copulanew
Lê Thành Đặng- 2121012946
2023-08-27
library(readxl)
library(rugarch)## Loading required package: parallel##
## Attaching package: 'rugarch'## The following object is masked from 'package:stats':
##
## sigmalibrary(goftest)
library(tidyverse)## ── Attaching core tidyverse packages ──────────────────────── tidyverse 2.0.0 ──
## ✔ dplyr 1.1.2 ✔ readr 2.1.4
## ✔ forcats 1.0.0 ✔ stringr 1.5.0
## ✔ ggplot2 3.4.2 ✔ tibble 3.2.1
## ✔ lubridate 1.9.2 ✔ tidyr 1.3.0
## ✔ purrr 1.0.1## ── Conflicts ────────────────────────────────────────── tidyverse_conflicts() ──
## ✖ dplyr::filter() masks stats::filter()
## ✖ dplyr::lag() masks stats::lag()
## ✖ purrr::reduce() masks rugarch::reduce()
## ℹ Use the ]8;;http://conflicted.r-lib.org/conflicted package]8;; to force all conflicts to become errorslibrary(tseries)## Registered S3 method overwritten by 'quantmod':
## method from
## as.zoo.data.frame zoolibrary(VineCopula)
library(ggplot2)Tương quan và kiểm định
data <- read_excel("D:/nckh/data/datareturn.xlsx")
#đọc dữ liệu vô ní
cor(data[, c("BTC", "ETH")], method = "pearson")## BTC ETH
## BTC 1.0000000 0.8350036
## ETH 0.8350036 1.0000000cor(data[, c("BTC", "ETH")], method = "spearman")## BTC ETH
## BTC 1.0000000 0.8214125
## ETH 0.8214125 1.0000000cor(data[, c("BTC", "ETH")], method = "kendall")## BTC ETH
## BTC 1.0000000 0.6466008
## ETH 0.6466008 1.0000000ggplot(data, aes(x = DATE, y= BTC))+
geom_line()+
labs(title = "BTC",x = "Ngày", y="Độ biến động")+
theme(plot.title = element_text(hjust = 0.5))
ggplot(data, aes(x = DATE, y= ETH))+
geom_line()+
labs(title = "ETH",x = "Ngày", y="Độ biến động")+
theme(plot.title = element_text(hjust = 0.5))
library(moments)
# mô tả thống kê ETH
data %>% summarise(Min = min(ETH),
Max = max(ETH),
Mean = mean(ETH),
StDev = sd(ETH),
Skewness = skewness(ETH),
Kurtosis = kurtosis(ETH))## # A tibble: 1 × 6
## Min Max Mean StDev Skewness Kurtosis
## <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 -59.0 23.1 0.0395 5.17 -1.09 14.6# mô tả thống kê BTC
data %>% summarise(Min = min(BTC),
Max = max(BTC),
Mean = mean(BTC),
StDev = sd(BTC),
Skewness = skewness(BTC),
Kurtosis = kurtosis(BTC))## # A tibble: 1 × 6
## Min Max Mean StDev Skewness Kurtosis
## <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 -48.1 17.9 0.0289 3.95 -1.13 16.9#kiểm định BTC
adf.test(data$BTC)## Warning in adf.test(data$BTC): p-value smaller than printed p-value##
## Augmented Dickey-Fuller Test
##
## data: data$BTC
## Dickey-Fuller = -11.443, Lag order = 12, p-value = 0.01
## alternative hypothesis: stationaryjarque.bera.test(data$BTC)##
## Jarque Bera Test
##
## data: data$BTC
## X-squared = 15311, df = 2, p-value < 2.2e-16Box.test(data$BTC, lag = 2, type = "Ljung-Box")##
## Box-Ljung test
##
## data: data$BTC
## X-squared = 13.545, df = 2, p-value = 0.001145Box.test(data$BTC, lag = 2, type = "Box-Pierce")##
## Box-Pierce test
##
## data: data$BTC
## X-squared = 13.52, df = 2, p-value = 0.001159#ETH
adf.test(data$ETH)## Warning in adf.test(data$ETH): p-value smaller than printed p-value##
## Augmented Dickey-Fuller Test
##
## data: data$ETH
## Dickey-Fuller = -11.375, Lag order = 12, p-value = 0.01
## alternative hypothesis: stationaryjarque.bera.test(data$ETH)##
## Jarque Bera Test
##
## data: data$ETH
## X-squared = 10694, df = 2, p-value < 2.2e-16Box.test(data$ETH, lag = 2, type = "Ljung-Box")##
## Box-Ljung test
##
## data: data$ETH
## X-squared = 19.556, df = 2, p-value = 5.669e-05Box.test(data$ETH, lag = 2, type = "Box-Pierce")##
## Box-Pierce test
##
## data: data$ETH
## X-squared = 19.52, df = 2, p-value = 5.773e-05GARCH V
autoarfima(data$BTC,ar.max = 2, ma.max = 2,criterion = "AIC", method = "full")$fit##
