : 1.14546
PHÂN PHỐI Generalized Error Distribution (ged)
sgx11ged.spec <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(1, 1)), mean.model = list(armaOrder = c(2, 2), include.mean = TRUE), distribution.model = "ged")
sgx11ged <- ugarchfit(sgx11ged.spec, SGX)
print(sgx11ged)
##
## *---------------------------------*
## * GARCH Model Fit *
## *---------------------------------*
##
## Conditional Variance Dynamics
## -----------------------------------
## GARCH Model : gjrGARCH(1,1)
## Mean Model : ARFIMA(2,0,2)
## Distribution : ged
##
## Optimal Parameters
## ------------------------------------
## Estimate Std. Error t value Pr(>|t|)
## mu 7.450129 0.185694 40.1205 0.000000
## ar1 0.446190 0.010892 40.9631 0.000000
## ar2 0.552292 0.010883 50.7469 0.000000
## ma1 -0.236650 0.028247 -8.3779 0.000000
## ma2 -0.632485 0.027481 -23.0156 0.000000
## omega 0.007304 0.003257 2.2424 0.024937
## alpha1 0.134245 0.033214 4.0418 0.000053
## beta1 0.868427 0.022360 38.8388 0.000000
## gamma1 -0.007345 0.038575 -0.1904 0.848998
## shape 1.964972 0.155907 12.6035 0.000000
##
## Robust Standard Errors:
## Estimate Std. Error t value Pr(>|t|)
## mu 7.450129 0.082958 89.80588 0.000000
## ar1 0.446190 0.001428 312.37016 0.000000
## ar2 0.552292 0.001451 380.51540 0.000000
## ma1 -0.236650 0.029336 -8.06693 0.000000
## ma2 -0.632485 0.027882 -22.68462 0.000000
## omega 0.007304 0.003845 1.89970 0.057472
## alpha1 0.134245 0.041649 3.22325 0.001267
## beta1 0.868427 0.026828 32.37016 0.000000
## gamma1 -0.007345 0.041535 -0.17683 0.859642
## shape 1.964972 0.244869 8.02459 0.000000
##
## LogLikelihood : -1257.882
##
## Information Criteria
## ------------------------------------
##
## Akaike 2.5282
## Bayes 2.5771
## Shibata 2.5280
## Hannan-Quinn 2.5468
##
## Weighted Ljung-Box Test on Standardized Residuals
## ------------------------------------
## statistic p-value
## Lag[1] 1.146 2.845e-01
## Lag[2*(p+q)+(p+q)-1][11] 27.889 0.000e+00
## Lag[4*(p+q)+(p+q)-1][19] 37.552 3.828e-13
## d.o.f=4
## H0 : No serial correlation
##
## Weighted Ljung-Box Test on Standardized Squared Residuals
## ------------------------------------
## statistic p-value
## Lag[1] 3.631 0.05670
## Lag[2*(p+q)+(p+q)-1][5] 9.101 0.01561
## Lag[4*(p+q)+(p+q)-1][9] 12.390 0.01477
## d.o.f=2
##
## Weighted ARCH LM Tests
## ------------------------------------
## Statistic Shape Scale P-Value
## ARCH Lag[3] 0.8196 0.500 2.000 0.36530
## ARCH Lag[5] 7.5451 1.440 1.667 0.02581
## ARCH Lag[7] 8.6056 2.315 1.543 0.03840
##
## Nyblom stability test
## ------------------------------------
## Joint Statistic: 7.7851
## Individual Statistics:
## mu 0.01724
## ar1 0.33295
## ar2 0.31433
## ma1 3.98457
## ma2 4.30822
## omega 0.29189
## alpha1 0.16291
## beta1 0.40872
## gamma1 0.22023
## shape 1.61476
##
## Asymptotic Critical Values (10% 5% 1%)
## Joint Statistic: 2.29 2.54 3.05
## Individual Statistic: 0.35 0.47 0.75
##
## Sign Bias Test
## ------------------------------------
## t-value prob sig
## Sign Bias 1.9318 0.0536712 *
## Negative Sign Bias 3.6246 0.0003041 ***
## Positive Sign Bias 0.3383 0.7351960
## Joint Effect 13.2594 0.0041079 ***
##
##
## Adjusted Pearson Goodness-of-Fit Test:
## ------------------------------------
## group statistic p-value(g-1)
## 1 20 52.65 0.0000528
## 2 30 66.80 0.0000820
## 3 40 77.96 0.0002102
## 4 50 84.79 0.0011423
##
##
## Elapsed time : 0.6841369
PHÂN PHỐI Generalized Error Distribution đối xứng (sged)
sgx11sged.spec <- ugarchspec(variance.model = list(model = 'gjrGARCH', garchOrder = c(1,1)), mean.model = list(armaOrder = c(2,2), include.mean = TRUE), distribution.model = 'sged')
sgx11sged <- ugarchfit(sgx11sged.spec, SGX)
print(sgx11sged)
##
## *---------------------------------*
## * 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 7.479284 0.193380 38.6766 0.000000
## ar1 0.437060 0.011776 37.1143 0.000000
## ar2 0.561287 0.011762 47.7203 0.000000
## ma1 -0.231529 0.028774 -8.0465 0.000000
## ma2 -0.635473 0.028331 -22.4304 0.000000
## omega 0.007083 0.003174 2.2320 0.025618
## alpha1 0.132688 0.033223 3.9938 0.000065
## beta1 0.870030 0.022094 39.3782 0.000000
## gamma1 -0.007368 0.038615 -0.1908 0.848683
## skew 1.034831 0.054037 19.1503 0.000000
## shape 2.004837 0.169221 11.8475 0.000000
##
## Robust Standard Errors:
## Estimate Std. Error t value Pr(>|t|)
## mu 7.479284 0.120130 62.25998 0.000000
## ar1 0.437060 0.001663 262.78561 0.000000
## ar2 0.561287 0.001582 354.85029 0.000000
## ma1 -0.231529 0.031763 -7.28931 0.000000
## ma2 -0.635473 0.031407 -20.23329 0.000000
## omega 0.007083 0.003922 1.80597 0.070923
## alpha1 0.132688 0.043095 3.07893 0.002077
## beta1 0.870030 0.028042 31.02632 0.000000
## gamma1 -0.007368 0.042143 -0.17482 0.861218
## skew 1.034831 0.084597 12.23251 0.000000
## shape 2.004837 0.311243 6.44139 0.000000
##
## LogLikelihood : -1257.665
##
## Information Criteria
## ------------------------------------
##
## Akaike 2.5297
## Bayes 2.5836
## Shibata 2.5295
## Hannan-Quinn 2.5502
##
## Weighted Ljung-Box Test on Standardized Residuals
## ------------------------------------
## statistic p-value
## Lag[1] 0.9288 3.352e-01
## Lag[2*(p+q)+(p+q)-1][11] 28.2920 0.000e+00
## Lag[4*(p+q)+(p+q)-1][19] 37.9374 2.295e-13
## d.o.f=4
## H0 : No serial correlation
##
## Weighted Ljung-Box Test on Standardized Squared Residuals
## ------------------------------------
## statistic p-value
## Lag[1] 3.465 0.06269
## Lag[2*(p+q)+(p+q)-1][5] 8.982 0.01673
## Lag[4*(p+q)+(p+q)-1][9] 12.339 0.01518
## d.o.f=2
##
## Weighted ARCH LM Tests
## ------------------------------------
## Statistic Shape Scale P-Value
## ARCH Lag[3] 0.9332 0.500 2.000 0.33403
## ARCH Lag[5] 7.7615 1.440 1.667 0.02290
## ARCH Lag[7] 8.8515 2.315 1.543 0.03378
##
## Nyblom stability test
## ------------------------------------
## Joint Statistic: 9.0131
## Individual Statistics:
## mu 0.02248
## ar1 0.36765
## ar2 0.34753
## ma1 4.10647
## ma2 4.38003
## omega 0.31126
## alpha1 0.18307
## beta1 0.44874
## gamma1 0.22120
## skew 0.31484
## shape 1.65185
##
## 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 1.882 0.0601941 *
## Negative Sign Bias 3.605 0.0003275 ***
## Positive Sign Bias 0.357 0.7211493
## Joint Effect 13.126 0.0043715 ***
##
##
## Adjusted Pearson Goodness-of-Fit Test:
## ------------------------------------
## group statistic p-value(g-1)
## 1 20 54.69 2.595e-05
## 2 30 68.06 5.566e-05
## 3 40 78.28 1.926e-04
## 4 50 92.96 1.526e-04
##
##
## Elapsed time : 1.209277
GJR-GARCH(12)
PHÂN PHỐI CHUẨN
sgx12n.spec <- ugarchspec(variance.model = list(model = 'gjrGARCH', garchOrder = c(1,2)), mean.model = list(armaOrder = c(2,2), include.mean = TRUE), distribution.model = 'norm')
sgx12n <- ugarchfit(sgx12n.spec, SGX)
print(sgx12n)
##
## *---------------------------------*
## * GARCH Model Fit *
## *---------------------------------*
##
## Conditional Variance Dynamics
## -----------------------------------
## GARCH Model : gjrGARCH(1,2)
## Mean Model : ARFIMA(2,0,2)
## Distribution : norm
##
## Optimal Parameters
## ------------------------------------
## Estimate Std. Error t value Pr(>|t|)
## mu 7.457126 0.185189 40.26770 0.000000
## ar1 0.440086 0.011549 38.10471 0.000000
## ar2 0.558338 0.011543 48.37124 0.000000
## ma1 -0.233100 0.027526 -8.46830 0.000000
## ma2 -0.635323 0.026420 -24.04740 0.000000
## omega 0.007404 0.002752 2.69031 0.007139
## alpha1 0.135356 0.017660 7.66441 0.000000
## beta1 0.867843 0.451302 1.92297 0.054483
## beta2 0.000000 0.415438 0.00000 1.000000
## gamma1 -0.008398 0.038206 -0.21982 0.826013
##
## Robust Standard Errors:
## Estimate Std. Error t value Pr(>|t|)
## mu 7.457126 0.069181 107.79077 0.000000
## ar1 0.440086 0.001432 307.36865 0.000000
## ar2 0.558338 0.001562 357.42714 0.000000
## ma1 -0.233100 0.024866 -9.37414 0.000000
## ma2 -0.635323 0.024428 -26.00770 0.000000
## omega 0.007404 0.005129 1.44345 0.148892
## alpha1 0.135356 0.075426 1.79457 0.072722
## beta1 0.867843 0.622255 1.39467 0.163114
## beta2 0.000000 0.558997 0.00000 1.000000
## gamma1 -0.008398 0.041893 -0.20047 0.841114
##
## LogLikelihood : -1257.906
##
## Information Criteria
## ------------------------------------
##
## Akaike 2.5282
## Bayes 2.5772
## Shibata 2.5280
## Hannan-Quinn 2.5468
##