## *----------------------------------*
## * ARFIMA Model Fit *
## *----------------------------------*
## Mean Model : ARFIMA(2,0,1)
## Distribution : norm
##
## Optimal Parameters
## ------------------------------------
## Estimate Std. Error t value Pr(>|t|)
## ar1 0.000000 NA NA NA
## ar2 0.051643 0.023276 2.2187 0.026505
## ma1 -0.067608 0.023294 -2.9024 0.003703
## sigma 3.932104 0.064556 60.9098 0.000000
##
## Robust Standard Errors:
## Estimate Std. Error t value Pr(>|t|)
## ar1 0.000000 NA NA NA
## ar2 0.051643 0.024829 2.0799 0.037531
## ma1 -0.067608 0.030535 -2.2141 0.026821
## sigma 3.932104 0.182365 21.5618 0.000000
##
## LogLikelihood : -5171.95
##
## Information Criteria
## ------------------------------------
##
## Akaike 5.5795
## Bayes 5.5884
## Shibata 5.5795
## Hannan-Quinn 5.5828
##
## Weighted Ljung-Box Test on Standardized Residuals
## ------------------------------------
## statistic p-value
## Lag[1] 0.00194 0.9649
## Lag[2*(p+q)+(p+q)-1][8] 1.93237 1.0000
## Lag[4*(p+q)+(p+q)-1][14] 3.72316 0.9845
##
## H0 : No serial correlation
##
## Weighted Ljung-Box Test on Standardized Squared Residuals
## ------------------------------------
## statistic p-value
## Lag[1] 3.697 0.05452
## Lag[2*(p+q)+(p+q)-1][2] 3.751 0.08797
## Lag[4*(p+q)+(p+q)-1][5] 6.957 0.05314
##
##
## ARCH LM Tests
## ------------------------------------
## Statistic DoF P-Value
## ARCH Lag[2] 3.765 2 0.15225
## ARCH Lag[5] 11.641 5 0.04005
## ARCH Lag[10] 19.237 10 0.03735
##
## Nyblom stability test
## ------------------------------------
## Joint Statistic: 0.495
## Individual Statistics:
## ar2 0.10226
## ma1 0.08025
## sigma 0.32241
##
## Asymptotic Critical Values (10% 5% 1%)
## Joint Statistic: 0.846 1.01 1.35
## Individual Statistic: 0.35 0.47 0.75
##
##
## Elapsed time : 0.04775715autoarfima(data$ETH,ar.max = 2, ma.max = 2,criterion = "AIC", method = "full")$fit##
## *----------------------------------*
## * ARFIMA Model Fit *
## *----------------------------------*
## Mean Model : ARFIMA(2,0,1)
## Distribution : norm
##
## Optimal Parameters
## ------------------------------------
## Estimate Std. Error t value Pr(>|t|)
## ar1 0.55326 0.201287 2.7486 0.005985
## ar2 0.10816 0.023326 4.6369 0.000004
## ma1 -0.63255 0.203120 -3.1142 0.001845
## sigma 5.13498 0.084305 60.9097 0.000000
##
## Robust Standard Errors:
## Estimate Std. Error t value Pr(>|t|)
## ar1 0.55326 0.207405 2.6675 0.007641
## ar2 0.10816 0.029176 3.7072 0.000210
## ma1 -0.63255 0.205392 -3.0797 0.002072
## sigma 5.13498 0.270933 18.9529 0.000000
##
## LogLikelihood : -5667.051
##
## Information Criteria
## ------------------------------------
##
## Akaike 6.1143
## Bayes 6.1263
## Shibata 6.1143
## Hannan-Quinn 6.1187
##
## Weighted Ljung-Box Test on Standardized Residuals
## ------------------------------------
## statistic p-value
## Lag[1] 0.02941 0.8638
## Lag[2*(p+q)+(p+q)-1][8] 2.19808 1.0000
## Lag[4*(p+q)+(p+q)-1][14] 7.24943 0.5113
##
## H0 : No serial correlation
##
## Weighted Ljung-Box Test on Standardized Squared Residuals
## ------------------------------------
## statistic p-value
## Lag[1] 11.10 8.645e-04
## Lag[2*(p+q)+(p+q)-1][2] 11.23 9.047e-04
## Lag[4*(p+q)+(p+q)-1][5] 20.08 1.842e-05
##
##
## ARCH LM Tests
## ------------------------------------
## Statistic DoF P-Value
## ARCH Lag[2] 11.02 2 4.044e-03
## ARCH Lag[5] 31.55 5 7.295e-06
## ARCH Lag[10] 37.21 10 5.215e-05
##
## Nyblom stability test
## ------------------------------------
## Joint Statistic: 0.3883
## Individual Statistics:
## ar1 0.03509
## ar2 0.09584
## ma1 0.03305
## sigma 0.21643
##
## Asymptotic Critical Values (10% 5% 1%)
## Joint Statistic: 1.07 1.24 1.6
## Individual Statistic: 0.35 0.47 0.75
##
##
## Elapsed time : 0.04064798###GARCH 11
#NORM
btc.garch11n.spec <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(1, 1)), mean.model = list(armaOrder = c(2, 1), include.mean = TRUE), distribution.model = "norm")
btc.garch11n.fit <- ugarchfit(spec = btc.garch11n.spec, data = data$BTC)
#STD
btc.garch11t.spec <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(1, 1)), mean.model = list(armaOrder = c(2, 1), include.mean = TRUE), distribution.model = "std")
btc.garch11t.fit <- ugarchfit(spec = btc.garch11t.spec, data= data$BTC)
##sstd
btc.garch11st.spec <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(1, 1)), mean.model = list(armaOrder = c(2, 1), include.mean = TRUE), distribution.model = "sstd")
btc.garch11st.fit <- ugarchfit(spec = btc.garch11st.spec, data = data$BTC)
##ged
btc.garch11g.spec <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(1, 1)), mean.model = list(armaOrder = c(2, 1), include.mean = TRUE), distribution.model = "ged")
btc.garch11g.fit <- ugarchfit(spec = btc.garch11g.spec, data = data$BTC)
#sged
btc.garch11sg.spec <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(1, 1)), mean.model = list(armaOrder = c(2, 1), include.mean = TRUE), distribution.model = "sged")
btc.garch11sg.fit <- ugarchfit(spec = btc.garch11sg.spec, data = data$BTC)##garch(1,2)
# GARCH(1,2) with NORM distribution
btc.garch12n.spec <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(1, 2)),
mean.model = list(armaOrder = c(2, 1), include.mean = TRUE),
distribution.model = "norm")
btc.garch12n.fit <- ugarchfit(spec = btc.garch12n.spec, data = data$BTC)
# GARCH(1,2) with STD distribution
btc.garch12t.spec <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(1, 2)),
mean.model = list(armaOrder = c(2, 1), include.mean = TRUE),
distribution.model = "std")
btc.garch12t.fit <- ugarchfit(spec = btc.garch12t.spec, data = data$BTC)
# GARCH(1,2) with SSTD distribution
btc.garch12st.spec <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(1, 2)),
mean.model = list(armaOrder = c(2, 1), include.mean = TRUE),
distribution.model = "sstd")
btc.garch12st.fit <- ugarchfit(spec = btc.garch12st.spec, data = data$BTC)
# GARCH(1,2) with GED distribution
btc.garch12g.spec <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(1, 2)),
mean.model = list(armaOrder = c(2, 1), include.mean = TRUE),
distribution.model = "ged")
btc.garch12g.fit <- ugarchfit(spec = btc.garch12g.spec, data = data$BTC)
# GARCH(1,2) with SGED distribution
btc.garch12sg.spec <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(1, 2)),
mean.model = list(armaOrder = c(2, 1), include.mean = TRUE),
distribution.model = "sged")
btc.garch12sg.fit <- ugarchfit(spec = btc.garch12sg.spec, data = data$BTC)#GARCH 21
# GARCH(2,1) with NORM distribution
btc.garch21n.spec <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(2, 1)),
mean.model = list(armaOrder = c(2, 1), include.mean = TRUE),
distribution.model = "norm")
btc.garch21n.fit <- ugarchfit(spec = btc.garch21n.spec, data = data$BTC)
# GARCH(2,1) with STD distribution
btc.garch21t.spec <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(2, 1)),
mean.model = list(armaOrder = c(2, 1), include.mean = TRUE),
distribution.model = "std")
btc.garch21t.fit <- ugarchfit(spec = btc.garch21t.spec, data = data$BTC)
# GARCH(2,1) with SSTD distribution
btc.garch21st.spec <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(2, 1)),
mean.model = list(armaOrder = c(2, 1), include.mean = TRUE),