## Weighted Ljung-Box Test on Standardized Residuals
## ------------------------------------
## statistic p-value
## Lag[1] 1.025 3.114e-01
## Lag[2*(p+q)+(p+q)-1][11] 28.135 0.000e+00
## Lag[4*(p+q)+(p+q)-1][19] 37.801 2.749e-13
## d.o.f=4
## H0 : No serial correlation
##
## Weighted Ljung-Box Test on Standardized Squared Residuals
## ------------------------------------
## statistic p-value
## Lag[1] 3.678 0.05514
## Lag[2*(p+q)+(p+q)-1][8] 11.826 0.01316
## Lag[4*(p+q)+(p+q)-1][14] 15.276 0.02199
## d.o.f=3
##
## Weighted ARCH LM Tests
## ------------------------------------
## Statistic Shape Scale P-Value
## ARCH Lag[4] 8.421 0.500 2.000 0.003709
## ARCH Lag[6] 8.690 1.461 1.711 0.016117
## ARCH Lag[8] 9.761 2.368 1.583 0.025679
##
## Nyblom stability test
## ------------------------------------
## Joint Statistic: 8.4359
## Individual Statistics:
## mu 0.01906
## ar1 0.33764
## ar2 0.31788
## ma1 4.06402
## ma2 4.32470
## omega 0.29187
## alpha1 0.16606
## beta1 0.41067
## beta2 0.44070
## gamma1 0.22492
##
## Asymptotic Critical Values (10% 5% 1%)
## Joint Statistic: 2.29 2.54 3.05
## Individual Statistic: 0.35 0.47 0.75
##
## Sign Bias Test
## ------------------------------------
## t-value prob sig
## Sign Bias 1.9343 0.0533538 *
## Negative Sign Bias 3.6276 0.0003005 ***
## Positive Sign Bias 0.3483 0.7276850
## Joint Effect 13.2898 0.0040499 ***
##
##
## Adjusted Pearson Goodness-of-Fit Test:
## ------------------------------------
## group statistic p-value(g-1)
## 1 20 53.89 3.433e-05
## 2 30 69.01 4.132e-05
## 3 40 80.51 1.039e-04
## 4 50 88.08 5.191e-04
##
##
## Elapsed time : 0.337148
PHÂN PHỐI STUDENT
sgx12std.spec <- ugarchspec(variance.model = list(model = 'gjrGARCH', garchOrder = c(1,2)), mean.model = list(armaOrder = c(2,2), include.mean = TRUE), distribution.model = 'std')
sgx12std <- ugarchfit(sgx12std.spec, SGX)
print(sgx12std)
##
## *---------------------------------*
## * GARCH Model Fit *
## *---------------------------------*
##
## Conditional Variance Dynamics
## -----------------------------------
## GARCH Model : gjrGARCH(1,2)
## Mean Model : ARFIMA(2,0,2)
## Distribution : std
##
## Optimal Parameters
## ------------------------------------
## Estimate Std. Error t value Pr(>|t|)
## mu 7.450841 0.183708 40.55808 0.000000
## ar1 0.442159 0.011341 38.98774 0.000000
## ar2 0.556320 0.011335 49.07792 0.000000
## ma1 -0.233698 0.027434 -8.51857 0.000000
## ma2 -0.635576 0.026376 -24.09671 0.000000
## omega 0.007026 0.003057 2.29803 0.021560
## alpha1 0.131292 0.017294 7.59195 0.000000
## beta1 0.870203 0.475554 1.82987 0.067269
## beta2 0.000000 0.439430 0.00000 1.000000
## gamma1 -0.004989 0.038227 -0.13052 0.896155
## shape 91.818382 155.705485 0.58969 0.555397
##
## Robust Standard Errors:
## Estimate Std. Error t value Pr(>|t|)
## mu 7.450841 0.069258 107.58126 0.000000
## ar1 0.442159 0.001397 316.55632 0.000000
## ar2 0.556320 0.001507 369.13605 0.000000
## ma1 -0.233698 0.025134 -9.29797 0.000000
## ma2 -0.635576 0.024847 -25.57936 0.000000
## omega 0.007026 0.004442 1.58176 0.113704
## alpha1 0.131292 0.071911 1.82575 0.067888
## beta1 0.870203 0.627495 1.38679 0.165506
## beta2 0.000000 0.567426 0.00000 1.000000
## gamma1 -0.004989 0.041990 -0.11882 0.905415
## shape 91.818382 175.322937 0.52371 0.600480
##
## LogLikelihood : -1257.878
##
## Information Criteria
## ------------------------------------
##
## Akaike 2.5302
## Bayes 2.5840
## Shibata 2.5299
## Hannan-Quinn 2.5506
##
## Weighted Ljung-Box Test on Standardized Residuals
## ------------------------------------
## statistic p-value
## Lag[1] 1.065 3.021e-01
## Lag[2*(p+q)+(p+q)-1][11] 27.743 0.000e+00
## Lag[4*(p+q)+(p+q)-1][19] 37.440 4.439e-13
## d.o.f=4
## H0 : No serial correlation
##
## Weighted Ljung-Box Test on Standardized Squared Residuals
## ------------------------------------
## statistic p-value
## Lag[1] 3.416 0.06458
## Lag[2*(p+q)+(p+q)-1][8] 11.595 0.01492
## Lag[4*(p+q)+(p+q)-1][14] 15.072 0.02417
## d.o.f=3
##
## Weighted ARCH LM Tests
## ------------------------------------
## Statistic Shape Scale P-Value
## ARCH Lag[4] 8.470 0.500 2.000 0.003611
## ARCH Lag[6] 8.747 1.461 1.711 0.015626
## ARCH Lag[8] 9.829 2.368 1.583 0.024798
##
## Nyblom stability test
## ------------------------------------
## Joint Statistic: 8.8917
## Individual Statistics:
## mu 0.01712
## ar1 0.34145
## ar2 0.32229
## ma1 3.97997
## ma2 4.30068
## omega 0.28759
## alpha1 0.15384
## beta1 0.39748
## beta2 0.42556
## gamma1 0.20944
## shape 0.85952
##
## 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 1.9404 0.0526111 *
## Negative Sign Bias 3.6318 0.0002958 ***
## Positive Sign Bias 0.3079 0.7582233
## Joint Effect 13.2894 0.0040509 ***
##
##
## Adjusted Pearson Goodness-of-Fit Test:
## ------------------------------------
## group statistic p-value(g-1)
## 1 20 52.57 5.428e-05
## 2 30 67.46 6.697e-05
## 3 40 79.79 1.269e-04
## 4 50 88.38 4.825e-04
##
##
## Elapsed time : 1.182771
PHÂN PHỐI ĐỐI XỨNG (sstd)
sgx12sstd.spec <- ugarchspec(variance.model = list( model = 'gjrGARCH', garchOrder = c(1,2)), mean.model = list(armaOrder = c(2,2), include.mean = TRUE), distribution.model = 'sstd')
sgx12sstd <- ugarchfit(sgx12sstd.spec, SGX)
print(sgx12sstd)
##
## *---------------------------------*
## * GARCH Model Fit *
## *---------------------------------*
##
## Conditional Variance Dynamics
## -----------------------------------
## GARCH Model : gjrGARCH(1,2)
## Mean Model : ARFIMA(2,0,2)
## Distribution : sstd
##
## Optimal Parameters
## ------------------------------------
## Estimate Std. Error t value Pr(>|t|)
## mu 7.468148 0.185662 40.224394 0.000000
## ar1 0.440718 0.011182 39.412714 0.000000
## ar2 0.557763 0.011178 49.899587 0.000000
## ma1 -0.232602 0.027408 -8.486502 0.000000
## ma2 -0.635873 0.026501 -23.994456 0.000000
## omega 0.006533 0.002854 2.289132 0.022072
## alpha1 0.126724 0.028506 4.445458 0.000009
## beta1 0.873504 0.556779 1.568851 0.116683
## beta2 0.000000 0.514638 0.000001 1.000000
## gamma1 -0.002433 0.037859 -0.064269 0.948756
## skew 1.033223 0.050695 20.381176 0.000000
## shape 59.999370 58.206986 1.030793 0.302638
##
## Robust Standard Errors:
## Estimate Std. Error t value Pr(>|t|)
## mu 7.468148 0.074446 100.316088 0.00000
## ar1 0.440718 0.001391 316.915564 0.00000
## ar2 0.557763 0.001509 369.635994 0.00000
## ma1 -0.232602 0.025517 -9.115399 0.00000
## ma2 -0.635873 0.025672 -24.769546 0.00000
## omega 0.006533 0.005075 1.287210 0.19802
## alpha1 0.126724 0.088621 1.429945 0.15273
## beta1 0.873504 0.866157 1.008482 0.31322
## beta2 0.000000 0.787140 0.000000 1.00000
## gamma1 -0.002433 0.041726 -0.058312 0.95350
## skew 1.033223 0.063949 16.157099 0.00000
## shape 59.999370 60.775556 0.987229 0.32353
##
## LogLikelihood : -1257.72
##
## Information Criteria
## ------------------------------------
##
## Akaike 2.5318
## Bayes 2.5906
## Shibata 2.5316
## Hannan-Quinn 2.5542
##
## Weighted Ljung-Box Test on Standardized Residuals
## ------------------------------------
## statistic p-value
## Lag[1] 1.002 3.168e-01
## Lag[2*(p+q)+(p+q)-1][11] 27.642 0.000e+00
## Lag[4*(p+q)+(p+q)-1][19] 37.337 5.086e-13
## d.o.f=4
## H0 : No serial correlation
##
## Weighted Ljung-Box Test on Standardized Squared Residuals
## ------------------------------------
## statistic p-value
## Lag[1] 3.082 0.07914
## Lag[2*(p+q)+(p+q)-1][8] 11.362 0.01692
## Lag[4*(p+q)+(p+q)-1][14] 14.895 0.02624
## d.o.f=3
##
## Weighted ARCH LM Tests
## ------------------------------------
## Statistic Shape Scale P-Value
## ARCH Lag[4] 8.606 0.500 2.000 0.003351
## ARCH Lag[6] 8.903 1.461 1.711 0.014364
## ARCH Lag[8] 10.009 2.368 1.583 0.022615
##
## Nyblom stability test
## ------------------------------------
## Joint Statistic: 9.9764
## Individual Statistics:
## mu 0.01812
## ar1 0.37274
## ar2 0.35388
## ma1 3.93859
## ma2 4.31659
## omega 0.30685
## alpha1 0.16498
## beta1 0.42674
## beta2 0.45606
## gamma1 0.19968
## skew 0.36883
## shape 0.75242
##
## Asymptotic Critical Values (10% 5% 1%)
## Joint Statistic: 2.69 2.96 3.51
## Individual Statistic: 0.35 0.47 0.75
##
## Sign Bias Test
## ------------------------------------
## t-value prob sig
## Sign Bias 1.9674 0.0494122 **
## Negative Sign Bias 3.6534 0.0002722 ***
## Positive Sign Bias 0.2614 0.7938308
## Joint Effect 13.4182 0.0038142 ***
##
##
## Adjusted Pearson Goodness-of-Fit Test:
## ------------------------------------
## group statistic p-value(g-1)
## 1 20 60.51 3.214e-06
## 2 30 67.58 6.454e-05
## 3 40 85.45 2.532e-05
## 4 50 94.96 9.104e-05
##
##
## Elapsed time : 1.163599
PHÂN PHỐI Generalized Error Distribution (ged)