distribution.model = "sstd")
btc.garch21st.fit <- ugarchfit(spec = btc.garch21st.spec, data = data$BTC)
# GARCH(2,1) with GED distribution
btc.garch21g.spec <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(2, 1)),
mean.model = list(armaOrder = c(2, 1), include.mean = TRUE),
distribution.model = "ged")
btc.garch21g.fit <- ugarchfit(spec = btc.garch21g.spec, data = data$BTC)
# GARCH(2,1) with SGED distribution
btc.garch21sg.spec <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(2, 1)),
mean.model = list(armaOrder = c(2, 1), include.mean = TRUE),
distribution.model = "sged")
btc.garch21sg.fit <- ugarchfit(spec = btc.garch21sg.spec, data = data$BTC)#GARCH 22
# GARCH(2,2) with NORM distribution and ARMA(2,1)
btc.garch22n.spec <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(2, 2)),
mean.model = list(armaOrder = c(2, 1), include.mean = TRUE),
distribution.model = "norm")
btc.garch22n.fit <- ugarchfit(spec = btc.garch22n.spec, data = data$BTC)
# GARCH(2,2) with STD distribution and ARMA(2,1)
btc.garch22t.spec <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(2, 2)),
mean.model = list(armaOrder = c(2, 1), include.mean = TRUE),
distribution.model = "std")
btc.garch22t.fit <- ugarchfit(spec = btc.garch22t.spec, data = data$BTC)
# GARCH(2,2) with SSTD distribution and ARMA(2,1)
btc.garch22st.spec <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(2, 2)),
mean.model = list(armaOrder = c(2, 1), include.mean = TRUE),
distribution.model = "sstd")
btc.garch22st.fit <- ugarchfit(spec = btc.garch22st.spec, data = data$BTC)
# GARCH(2,2) with GED distribution and ARMA(2,1)
btc.garch22g.spec <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(2, 2)),
mean.model = list(armaOrder = c(2, 1), include.mean = TRUE),
distribution.model = "ged")
btc.garch22g.fit <- ugarchfit(spec = btc.garch22g.spec, data = data$BTC)
# GARCH(2,2) with SGED distribution and ARMA(2,1)
btc.garch22sg.spec <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(2, 2)),
mean.model = list(armaOrder = c(2, 1), include.mean = TRUE),
distribution.model = "sged")
btc.garch22sg.fit <- ugarchfit(spec = btc.garch22sg.spec, data = data$BTC)CHỌN MÔ HÌNH BTC
btc.model.list <- list(garch11n = btc.garch11n.fit, garch11t = btc.garch11t.fit, garch11st = btc.garch11st.fit, garch11g = btc.garch11g.fit, garch11sg = btc.garch11sg.fit,
garch12n = btc.garch12n.fit, garch12t = btc.garch12t.fit, garch12st = btc.garch12st.fit, garch12g =
btc.garch12g.fit, garch12sg = btc.garch12sg.fit,
garch21n = btc.garch21n.fit, garch21t = btc.garch21t.fit, garch21st = btc.garch21st.fit, garch21g =
btc.garch21g.fit, garch21sg = btc.garch21sg.fit,
garch22n = btc.garch22n.fit, garch22t = btc.garch22t.fit, garch22st = btc.garch22st.fit, garch22g =
btc.garch22g.fit, garch22sg = btc.garch22sg.fit)
btc.info.mat <- sapply(btc.model.list, infocriteria)
rownames(btc.info.mat) <- rownames(infocriteria(btc.garch11n.fit))
btc.info.mat## garch11n garch11t garch11st garch11g garch11sg garch12n garch12t
## Akaike 5.497814 5.260249 5.261170 5.263723 5.264580 5.498892 5.261029
## Bayes 5.521645 5.287058 5.290957 5.290532 5.294368 5.525701 5.290817
## Shibata 5.497777 5.260202 5.261112 5.263677 5.264523 5.498846 5.260971
## Hannan-Quinn 5.506598 5.270130 5.272149 5.273605 5.275560 5.508774 5.272008
## garch12st garch12g garch12sg garch21n garch21t garch21st garch21g
## Akaike 5.261925 5.264373 5.265328 5.498362 5.259547 5.260545 5.263696
## Bayes 5.294692 5.294161 5.298094 5.528150 5.292314 5.296290 5.296463
## Shibata 5.261856 5.264316 5.265258 5.498304 5.259477 5.260462 5.263626
## Hannan-Quinn 5.274003 5.275353 5.277405 5.509341 5.271624 5.273720 5.275773
## garch21sg garch22n garch22t garch22st garch22g garch22sg
## Akaike 5.264723 5.499440 5.260625 5.261623 5.264821 5.265797
## Bayes 5.300468 5.532207 5.296371 5.300347 5.300566 5.304521
## Shibata 5.264640 5.499370 5.260542 5.261525 5.264738 5.265700
## Hannan-Quinn 5.277898 5.511517 5.273800 5.275896 5.277996 5.280070btc.inds <- which(btc.info.mat == min(btc.info.mat), arr.ind=TRUE)
model.btc <- colnames(btc.info.mat)[btc.inds[,2]]