sgx12ged.spec <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(1,2)), mean.model = list(armaOrder = c(2,2), include.mean = TRUE), distribution.model = "ged")
sgx12ged <- ugarchfit(sgx12ged.spec, SGX)
print(sgx12ged)
##
## *---------------------------------*
## * GARCH Model Fit *
## *---------------------------------*
##
## Conditional Variance Dynamics
## -----------------------------------
## GARCH Model : gjrGARCH(1,2)
## Mean Model : ARFIMA(2,0,2)
## Distribution : ged
##
## Optimal Parameters
## ------------------------------------
## Estimate Std. Error t value Pr(>|t|)
## mu 7.450117 0.185474 40.16804 0.000000
## ar1 0.446186 0.010889 40.97465 0.000000
## ar2 0.552295 0.010883 50.74865 0.000000
## ma1 -0.236647 0.028208 -8.38942 0.000000
## ma2 -0.632488 0.027159 -23.28850 0.000000
## omega 0.007304 0.002986 2.44622 0.014436
## alpha1 0.134245 0.011730 11.44448 0.000000
## beta1 0.868427 0.441689 1.96615 0.049281
## beta2 0.000000 0.407592 0.00000 1.000000
## gamma1 -0.007344 0.038574 -0.19039 0.849003
## shape 1.964968 0.147686 13.30504 0.000000
##
## Robust Standard Errors:
## Estimate Std. Error t value Pr(>|t|)
## mu 7.450117 0.085149 87.49466 0.00000
## ar1 0.446186 0.001376 324.21688 0.00000
## ar2 0.552295 0.001452 380.29404 0.00000
## ma1 -0.236647 0.029122 -8.12610 0.00000
## ma2 -0.632488 0.027889 -22.67881 0.00000
## omega 0.007304 0.004508 1.62038 0.10515
## alpha1 0.134245 0.068476 1.96047 0.04994
## beta1 0.868427 0.562975 1.54257 0.12294
## beta2 0.000000 0.507291 0.00000 1.00000
## gamma1 -0.007344 0.041582 -0.17662 0.85981
## shape 1.964968 0.247040 7.95406 0.00000
##
## LogLikelihood : -1257.882
##
## Information Criteria
## ------------------------------------
##
## Akaike 2.5302
## Bayes 2.5840
## Shibata 2.5299
## Hannan-Quinn 2.5506
##
## Weighted Ljung-Box Test on Standardized Residuals
## ------------------------------------
## statistic p-value
## Lag[1] 1.146 2.845e-01
## Lag[2*(p+q)+(p+q)-1][11] 27.889 0.000e+00
## Lag[4*(p+q)+(p+q)-1][19] 37.552 3.828e-13
## d.o.f=4
## H0 : No serial correlation
##
## Weighted Ljung-Box Test on Standardized Squared Residuals
## ------------------------------------
## statistic p-value
## Lag[1] 3.631 0.05670
## Lag[2*(p+q)+(p+q)-1][8] 11.766 0.01360
## Lag[4*(p+q)+(p+q)-1][14] 15.211 0.02267
## d.o.f=3
##
## Weighted ARCH LM Tests
## ------------------------------------
## Statistic Shape Scale P-Value
## ARCH Lag[4] 8.407 0.500 2.000 0.003739
## ARCH Lag[6] 8.679 1.461 1.711 0.016208
## ARCH Lag[8] 9.740 2.368 1.583 0.025960
##
## Nyblom stability test
## ------------------------------------
## Joint Statistic: 9.4699
## Individual Statistics:
## mu 0.01724
## ar1 0.33296
## ar2 0.31434
## ma1 3.98450
## ma2 4.30820
## omega 0.29188
## alpha1 0.16291
## beta1 0.40871
## beta2 0.43848
## gamma1 0.22023
## shape 1.61476
##
## 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 1.9318 0.0536712 *
## Negative Sign Bias 3.6246 0.0003041 ***
## Positive Sign Bias 0.3383 0.7351983
## Joint Effect 13.2594 0.0041079 ***
##
##
## Adjusted Pearson Goodness-of-Fit Test:
## ------------------------------------
## group statistic p-value(g-1)
## 1 20 52.65 0.0000528
## 2 30 66.80 0.0000820
## 3 40 77.96 0.0002102
## 4 50 84.79 0.0011423
##
##
## Elapsed time : 0.6698198
PHÂN PHỐI Generalized Error Distribution đối xứng (sged)
sgx12sged.spec <- ugarchspec(variance.model = list(model = 'gjrGARCH', garchOrder = c(1,2)), mean.model = list(armaOrder = c(2,2), include.mean = TRUE), distribution.model = 'sged')
sgx12sged <- ugarchfit(sgx12sged.spec, SGX)
print(sgx12sged)
##
## *---------------------------------*
## * GARCH Model Fit *
## *---------------------------------*
##
## Conditional Variance Dynamics
## -----------------------------------
## GARCH Model : gjrGARCH(1,2)
## Mean Model : ARFIMA(2,0,2)
## Distribution : sged
##
## Optimal Parameters
## ------------------------------------
## Estimate Std. Error t value Pr(>|t|)
## mu 7.479288 0.193147 38.72325 0.000000
## ar1 0.437065 0.011771 37.13150 0.000000
## ar2 0.561283 0.011762 47.72125 0.000000
## ma1 -0.231532 0.028736 -8.05709 0.000000
## ma2 -0.635469 0.027987 -22.70605 0.000000
## omega 0.007083 0.002885 2.45550 0.014069
## alpha1 0.132688 0.014217 9.33334 0.000000
## beta1 0.870030 0.452961 1.92076 0.054762
## beta2 0.000000 0.418031 0.00000 1.000000
## gamma1 -0.007368 0.038614 -0.19081 0.848678
## skew 1.034831 0.054026 19.15441 0.000000
## shape 2.004836 0.159883 12.53943 0.000000
##
## Robust Standard Errors:
## Estimate Std. Error t value Pr(>|t|)
## mu 7.479288 0.122805 60.90353 0.00000
## ar1 0.437065 0.001604 272.47654 0.00000
## ar2 0.561283 0.001585 354.22740 0.00000
## ma1 -0.231532 0.031594 -7.32844 0.00000
## ma2 -0.635469 0.031619 -20.09782 0.00000
## omega 0.007083 0.004650 1.52338 0.12766
## alpha1 0.132688 0.072499 1.83020 0.06722
## beta1 0.870030 0.599006 1.45246 0.14638
## beta2 0.000000 0.539804 0.00000 1.00000
## gamma1 -0.007368 0.042169 -0.17472 0.86130
## skew 1.034831 0.084785 12.20533 0.00000
## shape 2.004836 0.316736 6.32968 0.00000
##
## LogLikelihood : -1257.665
##
## Information Criteria
## ------------------------------------
##
## Akaike 2.5317
## Bayes 2.5905
## Shibata 2.5315
## Hannan-Quinn 2.5541
##
## Weighted Ljung-Box Test on Standardized Residuals
## ------------------------------------
## statistic p-value
## Lag[1] 0.9288 3.352e-01
## Lag[2*(p+q)+(p+q)-1][11] 28.2920 0.000e+00
## Lag[4*(p+q)+(p+q)-1][19] 37.9373 2.295e-13
## d.o.f=4
## H0 : No serial correlation
##
## Weighted Ljung-Box Test on Standardized Squared Residuals
## ------------------------------------
## statistic p-value
## Lag[1] 3.465 0.06269
## Lag[2*(p+q)+(p+q)-1][8] 11.704 0.01407
## Lag[4*(p+q)+(p+q)-1][14] 15.195 0.02283
## d.o.f=3
##
## Weighted ARCH LM Tests
## ------------------------------------
## Statistic Shape Scale P-Value
## ARCH Lag[4] 8.535 0.500 2.000 0.003484
## ARCH Lag[6] 8.820 1.461 1.711 0.015025
## ARCH Lag[8] 9.909 2.368 1.583 0.023800
##
## Nyblom stability test
## ------------------------------------
## Joint Statistic: 10.7265
## Individual Statistics:
## mu 0.02248
## ar1 0.36765
## ar2 0.34753
## ma1 4.10648
## ma2 4.38002
## omega 0.31126
## alpha1 0.18307
## beta1 0.44874
## beta2 0.48159
## gamma1 0.22120
## skew 0.31484
## shape 1.65185
##
## Asymptotic Critical Values (10% 5% 1%)
## Joint Statistic: 2.69 2.96 3.51
## Individual Statistic: 0.35 0.47 0.75
##
## Sign Bias Test
## ------------------------------------
## t-value prob sig
## Sign Bias 1.882 0.0601937 *
## Negative Sign Bias 3.605 0.0003275 ***
## Positive Sign Bias 0.357 0.7211474
## Joint Effect 13.126 0.0043714 ***
##
##
## Adjusted Pearson Goodness-of-Fit Test:
## ------------------------------------
## group statistic p-value(g-1)
## 1 20 54.69 2.595e-05
## 2 30 68.06 5.566e-05
## 3 40 78.28 1.926e-04
## 4 50 92.96 1.526e-04
##
##
## Elapsed time : 1.526122
GJR-GARCH(21)
PHÂN PHỐI CHUẨN
sgx21n.spec <- ugarchspec(variance.model = list(model = 'gjrGARCH', garchOrder = c(2,1)), mean.model = list(armaOrder = c(2,2), include.mean = TRUE), distribution.model = 'norm')
sgx21n <- ugarchfit(sgx21n.spec, SGX)
print(sgx21n)
##
## *---------------------------------*
## * GARCH Model Fit *
## *---------------------------------*
##
## Conditional Variance Dynamics
## -----------------------------------
## GARCH Model : gjrGARCH(2,1)
## Mean Model : ARFIMA(2,0,2)
## Distribution : norm
##
## Optimal Parameters
## ------------------------------------
## Estimate Std. Error t value Pr(>|t|)
## mu 7.409277 0.135438 5.4706e+01 0.00000
## ar1 0.457257 0.010445 4.3776e+01 0.00000
## ar2 0.540432 0.004878 1.1080e+02 0.00000
## ma1 -0.242441 0.040632 -5.9668e+00 0.00000
## ma2 -0.623333 0.078023 -7.9890e+00 0.00000
## omega 0.007952 0.000298 2.6687e+01 0.00000
## alpha1 0.090683 0.002847 3.1856e+01 0.00000
## alpha2 0.000000 0.011334 1.7000e-05 0.99999
## beta1 0.882426 0.000050 1.7488e+04 0.00000
## gamma1 -0.209070 0.018021 -1.1601e+01 0.00000
## gamma2 0.259791 0.021214 1.2246e+01 0.00000
##
## Robust Standard Errors:
## Estimate Std. Error t value Pr(>|t|)
## mu 7.409277 0.482333 15.361336 0.000000
## ar1 0.457257 0.043226 10.578202 0.000000
## ar2 0.540432 0.023382 23.113535 0.000000
## ma1 -0.242441 0.180528 -1.342955 0.179286
## ma2 -0.623333 0.314488 -1.982055 0.047473
## omega 0.007952 0.003611 2.202075 0.027660
## alpha1 0.090683 0.033331 2.720655 0.006515
## alpha2 0.000000 0.038743 0.000005 0.999996
## beta1 0.882426 0.000117 7511.282693 0.000000
## gamma1 -0.209070 0.020212 -10.343891 0.000000
## gamma2 0.259791 0.036047 7.207023 0.000000
##
## LogLikelihood : -1249.185
##
## Information Criteria
## ------------------------------------
##
## Akaike 2.5128
## Bayes 2.5667
## Shibata 2.5126
## Hannan-Quinn 2.5333
##
## Weighted Ljung-Box Test on Standardized Residuals
## ------------------------------------
## statistic p-value
## Lag[1] 0.904 3.417e-01
## Lag[2*(p+q)+(p+q)-1][11] 24.385 0.000e+00
## Lag[4*(p+q)+(p+q)-1][19] 33.963 4.131e-11
## d.o.f=4
## H0 : No serial correlation
##
## Weighted Ljung-Box Test on Standardized Squared Residuals
## ------------------------------------
## statistic p-value
## Lag[1] 1.559 0.21184
## Lag[2*(p+q)+(p+q)-1][8] 10.729 0.02372
## Lag[4*(p+q)+(p+q)-1][14] 15.664 0.01834
## d.o.f=3
##
## Weighted ARCH LM Tests
## ------------------------------------
## Statistic Shape Scale P-Value
## ARCH Lag[4] 8.739 0.500 2.000 0.003115
## ARCH Lag[6] 9.248 1.461 1.711 0.011920
## ARCH Lag[8] 12.296 2.368 1.583 0.006816
##
## Nyblom stability test
## ------------------------------------
## Joint Statistic: 6.8514
## Individual Statistics:
## mu 0.03081
## ar1 0.29252
## ar2 0.25877
## ma1 3.46303
## ma2 3.63152
## omega 0.28628
## alpha1 0.06594
## alpha2 0.16258
## beta1 0.35314
## gamma1 0.12787
## gamma2 0.23233
##
## 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 1.6171 0.1062
## Negative Sign Bias 0.7976 0.4253
## Positive Sign Bias 0.2712 0.7863
## Joint Effect 3.2480 0.3549
##
##
## Adjusted Pearson Goodness-of-Fit Test:
## ------------------------------------
## group statistic p-value(g-1)
## 1 20 93.65 7.434e-12
## 2 30 85.11 2.023e-07
## 3 40 112.89 4.125e-09
## 4 50 124.27 1.813e-08
##
##
## Elapsed time : 0.5286181
PHÂN PHỐI STUDENT
sgx21std.spec <- ugarchspec(variance.model = list(model = 'gjrGARCH', garchOrder = c(2,1)), mean.model = list(armaOrder = c(2,2), include.mean = TRUE), distribution.model = 'std')
sgx21std <- ugarchfit(sgx21std.spec, SGX)
print(sgx21std)
##
## *---------------------------------*
## * GARCH Model Fit *
## *---------------------------------*
##
## Conditional Variance Dynamics
## -----------------------------------
## GARCH Model : gjrGARCH(2,1)
## Mean Model : ARFIMA(2,0,2)
## Distribution : std
##
## Optimal Parameters
## ------------------------------------
## Estimate Std. Error t value Pr(>|t|)
## mu 7.421743 0.172987 42.90358 0.000000
## ar1 0.450276 0.007514 59.92324 0.000000
## ar2 0.548180 0.007505 73.03737 0.000000
## ma1 -0.238192 0.025547 -9.32382 0.000000
## ma2 -0.630331 0.025043 -25.17004 0.000000
## omega 0.009064 0.004132 2.19343 0.028276
## alpha1 0.122662 0.061718 1.98747 0.046871
## alpha2 0.011505 0.080309 0.14325 0.886089
## beta1 0.848661 0.030611 27.72379 0.000000
## gamma1 -0.118465 0.063155 -1.87577 0.060686
## gamma2 0.150808 0.082101 1.83686 0.066231
## shape 98.192315 161.053787 0.60969 0.542070
##
## Robust Standard Errors:
## Estimate Std. Error t value Pr(>|t|)
## mu 7.421743 0.066276 111.98172 0.000000
## ar1 0.450276 0.001154 390.21262 0.000000
## ar2 0.548180 0.001229 445.98629 0.000000
## ma1 -0.238192 0.025244 -9.43540 0.000000
## ma2 -0.630331 0.024963 -25.25109 0.000000
## omega 0.009064 0.005129 1.76728 0.077182
## alpha1 0.122662 0.067482 1.81771 0.069109
## alpha2 0.011505 0.101705 0.11312 0.909937
## beta1 0.848661 0.041615 20.39315 0.000000
## gamma1 -0.118465 0.076419 -1.55020 0.121094
## gamma2 0.150808 0.096897 1.55637 0.119620
## shape 98.192315 121.770693 0.80637 0.420029
##
## LogLikelihood : -1251.617
##
## Information Criteria
## ------------------------------------
##
## Akaike 2.5197
## Bayes 2.5784
## Shibata 2.5194
## Hannan-Quinn 2.5420
##
## Weighted Ljung-Box Test on Standardized Residuals
## ------------------------------------
## statistic p-value
## Lag[1] 0.8815 3.478e-01
## Lag[2*(p+q)+(p+q)-1][11] 25.4133 0.000e+00
## Lag[4*(p+q)+(p+q)-1][19] 35.3309 7.069e-12
## d.o.f=4
## H0 : No serial correlation
##
## Weighted Ljung-Box Test on Standardized Squared Residuals
## ------------------------------------
## statistic p-value
## Lag[1] 0.006643 0.9350
## Lag[2*(p+q)+(p+q)-1][8] 7.810995 0.1036
## Lag[4*(p+q)+(p+q)-1][14] 11.280854 0.1232
## d.o.f=3
##
## Weighted ARCH LM Tests
## ------------------------------------
## Statistic Shape Scale P-Value
## ARCH Lag[4] 6.971 0.500 2.000 0.008285
## ARCH Lag[6] 7.028 1.461 1.711 0.039247
## ARCH Lag[8] 8.561 2.368 1.583 0.047067
##
## Nyblom stability test
## ------------------------------------
## Joint Statistic: 7.943
## Individual Statistics:
## mu 0.01213
## ar1 0.33264
## ar2 0.30686
## ma1 3.59223
## ma2 4.10058
## omega 0.30158
## alpha1 0.10699
## alpha2 0.22498
## beta1 0.34575
## gamma1 0.14047
## gamma2 0.27087
## shape 0.98083
##
## Asymptotic Critical Values (10% 5% 1%)
## Joint Statistic: 2.69 2.96 3.51
## Individual Statistic: 0.35 0.47 0.75
##
## Sign Bias Test
## ------------------------------------
## t-value prob sig
## Sign Bias 1.6643 0.09637 *
## Negative Sign Bias 2.2701 0.02341 **
## Positive Sign Bias 0.2623 0.79316
## Joint Effect 5.8585 0.11870
##
##
## Adjusted Pearson Goodness-of-Fit Test:
## ------------------------------------
## group statistic p-value(g-1)
## 1 20 77.70 4.621e-09
## 2 30 75.35 5.424e-06
## 3 40 90.08 6.421e-06
## 4 50 101.54 1.551e-05
##
##
## Elapsed time : 1.217238
PHÂN PHỐI ĐỐI XỨNG (sstd)
sgx21sstd.spec <- ugarchspec(variance.model = list( model = 'gjrGARCH', garchOrder = c(2,1)), mean.model = list(armaOrder = c(2,2), include.mean = TRUE), distribution.model = 'sstd')
sgx21sstd <- ugarchfit(sgx21sstd.spec, SGX)
print(sgx21sstd)
##
## *---------------------------------*
## * GARCH Model Fit *
## *---------------------------------*
##
## Conditional Variance Dynamics
## -----------------------------------
## GARCH Model : gjrGARCH(2,1)
## Mean Model : ARFIMA(2,0,2)
## Distribution : sstd
##
## Optimal Parameters
## ------------------------------------
## Estimate Std. Error t value Pr(>|t|)
## mu 7.436206 0.172865 43.017502 0.000000
## ar1 0.452003 0.007526 60.057545 0.000000
## ar2 0.546553 0.007518 72.699668 0.000000
## ma1 -0.238992 0.025529 -9.361680 0.000000
## ma2 -0.629874 0.025127 -25.067597 0.000000
## omega 0.008272 0.004157 1.989893 0.046603
## alpha1 0.124212 0.062090 2.000513 0.045445
## alpha2 0.000002 0.082810 0.000019 0.999985
## beta1 0.855260 0.032089 26.652973 0.000000
## gamma1 -0.119424 0.063356 -1.884959 0.059435
## gamma2 0.158041 0.082440 1.917037 0.055233
## skew 1.040537 0.054180 19.205146 0.000000
## shape 59.999711 56.759277 1.057091 0.290470
##
## Robust Standard Errors:
## Estimate Std. Error t value Pr(>|t|)
## mu 7.436206 0.066427 111.945561 0.000000
## ar1 0.452003 0.001231 367.095558 0.000000
## ar2 0.546553 0.001303 419.617995 0.000000
## ma1 -0.238992 0.025355 -9.425941 0.000000
## ma2 -0.629874 0.025372 -24.825323 0.000000
## omega 0.008272 0.006138 1.347548 0.177804
## alpha1 0.124212 0.072300 1.718016 0.085794
## alpha2 0.000002 0.122571 0.000013 0.999990
## beta1 0.855260 0.051605 16.573065 0.000000
## gamma1 -0.119424 0.081370 -1.467660 0.142197
## gamma2 0.158041 0.112496 1.404865 0.160062
## skew 1.040537 0.081943 12.698361 0.000000
## shape 59.999711 41.120522 1.459118 0.144533
##
## LogLikelihood : -1251.406
##
## Information Criteria
## ------------------------------------
##
## Akaike 2.5212
## Bayes 2.5849
## Shibata 2.5209
## Hannan-Quinn 2.5454
##
## Weighted Ljung-Box Test on Standardized Residuals
## ------------------------------------
## statistic p-value
## Lag[1] 0.836 3.606e-01
## Lag[2*(p+q)+(p+q)-1][11] 25.134 0.000e+00
## Lag[4*(p+q)+(p+q)-1][19] 35.106 9.463e-12
## d.o.f=4
## H0 : No serial correlation
##
## Weighted Ljung-Box Test on Standardized Squared Residuals
## ------------------------------------
## statistic p-value
## Lag[1] 0.003225 0.9547
## Lag[2*(p+q)+(p+q)-1][8] 7.767723 0.1058
## Lag[4*(p+q)+(p+q)-1][14] 11.334264 0.1206
## d.o.f=3
##
## Weighted ARCH LM Tests
## ------------------------------------
## Statistic Shape Scale P-Value
## ARCH Lag[4] 7.171 0.500 2.000 0.007411
## ARCH Lag[6] 7.243 1.461 1.711 0.034992
## ARCH Lag[8] 8.814 2.368 1.583 0.041492
##
## Nyblom stability test
## ------------------------------------
## Joint Statistic: 8.6596
## Individual Statistics:
## mu 0.01186
## ar1 0.36525
## ar2 0.33928
## ma1 3.55601
## ma2 4.14021
## omega 0.32916
## alpha1 0.11374
## alpha2 0.21821
## beta1 0.36879
## gamma1 0.12825
## gamma2 0.23386
## skew 0.40919
## shape 0.81020
##
## 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 1.6118 0.10732
## Negative Sign Bias 2.2794 0.02285 **
## Positive Sign Bias 0.3133 0.75409
## Joint Effect 5.8595 0.11865
##
##
## Adjusted Pearson Goodness-of-Fit Test:
## ------------------------------------
## group statistic p-value(g-1)
## 1 20 72.23 3.896e-08
## 2 30 72.06 1.574e-05
## 3 40 93.35 2.369e-06
## 4 50 94.86 9.345e-05
##
##
## Elapsed time : 1.662677
PHÂN PHỐI Generalized Error Distribution (ged)
sgx21ged.spec <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(2,1)), mean.model = list(armaOrder = c(2,2), include.mean = TRUE), distribution.model = "ged")
sgx21ged <- ugarchfit(sgx21ged.spec, SGX)
print(sgx21ged)
##
## *---------------------------------*
## * GARCH Model Fit *
## *---------------------------------*
##
## Conditional Variance Dynamics
## -----------------------------------
## GARCH Model : gjrGARCH(2,1)
## Mean Model : ARFIMA(2,0,2)
## Distribution : ged
##
## Optimal Parameters
## ------------------------------------
## Estimate Std. Error t value Pr(>|t|)
## mu 7.429268 0.176237 42.15510 0.000000
## ar1 0.448433 0.007604 58.97578 0.000000
## ar2 0.549954 0.007594 72.42249 0.000000
## ma1 -0.237511 0.026294 -9.03299 0.000000
## ma2 -0.629894 0.026176 -24.06405 0.000000
## omega 0.009569 0.004108 2.32951 0.019832
## alpha1 0.120364 0.060832 1.97865 0.047856
## alpha2 0.020413 0.079913 0.25544 0.798386
## beta1 0.844891 0.030032 28.13284 0.000000
## gamma1 -0.116177 0.062259 -1.86603 0.062037
## gamma2 0.142569 0.082453 1.72909 0.083793
## shape 2.004572 0.162686 12.32175 0.000000
##
## Robust Standard Errors:
## Estimate Std. Error t value Pr(>|t|)
## mu 7.429268 0.079159 93.85262 0.000000
## ar1 0.448433 0.001210 370.64981 0.000000
## ar2 0.549954 0.001261 436.08123 0.000000
## ma1 -0.237511 0.029065 -8.17159 0.000000
## ma2 -0.629894 0.028140 -22.38428 0.000000
## omega 0.009569 0.005202 1.83960 0.065828
## alpha1 0.120364 0.067969 1.77087 0.076582
## alpha2 0.020413 0.103182 0.19783 0.843177
## beta1 0.844891 0.040757 20.72981 0.000000
## gamma1 -0.116177 0.076708 -1.51454 0.129888
## gamma2 0.142569 0.099340 1.43517 0.151239
## shape 2.004572 0.257869 7.77359 0.000000
##
## LogLikelihood : -1251.573
##
## Information Criteria
## ------------------------------------
##
## Akaike 2.5196
## Bayes 2.5783
## Shibata 2.5193
## Hannan-Quinn 2.5419
##
## Weighted Ljung-Box Test on Standardized Residuals
## ------------------------------------
## statistic p-value
## Lag[1] 0.8851 3.468e-01
## Lag[2*(p+q)+(p+q)-1][11] 25.7916 0.000e+00
## Lag[4*(p+q)+(p+q)-1][19] 35.6502 4.665e-12
## d.o.f=4
## H0 : No serial correlation
##
## Weighted Ljung-Box Test on Standardized Squared Residuals
## ------------------------------------
## statistic p-value
## Lag[1] 0.009228 0.9235
## Lag[2*(p+q)+(p+q)-1][8] 7.857314 0.1014
## Lag[4*(p+q)+(p+q)-1][14] 11.272823 0.1236
## d.o.f=3
##
## Weighted ARCH LM Tests
## ------------------------------------
## Statistic Shape Scale P-Value
## ARCH Lag[4] 6.904 0.500 2.000 0.008598
## ARCH Lag[6] 6.954 1.461 1.711 0.040808
## ARCH Lag[8] 8.470 2.368 1.583 0.049254
##
## Nyblom stability test
## ------------------------------------
## Joint Statistic: 8.8282
## Individual Statistics:
## mu 0.01364
## ar1 0.33440
## ar2 0.30743
## ma1 3.63764
## ma2 4.12716
## omega 0.30786
## alpha1 0.11886
## alpha2 0.25003
## beta1 0.36047
## gamma1 0.15154
## gamma2 0.30267
## shape 1.82882
##
## Asymptotic Critical Values (10% 5% 1%)
## Joint Statistic: 2.69 2.96 3.51
## Individual Statistic: 0.35 0.47 0.75
##
## Sign Bias Test
## ------------------------------------
## t-value prob sig
## Sign Bias 1.656 0.09804 *
## Negative Sign Bias 2.251 0.02462 **
## Positive Sign Bias 0.236 0.81347
## Joint Effect 5.731 0.12547
##
##
## Adjusted Pearson Goodness-of-Fit Test:
## ------------------------------------
## group statistic p-value(g-1)
## 1 20 83.16 5.271e-10
## 2 30 78.35 2.017e-06
## 3 40 96.38 9.228e-07
## 4 50 98.55 3.509e-05
##
##
## Elapsed time : 1.181122
PHÂN PHỐI Generalized Error Distribution đối xứng (sged)
sgx21sged.spec <- ugarchspec(variance.model = list(model = 'gjrGARCH', garchOrder = c(2,1)), mean.model = list(armaOrder = c(2,2), include.mean = TRUE), distribution.model = 'sged')
sgx21sged <- ugarchfit(sgx21sged.spec, SGX)
print(sgx21sged)
##
## *---------------------------------*
## * 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 7.454337 0.180311 41.34155 0.000000
## ar1 0.443181 0.008279 53.52990 0.000000
## ar2 0.555130 0.008263 67.18121 0.000000
## ma1 -0.234663 0.026493 -8.85760 0.000000
## ma2 -0.631647 0.026635 -23.71475 0.000000
## omega 0.009081 0.004018 2.26025 0.023806
## alpha1 0.123883 0.060704 2.04079 0.041272
## alpha2 0.009697 0.081558 0.11889 0.905361
## beta1 0.849930 0.030683 27.70072 0.000000
## gamma1 -0.118439 0.061976 -1.91105 0.055998
## gamma2 0.148793 0.082671 1.79982 0.071889
## skew 1.045825 0.056139 18.62912 0.000000
## shape 2.050184 0.173796 11.79649 0.000000
##
## Robust Standard Errors:
## Estimate Std. Error t value Pr(>|t|)
## mu 7.454337 0.093820 79.453347 0.000000
## ar1 0.443181 0.001393 318.115068 0.000000
## ar2 0.555130 0.001410 393.796897 0.000000
## ma1 -0.234663 0.030075 -7.802640 0.000000
## ma2 -0.631647 0.029367 -21.508522 0.000000
## omega 0.009081 0.005871 1.546926 0.121881
## alpha1 0.123883 0.071631 1.729472 0.083725
## alpha2 0.009697 0.122535 0.079134 0.936926
## beta1 0.849930 0.049627 17.126458 0.000000
## gamma1 -0.118439 0.079962 -1.481194 0.138555
## gamma2 0.148793 0.113225 1.314137 0.188800
## skew 1.045825 0.097797 10.693884 0.000000
## shape 2.050184 0.316711 6.473364 0.000000
##
## LogLikelihood : -1251.217
##
## Information Criteria
## ------------------------------------
##
## Akaike 2.5209
## Bayes 2.5845
## Shibata 2.5205
## Hannan-Quinn 2.5451
##
## Weighted Ljung-Box Test on Standardized Residuals
## ------------------------------------
## statistic p-value
## Lag[1] 0.7295 3.930e-01
## Lag[2*(p+q)+(p+q)-1][11] 26.0119 0.000e+00
## Lag[4*(p+q)+(p+q)-1][19] 35.8795 3.459e-12
## d.o.f=4
## H0 : No serial correlation
##
## Weighted Ljung-Box Test on Standardized Squared Residuals
## ------------------------------------
## statistic p-value
## Lag[1] 0.01652 0.8977
## Lag[2*(p+q)+(p+q)-1][8] 7.86507 0.1010
## Lag[4*(p+q)+(p+q)-1][14] 11.37018 0.1190
## d.o.f=3
##
## Weighted ARCH LM Tests
## ------------------------------------
## Statistic Shape Scale P-Value
## ARCH Lag[4] 7.127 0.500 2.000 0.007594
## ARCH Lag[6] 7.191 1.461 1.711 0.035983
## ARCH Lag[8] 8.741 2.368 1.583 0.043033
##
## Nyblom stability test
## ------------------------------------
## Joint Statistic: 9.7217
## Individual Statistics:
## mu 0.01723
## ar1 0.38413
## ar2 0.35421
## ma1 3.74735
## ma2 4.26853
## omega 0.33821
## alpha1 0.13394
## alpha2 0.25827
## beta1 0.39915
## gamma1 0.14210
## gamma2 0.28657
## skew 0.32613
## shape 1.80294
##
## 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 1.5318 0.12590
## Negative Sign Bias 2.2232 0.02643 **
## Positive Sign Bias 0.3382 0.73525
## Joint Effect 5.5543 0.13543
##
##
## Adjusted Pearson Goodness-of-Fit Test:
## ------------------------------------
## group statistic p-value(g-1)
## 1 20 75.27 1.200e-08
## 2 30 77.33 2.830e-06
## 3 40 91.12 4.691e-06
## 4 50 94.46 1.037e-04
##
##
## Elapsed time : 1.792915
GJR-GARCH(22)
PHÂN PHỐI CHUẨN
sgx22n.spec <- ugarchspec(variance.model = list(model = 'gjrGARCH', garchOrder = c(2,2)), mean.model = list(armaOrder = c(2,2), include.mean = TRUE), distribution.model = 'norm')
sgx22n <- ugarchfit(sgx22n.spec, SGX)
print(sgx22n)
##
## *---------------------------------*
## * GARCH Model Fit *
## *---------------------------------*
##
## Conditional Variance Dynamics
## -----------------------------------
## GARCH Model : gjrGARCH(2,2)
## Mean Model : ARFIMA(2,0,2)
## Distribution : norm
##
## Optimal Parameters
## ------------------------------------
## Estimate Std. Error t value Pr(>|t|)
## mu 7.428427 0.173531 42.80743 0.000000
## ar1 0.449141 0.007568 59.34578 0.000000
## ar2 0.549254 0.007559 72.65842 0.000000
## ma1 -0.237939 0.025372 -9.37791 0.000000
## ma2 -0.629574 0.024756 -25.43093 0.000000
## omega 0.009540 0.002381 4.00592 0.000062
## alpha1 0.120515 0.059254 2.03388 0.041963
## alpha2 0.020041 0.067699 0.29603 0.767209
## beta1 0.845033 0.486408 1.73729 0.082335
## beta2 0.000000 0.431700 0.00000 1.000000
## gamma1 -0.116347 0.061982 -1.87711 0.060503
## gamma2 0.143023 0.080507 1.77653 0.075646
##
## Robust Standard Errors:
## Estimate Std. Error t value Pr(>|t|)
## mu 7.428427 0.066430 111.82368 0.000000
## ar1 0.449141 0.001172 383.16046 0.000000
## ar2 0.549254 0.001264 434.55981 0.000000
## ma1 -0.237939 0.024739 -9.61780 0.000000
## ma2 -0.629574 0.024912 -25.27185 0.000000
## omega 0.009540 0.007462 1.27841 0.201106
## alpha1 0.120515 0.066805 1.80399 0.071232
## alpha2 0.020041 0.127190 0.15757 0.874800
## beta1 0.845033 0.551493 1.53227 0.125457
## beta2 0.000000 0.469029 0.00000 1.000000
## gamma1 -0.116347 0.076919 -1.51260 0.130382
## gamma2 0.143023 0.099369 1.43932 0.150060
##
## LogLikelihood : -1251.573
##
## Information Criteria
## ------------------------------------
##
## Akaike 2.5196
## Bayes 2.5783
## Shibata 2.5193
## Hannan-Quinn 2.5419
##
## Weighted Ljung-Box Test on Standardized Residuals
## ------------------------------------
## statistic p-value
## Lag[1] 0.8955 3.440e-01
## Lag[2*(p+q)+(p+q)-1][11] 25.7544 0.000e+00
## Lag[4*(p+q)+(p+q)-1][19] 35.6144 4.888e-12
## d.o.f=4
## H0 : No serial correlation
##
## Weighted Ljung-Box Test on Standardized Squared Residuals
## ------------------------------------
## statistic p-value
## Lag[1] 0.009153 0.9238
## Lag[2*(p+q)+(p+q)-1][11] 9.521247 0.1165
## Lag[4*(p+q)+(p+q)-1][19] 14.515139 0.1163
## d.o.f=4
##
## Weighted ARCH LM Tests
## ------------------------------------
## Statistic Shape Scale P-Value
## ARCH Lag[5] 0.01374 0.500 2.000 0.9067
## ARCH Lag[7] 0.49925 1.473 1.746 0.8974
## ARCH Lag[9] 2.05147 2.402 1.619 0.7485
##
## Nyblom stability test
## ------------------------------------
## Joint Statistic: 9.7639
## Individual Statistics:
## mu 0.01347
## ar1 0.33359
## ar2 0.30682
## ma1 3.63095
## ma2 4.12594
## omega 0.30728
## alpha1 0.11890
## alpha2 0.25003
## beta1 0.36067
## beta2 0.38964
## gamma1 0.15151
## gamma2 0.30275
##
## Asymptotic Critical Values (10% 5% 1%)
## Joint Statistic: 2.69 2.96 3.51
## Individual Statistic: 0.35 0.47 0.75
##
## Sign Bias Test
## ------------------------------------
## t-value prob sig
## Sign Bias 1.6566 0.09792 *
## Negative Sign Bias 2.2516 0.02456 **
## Positive Sign Bias 0.2379 0.81200
## Joint Effect 5.7384 0.12506
##
##
## Adjusted Pearson Goodness-of-Fit Test:
## ------------------------------------
## group statistic p-value(g-1)
## 1 20 84.80 2.733e-10
## 2 30 77.45 2.720e-06
## 3 40 97.90 5.722e-07
## 4 50 97.35 4.837e-05
##
##
## Elapsed time : 0.514236
PHÂN PHỐI STUDENT
sgx22std.spec <- ugarchspec(variance.model = list(model = 'gjrGARCH', garchOrder = c(2,2)), mean.model = list(armaOrder = c(2,2), include.mean = TRUE), distribution.model = 'std')
sgx22std <- ugarchfit(sgx22std.spec, SGX)
print(sgx22std)
##
## *---------------------------------*
## * GARCH Model Fit *
## *---------------------------------*
##
## Conditional Variance Dynamics
## -----------------------------------
## GARCH Model : gjrGARCH(2,2)
## Mean Model : ARFIMA(2,0,2)
## Distribution : std
##
## Optimal Parameters
## ------------------------------------
## Estimate Std. Error t value Pr(>|t|)
## mu 7.418710 0.172148 43.09489 0.000000
## ar1 0.453328 0.007414 61.14179 0.000000
## ar2 0.545169 0.007405 73.61767 0.000000
## ma1 -0.240535 0.025286 -9.51262 0.000000
## ma2 -0.628764 0.024792 -25.36188 0.000000
## omega 0.008980 0.002581 3.47878 0.000504
## alpha1 0.122509 0.060849 2.01333 0.044080
## alpha2 0.009827 0.067052 0.14656 0.883478
## beta1 0.849362 0.519444 1.63514 0.102020
## beta2 0.000000 0.462378 0.00000 1.000000
## gamma1 -0.117960 0.063203 -1.86637 0.061990
## gamma2 0.152563 0.081298 1.87658 0.060575
## shape 80.059232 106.267579 0.75337 0.451225
##
## Robust Standard Errors:
## Estimate Std. Error t value Pr(>|t|)
## mu 7.418710 0.064741 114.591366 0.000000
## ar1 0.453328 0.001134 399.869721 0.000000
## ar2 0.545169 0.001201 453.901420 0.000000
## ma1 -0.240535 0.025027 -9.610947 0.000000
## ma2 -0.628764 0.025094 -25.056275 0.000000
## omega 0.008980 0.006980 1.286640 0.198220
## alpha1 0.122509 0.067074 1.826483 0.067777
## alpha2 0.009827 0.121211 0.081076 0.935382
## beta1 0.849362 0.585586 1.450448 0.146934
## beta2 0.000000 0.504081 0.000000 1.000000
## gamma1 -0.117960 0.076365 -1.544694 0.122420
## gamma2 0.152563 0.094563 1.613359 0.106666
## shape 80.059232 80.909984 0.989485 0.322426
##
## LogLikelihood : -1251.649
##
## Information Criteria
## ------------------------------------
##
## Akaike 2.5217
## Bayes 2.5854
## Shibata 2.5214
## Hannan-Quinn 2.5459
##
## Weighted Ljung-Box Test on Standardized Residuals
## ------------------------------------
## statistic p-value
## Lag[1] 0.8969 3.436e-01
## Lag[2*(p+q)+(p+q)-1][11] 25.2650 0.000e+00
## Lag[4*(p+q)+(p+q)-1][19] 35.2075 8.298e-12
## d.o.f=4
## H0 : No serial correlation
##
## Weighted Ljung-Box Test on Standardized Squared Residuals
## ------------------------------------
## statistic p-value
## Lag[1] 0.006388 0.9363
## Lag[2*(p+q)+(p+q)-1][11] 9.443098 0.1204
## Lag[4*(p+q)+(p+q)-1][19] 14.559853 0.1145
## d.o.f=4
##
## Weighted ARCH LM Tests
## ------------------------------------
## Statistic Shape Scale P-Value
## ARCH Lag[5] 0.01464 0.500 2.000 0.9037
## ARCH Lag[7] 0.49180 1.473 1.746 0.8994
## ARCH Lag[9] 2.11451 2.402 1.619 0.7362
##
## Nyblom stability test
## ------------------------------------
## Joint Statistic: 10.3358
## Individual Statistics:
## mu 0.01149
## ar1 0.33006
## ar2 0.30484
## ma1 3.61858
## ma2 4.13586
## omega 0.29757
## alpha1 0.10314
## alpha2 0.21565
## beta1 0.33729
## beta2 0.36469
## gamma1 0.14105
## gamma2 0.26441
## shape 0.96256
##
## 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 1.660 0.09725 *
## Negative Sign Bias 2.275 0.02314 **
## Positive Sign Bias 0.262 0.79337
## Joint Effect 5.862 0.11855
##
##
## Adjusted Pearson Goodness-of-Fit Test:
## ------------------------------------
## group statistic p-value(g-1)
## 1 20 75.94 9.206e-09
## 2 30 75.00 6.100e-06
## 3 40 90.24 6.119e-06
## 4 50 96.05 6.825e-05
##
##
## Elapsed time : 1.644891
PHÂN PHỐI ĐỐI XỨNG (sstd)
sgx22sstd.spec <- ugarchspec(variance.model = list( model = 'gjrGARCH', garchOrder = c(2,2)), mean.model = list(armaOrder = c(2,2), include.mean = TRUE), distribution.model = 'sstd')
sgx22sstd <- ugarchfit(sgx22sstd.spec, SGX)
print(sgx22sstd)
##
## *---------------------------------*
## * GARCH Model Fit *
## *---------------------------------*
##
## Conditional Variance Dynamics
## -----------------------------------
## GARCH Model : gjrGARCH(2,2)
## Mean Model : ARFIMA(2,0,2)
## Distribution : sstd
##
## Optimal Parameters
## ------------------------------------
## Estimate Std. Error t value Pr(>|t|)
## mu 7.439139 0.179206 41.511652 0.000000
## ar1 0.465164 0.003747 124.131508 0.000000
## ar2 0.532715 0.003796 140.340724 0.000000
## ma1 -0.245374 0.023012 -10.662751 0.000000
## ma2 -0.620988 0.023572 -26.344675 0.000000
## omega 0.006791 0.002999 2.264646 0.023534
## alpha1 0.080195 0.000246 325.811287 0.000000
## alpha2 0.000000 0.018072 0.000004 0.999997
## beta1 0.890223 0.000330 2694.147046 0.000000
## beta2 0.000000 0.010951 0.000013 0.999989
## gamma1 -0.200008 0.001580 -126.602530 0.000000
## gamma2 0.256084 0.034220 7.483371 0.000000
## skew 1.071306 0.057404 18.662726 0.000000
## shape 59.999809 51.988249 1.154103 0.248458
##
## Robust Standard Errors:
## Estimate Std. Error t value Pr(>|t|)
## mu 7.439139 0.086540 85.961776 0.000000
## ar1 0.465164 0.001179 394.451044 0.000000
## ar2 0.532715 0.001371 388.655702 0.000000
## ma1 -0.245374 0.025474 -9.632145 0.000000
## ma2 -0.620988 0.024951 -24.888631 0.000000
## omega 0.006791 0.003919 1.732953 0.083104
## alpha1 0.080195 0.002005 40.002682 0.000000
## alpha2 0.000000 0.024698 0.000003 0.999998
## beta1 0.890223 0.000386 2306.304795 0.000000
## beta2 0.000000 0.014711 0.000010 0.999992
## gamma1 -0.200008 0.001673 -119.539262 0.000000
## gamma2 0.256084 0.040633 6.302376 0.000000
## skew 1.071306 0.079991 13.392822 0.000000
## shape 59.999809 40.570318 1.478909 0.139165
##
## LogLikelihood : -1248.421
##
## Information Criteria
## ------------------------------------
##
## Akaike 2.5173
## Bayes 2.5858
## Shibata 2.5169
## Hannan-Quinn 2.5433
##
## Weighted Ljung-Box Test on Standardized Residuals
## ------------------------------------
## statistic p-value
## Lag[1] 1.00 3.172e-01
## Lag[2*(p+q)+(p+q)-1][11] 23.63 0.000e+00
## Lag[4*(p+q)+(p+q)-1][19] 33.29 9.764e-11
## d.o.f=4
## H0 : No serial correlation
##
## Weighted Ljung-Box Test on Standardized Squared Residuals
## ------------------------------------
## statistic p-value
## Lag[1] 1.857 0.17300
## Lag[2*(p+q)+(p+q)-1][11] 14.025 0.01393
## Lag[4*(p+q)+(p+q)-1][19] 21.578 0.00624
## d.o.f=4
##
## Weighted ARCH LM Tests
## ------------------------------------
## Statistic Shape Scale P-Value
## ARCH Lag[5] 0.1131 0.500 2.000 0.7366
## ARCH Lag[7] 2.2193 1.473 1.746 0.4577
## ARCH Lag[9] 5.2491 2.402 1.619 0.2418
##
## Nyblom stability test
## ------------------------------------
## Joint Statistic: 12.1513
## Individual Statistics:
## mu 0.02880
## ar1 0.32523
## ar2 0.28849
## ma1 3.23686
## ma2 3.53882
## omega 0.31915
## alpha1 0.05350
## alpha2 0.13216
## beta1 0.36470
## beta2 0.40749
## gamma1 0.08192
## gamma2 0.15664
## skew 0.32132
## shape 0.72057
##
## Asymptotic Critical Values (10% 5% 1%)
## Joint Statistic: 3.08 3.34 3.9
## Individual Statistic: 0.35 0.47 0.75
##
## Sign Bias Test
## ------------------------------------
## t-value prob sig
## Sign Bias 1.3753 0.1694
## Negative Sign Bias 0.7451 0.4564
## Positive Sign Bias 0.2513 0.8016
## Joint Effect 2.2545 0.5213
##
##
## Adjusted Pearson Goodness-of-Fit Test:
## ------------------------------------
## group statistic p-value(g-1)
## 1 20 87.39 9.593e-11
## 2 30 96.23 3.885e-09
## 3 40 116.32 1.275e-09
## 4 50 114.60 3.570e-07
##
##
## Elapsed time : 1.850571
PHÂN PHỐI Generalized Error Distribution (ged)
sgx22ged.spec <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(2,2)), mean.model = list(armaOrder = c(2,2), include.mean = TRUE), distribution.model = "ged")
sgx22ged <- ugarchfit(sgx22ged.spec, SGX)
print(sgx22ged)
##
## *---------------------------------*
## * GARCH Model Fit *
## *---------------------------------*
##
## Conditional Variance Dynamics
## -----------------------------------
## GARCH Model : gjrGARCH(2,2)
## Mean Model : ARFIMA(2,0,2)
## Distribution : ged
##
## Optimal Parameters
## ------------------------------------
## Estimate Std. Error t value Pr(>|t|)
## mu 7.429281 0.176179 42.16893 0.000000
## ar1 0.448422 0.007604 58.97240 0.000000
## ar2 0.549964 0.007594 72.41939 0.000000
## ma1 -0.237496 0.026097 -9.10040 0.000000
## ma2 -0.629900 0.026004 -24.22335 0.000000
## omega 0.009571 0.002716 3.52384 0.000425
## alpha1 0.120335 0.059369 2.02691 0.042672
## alpha2 0.020472 0.069970 0.29258 0.769845
## beta1 0.844873 0.483702 1.74668 0.080692
## beta2 0.000000 0.429672 0.00000 1.000000
## gamma1 -0.116163 0.062175 -1.86832 0.061717
## gamma2 0.142539 0.081897 1.74046 0.081779
## shape 2.004638 0.162124 12.36483 0.000000
##
## Robust Standard Errors:
## Estimate Std. Error t value Pr(>|t|)
## mu 7.429281 0.078620 94.49651 0.000000
## ar1 0.448422 0.001206 371.80558 0.000000
## ar2 0.549964 0.001259 436.86417 0.000000
## ma1 -0.237496 0.028706 -8.27326 0.000000
## ma2 -0.629900 0.028056 -22.45121 0.000000
## omega 0.009571 0.007043 1.35894 0.174166
## alpha1 0.120335 0.066974 1.79673 0.072378
## alpha2 0.020472 0.123219 0.16614 0.868047
## beta1 0.844873 0.533360 1.58406 0.113181
## beta2 0.000000 0.454683 0.00000 1.000000
## gamma1 -0.116163 0.076050 -1.52746 0.126648
## gamma2 0.142539 0.097267 1.46543 0.142804
## shape 2.004638 0.260253 7.70265 0.000000
##
## LogLikelihood : -1251.573
##
## Information Criteria
## ------------------------------------
##
## Akaike 2.5216
## Bayes 2.5852
## Shibata 2.5212
## Hannan-Quinn 2.5458
##
## Weighted Ljung-Box Test on Standardized Residuals
## ------------------------------------
## statistic p-value
## Lag[1] 0.8855 3.467e-01
## Lag[2*(p+q)+(p+q)-1][11] 25.7922 0.000e+00
## Lag[4*(p+q)+(p+q)-1][19] 35.6505 4.663e-12
## d.o.f=4
## H0 : No serial correlation
##
## Weighted Ljung-Box Test on Standardized Squared Residuals
## ------------------------------------
## statistic p-value
## Lag[1] 0.00911 0.9240
## Lag[2*(p+q)+(p+q)-1][11] 9.52552 0.1163
## Lag[4*(p+q)+(p+q)-1][19] 14.51810 0.1162
## d.o.f=4
##
## Weighted ARCH LM Tests
## ------------------------------------
## Statistic Shape Scale P-Value
## ARCH Lag[5] 0.01343 0.500 2.000 0.9078
## ARCH Lag[7] 0.50064 1.473 1.746 0.8970
## ARCH Lag[9] 2.05548 2.402 1.619 0.7477
##
## Nyblom stability test
## ------------------------------------
## Joint Statistic: 11.2675
## Individual Statistics:
## mu 0.01364
## ar1 0.33443
## ar2 0.30745
## ma1 3.63701
## ma2 4.12683
## omega 0.30806
## alpha1 0.11894
## alpha2 0.25032
## beta1 0.36071
## beta2 0.38964
## gamma1 0.15153
## gamma2 0.30299
## shape 1.82936
##
## 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 1.6559 0.09806 *
## Negative Sign Bias 2.2504 0.02464 **
## Positive Sign Bias 0.2357 0.81371
## Joint Effect 5.7289 0.12557
##
##
## Adjusted Pearson Goodness-of-Fit Test:
## ------------------------------------
## group statistic p-value(g-1)
## 1 20 83.16 5.271e-10
## 2 30 78.35 2.017e-06
## 3 40 96.38 9.228e-07
## 4 50 98.55 3.509e-05
##
##
## Elapsed time : 1.272338
PHÂN PHỐI Generalized Error Distribution đối xứng (sged)
sgx22sged.spec <- ugarchspec(variance.model = list(model = 'gjrGARCH', garchOrder = c(2,2)), mean.model = list(armaOrder = c(2,2), include.mean = TRUE), distribution.model = 'sged')
sgx22sged <- ugarchfit(sgx22sged.spec, SGX)
print(sgx22sged)
##
## *---------------------------------*
## * GARCH Model Fit *
## *---------------------------------*
##
## Conditional Variance Dynamics
## -----------------------------------
## GARCH Model : gjrGARCH(2,2)
## Mean Model : ARFIMA(2,0,2)
## Distribution : sged
##
## Optimal Parameters
## ------------------------------------
## Estimate Std. Error t value Pr(>|t|)
## mu 7.454066 0.180040 41.40230 0.000000
## ar1 0.443320 0.008266 53.63262 0.000000
## ar2 0.554993 0.008251 67.26121 0.000000
## ma1 -0.234788 0.026287 -8.93188 0.000000
## ma2 -0.631565 0.026471 -23.85884 0.000000
## omega 0.009058 0.002488 3.64009 0.000273
## alpha1 0.123982 0.059148 2.09614 0.036069
## alpha2 0.009555 0.071889 0.13291 0.894268
## beta1 0.849995 0.513953 1.65384 0.098160
## beta2 0.000000 0.457953 0.00000 1.000000
## gamma1 -0.118517 0.061917 -1.91412 0.055605
## gamma2 0.149012 0.081773 1.82227 0.068415
## skew 1.045834 0.056098 18.64294 0.000000
## shape 2.049751 0.173518 11.81291 0.000000
##
## Robust Standard Errors:
## Estimate Std. Error t value Pr(>|t|)
## mu 7.454066 0.091670 81.314059 0.000000
## ar1 0.443320 0.001388 319.294632 0.000000
## ar2 0.554993 0.001410 393.723319 0.000000
## ma1 -0.234788 0.029425 -7.979223 0.000000
## ma2 -0.631565 0.029128 -21.682222 0.000000
## omega 0.009058 0.007993 1.133262 0.257104
## alpha1 0.123982 0.069658 1.779862 0.075098
## alpha2 0.009555 0.146110 0.065393 0.947861
## beta1 0.849995 0.616468 1.378814 0.167952
## beta2 0.000000 0.524520 0.000000 1.000000
## gamma1 -0.118517 0.079004 -1.500144 0.133577
## gamma2 0.149012 0.109506 1.360769 0.173587
## skew 1.045834 0.096895 10.793430 0.000000
## shape 2.049751 0.319503 6.415432 0.000000
##
## LogLikelihood : -1251.217
##
## Information Criteria
## ------------------------------------
##
## Akaike 2.5229
## Bayes 2.5914
## Shibata 2.5225
## Hannan-Quinn 2.5489
##
## Weighted Ljung-Box Test on Standardized Residuals
## ------------------------------------
## statistic p-value
## Lag[1] 0.7281 3.935e-01
## Lag[2*(p+q)+(p+q)-1][11] 25.9961 0.000e+00
## Lag[4*(p+q)+(p+q)-1][19] 35.8652 3.524e-12
## d.o.f=4
## H0 : No serial correlation
##
## Weighted Ljung-Box Test on Standardized Squared Residuals
## ------------------------------------
## statistic p-value
## Lag[1] 0.0163 0.8984
## Lag[2*(p+q)+(p+q)-1][11] 9.5767 0.1138
## Lag[4*(p+q)+(p+q)-1][19] 14.7160 0.1083
## d.o.f=4
##
## Weighted ARCH LM Tests
## ------------------------------------
## Statistic Shape Scale P-Value
## ARCH Lag[5] 0.0109 0.500 2.000 0.9169
## ARCH Lag[7] 0.5271 1.473 1.746 0.8899
## ARCH Lag[9] 2.1117 2.402 1.619 0.7367
##
## Nyblom stability test
## ------------------------------------
## Joint Statistic: 12.2201
## Individual Statistics:
## mu 0.0172
## ar1 0.3842
## ar2 0.3543
## ma1 3.7504
## ma2 4.2720
## omega 0.3365
## alpha1 0.1343
## alpha2 0.2590
## beta1 0.3992
## beta2 0.4308
## gamma1 0.1424
## gamma2 0.2881
## skew 0.3262
## shape 1.8022
##
## Asymptotic Critical Values (10% 5% 1%)
## Joint Statistic: 3.08 3.34 3.9
## Individual Statistic: 0.35 0.47 0.75
##
## Sign Bias Test
## ------------------------------------
## t-value prob sig
## Sign Bias 1.5330 0.12560
## Negative Sign Bias 2.2256 0.02626 **
## Positive Sign Bias 0.3395 0.73430
## Joint Effect 5.5669 0.13469
##
##
## Adjusted Pearson Goodness-of-Fit Test:
## ------------------------------------
## group statistic p-value(g-1)
## 1 20 75.27 1.200e-08
## 2 30 77.33 2.830e-06
## 3 40 91.12 4.691e-06
## 4 50 95.55 7.783e-05
##
##
## Elapsed time : 2.00112
LỰA CHỌN MÔ HÌNH GJR-GARCH
LỰA CHỌN MÔ HÌNH BIÊN PHÙ HỢP NHẤT CHO CHUỖI SGX
sgx.model.list <- list(garch11n = sgx11n,
garch11std = sgx11std,
garch11sstd = sgx11sstd,
garch11ged = sgx11ged,
garch11sged = sgx11sged,
garch12n = sgx12n,
garch12std = sgx12std,
garch12sstd = sgx12sstd,
garch12ged = sgx12ged,
garch12sged = sgx12sged,
garch21n = sgx21n,
garch21std = sgx21std,
garch21sstd = sgx21sstd,
garch21ged = sgx21ged,
garch21sged = sgx21sged,
garch22n = sgx22n,
garch22std = sgx22std,
garch22sstd = sgx22sstd,
garch22ged = sgx22ged,
garch22sged = sgx22sged)
sgx.info.mat <- sapply(sgx.model.list, infocriteria)
rownames(sgx.info.mat) <- rownames(infocriteria(sgx11n))
sgx.info.mat
## garch11n garch11std garch11sstd garch11ged garch11sged garch12n
## Akaike 2.526233 2.528161 2.529850 2.528179 2.529741 2.528227
## Bayes 2.570298 2.577122 2.583707 2.577140 2.583597 2.577188
## Shibata 2.526074 2.527965 2.529613 2.527983 2.529504 2.528031
## Hannan-Quinn 2.542978 2.546767 2.550317 2.546785 2.550207 2.546833
## garch12std garch12sstd garch12ged garch12sged garch21n garch21std
## Akaike 2.530165 2.531844 2.530173 2.531735 2.512831 2.519675
## Bayes 2.584022 2.590597 2.584030 2.590487 2.566688 2.578428
## Shibata 2.529928 2.531562 2.529936 2.531453 2.512594 2.519393
## Hannan-Quinn 2.550632 2.554171 2.550639 2.554062 2.533298 2.542002
## garch21sstd garch21ged garch21sged garch22n garch22std garch22sstd
## Akaike 2.521248 2.519586 2.520872 2.519587 2.521734 2.517290
## Bayes 2.584897 2.578339 2.584520 2.578340 2.585383 2.585835
## Shibata 2.520918 2.519304 2.520541 2.519305 2.521403 2.516908
## Hannan-Quinn 2.545436 2.541913 2.545059 2.541914 2.545921 2.543338
## garch22ged garch22sged
## Akaike 2.521580 2.522865
## Bayes 2.585229 2.591410
## Shibata 2.521250 2.522483
## Hannan-Quinn 2.545768 2.548913
sgx.inds <- which(sgx.info.mat == min(sgx.info.mat), arr.ind = TRUE)
model.sgx <- colnames(sgx.info.mat)[sgx.inds[,2]]
model.sgx
## [1] "garch21n"
THAM SỐ ƯỚC LƯỢNG MÔ HÌNH BIÊN PHÙ HỢP NHẤT
sgx21n
##
## *---------------------------------*
## * GARCH Model Fit *
## *---------------------------------*
##
## Conditional Variance Dynamics
## -----------------------------------
## GARCH Model : gjrGARCH(2,1)
## Mean Model : ARFIMA(2,0,2)
## Distribution : norm
##
## Optimal Parameters
## ------------------------------------
## Estimate Std. Error t value Pr(>|t|)
## mu 7.409277 0.135438 5.4706e+01 0.00000
## ar1 0.457257 0.010445 4.3776e+01 0.00000
## ar2 0.540432 0.004878 1.1080e+02 0.00000
## ma1 -0.242441 0.040632 -5.9668e+00 0.00000
## ma2 -0.623333 0.078023 -7.9890e+00 0.00000
## omega 0.007952 0.000298 2.6687e+01 0.00000
## alpha1 0.090683 0.002847 3.1856e+01 0.00000
## alpha2 0.000000 0.011334 1.7000e-05 0.99999
## beta1 0.882426 0.000050 1.7488e+04 0.00000
## gamma1 -0.209070 0.018021 -1.1601e+01 0.00000
## gamma2 0.259791 0.021214 1.2246e+01 0.00000
##
## Robust Standard Errors:
## Estimate Std. Error t value Pr(>|t|)
## mu 7.409277 0.482333 15.361336 0.000000
## ar1 0.457257 0.043226 10.578202 0.000000
## ar2 0.540432 0.023382 23.113535 0.000000
## ma1 -0.242441 0.180528 -1.342955 0.179286
## ma2 -0.623333 0.314488 -1.982055 0.047473
## omega 0.007952 0.003611 2.202075 0.027660
## alpha1 0.090683 0.033331 2.720655 0.006515
## alpha2 0.000000 0.038743 0.000005 0.999996
## beta1 0.882426 0.000117 7511.282693 0.000000
## gamma1 -0.209070 0.020212 -10.343891 0.000000
## gamma2 0.259791 0.036047 7.207023 0.000000
##
## LogLikelihood : -1249.185
##
## Information Criteria
## ------------------------------------
##
## Akaike 2.5128
## Bayes 2.5667
## Shibata 2.5126
## Hannan-Quinn 2.5333
##
## Weighted Ljung-Box Test on Standardized Residuals
## ------------------------------------
## statistic p-value
## Lag[1] 0.904 3.417e-01
## Lag[2*(p+q)+(p+q)-1][11] 24.385 0.000e+00
## Lag[4*(p+q)+(p+q)-1][19] 33.963 4.131e-11
## d.o.f=4
## H0 : No serial correlation
##
## Weighted Ljung-Box Test on Standardized Squared Residuals
## ------------------------------------
## statistic p-value
## Lag[1] 1.559 0.21184
## Lag[2*(p+q)+(p+q)-1][8] 10.729 0.02372
## Lag[4*(p+q)+(p+q)-1][14] 15.664 0.01834
## d.o.f=3
##
## Weighted ARCH LM Tests
## ------------------------------------
## Statistic Shape Scale P-Value
## ARCH Lag[4] 8.739 0.500 2.000 0.003115
## ARCH Lag[6] 9.248 1.461 1.711 0.011920
## ARCH Lag[8] 12.296 2.368 1.583 0.006816
##
## Nyblom stability test
## ------------------------------------
## Joint Statistic: 6.8514
## Individual Statistics:
## mu 0.03081
## ar1 0.29252
## ar2 0.25877
## ma1 3.46303
## ma2 3.63152
## omega 0.28628
## alpha1 0.06594
## alpha2 0.16258
## beta1 0.35314
## gamma1 0.12787
## gamma2 0.23233
##
## 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 1.6171 0.1062
## Negative Sign Bias 0.7976 0.4253
## Positive Sign Bias 0.2712 0.7863
## Joint Effect 3.2480 0.3549
##
##
## Adjusted Pearson Goodness-of-Fit Test:
## ------------------------------------
## group statistic p-value(g-1)
## 1 20 93.65 7.434e-12
## 2 30 85.11 2.023e-07
## 3 40 112.89 4.125e-09
## 4 50 124.27 1.813e-08
##
##
## Elapsed time : 0.5286181
TRÍCH XUẤT CHUỖI PHẦN DƯ CỦA CHUỖI LỢI SUẤT SGX
sgx.res <- residuals(sgx21n)/sigma(sgx21n)
fitdist(distribution = 'norm' , sgx.res, control = list())
## $pars
## mu sigma
## 0.04993222 0.99128476
##
## $convergence
## [1] 0
##
## $values
## [1] 1414.416 1414.416 1414.416
##
## $lagrange
## [1] 0
##
## $hessian
## [,1] [,2]
## [1,] 1 0.000
## [2,] 0 2038.455
##
## $ineqx0
## NULL
##
## $nfuneval
## [1] 30
##
## $outer.iter
## [1] 2
##
## $elapsed
## Time difference of 0.00407505 secs
##
## $vscale
## [1] 1 1 1
u <- pdist(distribution = 'norm' , q = sgx.res, mu = 0.04993222 , sigma = 0.99128476)
print(u)
## m.c.seq.row..seq.n...seq.col..drop...FALSE.
## 1-01-01 0.48864362
## 2-01-01 0.45082182
## 3-01-01 0.79073131
## 4-01-01 0.43807505
## 5-01-01 0.45516812
## 6-01-01 0.58845281
## 7-01-01 0.30344977
## 8-01-01 0.47224690
## 9-01-01 0.39971841
## 10-01-01 0.43730514
## ...
## 994-01-01 0.59530410
## 995-01-01 0.85782320
## 996-01-01 0.79584407
## 997-01-01 0.03479422
## 998-01-01 0.04563937
## 999-01-01 0.76541969
## 1000-01-01 0.09994958
## 1001-01-01 0.29459338
## 1002-01-01 0.05455010
## 1003-01-01 0.76806037
LỰA CHỌN MÔ HÌNH COPULA VÀ ƯỚC LƯỢNG THAM SỐ
?BiCopSelect
## No documentation for 'BiCopSelect' in specified packages and libraries:
## you could try '??BiCopSelect'