model.btc## [1] "garch21t"btc.garch21t.fit##
## *---------------------------------*
## * GARCH Model Fit *
## *---------------------------------*
##
## Conditional Variance Dynamics
## -----------------------------------
## GARCH Model : gjrGARCH(2,1)
## Mean Model : ARFIMA(2,0,1)
## Distribution : std
##
## Optimal Parameters
## ------------------------------------
## Estimate Std. Error t value Pr(>|t|)
## mu 0.094507 0.057211 1.65190 0.098555
## ar1 0.125511 0.595380 0.21081 0.833037
## ar2 0.032668 0.040824 0.80021 0.423588
## ma1 -0.188052 0.595791 -0.31563 0.752280
## omega 0.172159 0.122519 1.40516 0.159974
## alpha1 0.016661 0.029510 0.56459 0.572351
## alpha2 0.066135 0.033252 1.98889 0.046714
## beta1 0.925372 0.017862 51.80654 0.000000
## gamma1 0.114086 0.061736 1.84797 0.064607
## gamma2 -0.132424 0.061129 -2.16630 0.030289
## shape 3.210383 0.222968 14.39838 0.000000
##
## Robust Standard Errors:
## Estimate Std. Error t value Pr(>|t|)
## mu 0.094507 0.055903 1.69056 0.090921
## ar1 0.125511 0.362723 0.34603 0.729324
## ar2 0.032668 0.030919 1.05655 0.290717
## ma1 -0.188052 0.359810 -0.52264 0.601223
## omega 0.172159 0.199092 0.86472 0.387190
## alpha1 0.016661 0.029338 0.56791 0.570097
## alpha2 0.066135 0.033015 2.00317 0.045159
## beta1 0.925372 0.025536 36.23814 0.000000
## gamma1 0.114086 0.064126 1.77909 0.075225
## gamma2 -0.132424 0.067882 -1.95081 0.051080
## shape 3.210383 0.213301 15.05097 0.000000
##
## LogLikelihood : -4867.23
##
## Information Criteria
## ------------------------------------
##
## Akaike 5.2595
## Bayes 5.2923
## Shibata 5.2595
## Hannan-Quinn 5.2716
##
## Weighted Ljung-Box Test on Standardized Residuals
## ------------------------------------
## statistic p-value
## Lag[1] 5.325 2.102e-02
## Lag[2*(p+q)+(p+q)-1][8] 9.340 3.904e-10
## Lag[4*(p+q)+(p+q)-1][14] 11.495 4.083e-02
## d.o.f=3
## H0 : No serial correlation
##
## Weighted Ljung-Box Test on Standardized Squared Residuals
## ------------------------------------
## statistic p-value
## Lag[1] 0.01779 0.8939
## Lag[2*(p+q)+(p+q)-1][8] 1.97755 0.8623
## Lag[4*(p+q)+(p+q)-1][14] 2.72734 0.9690
## d.o.f=3
##
## Weighted ARCH LM Tests
## ------------------------------------
## Statistic Shape Scale P-Value
## ARCH Lag[4] 2.067 0.500 2.000 0.1505
## ARCH Lag[6] 2.232 1.461 1.711 0.4418
## ARCH Lag[8] 2.329 2.368 1.583 0.6749
##
## Nyblom stability test
## ------------------------------------
## Joint Statistic: 4.8561
## Individual Statistics:
## mu 0.13673
## ar1 0.07998
## ar2 0.36941
## ma1 0.06251
## omega 0.34649
## alpha1 0.47602
## alpha2 0.57143
## beta1 0.36317
## gamma1 0.51094
## gamma2 0.55695
## shape 0.35809
##
## 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 1.49272 0.1357
## Negative Sign Bias 0.06678 0.9468
## Positive Sign Bias 1.42768 0.1536
## Joint Effect 3.03923 0.3856
##
##
## Adjusted Pearson Goodness-of-Fit Test:
## ------------------------------------
## group statistic p-value(g-1)
## 1 20 30.49 0.04591
## 2 30 35.97 0.17443
## 3 40 54.15 0.05405
## 4 50 59.85 0.13773
##
##
## Elapsed time : 1.22368btc.res <- residuals(btc.garch21t.fit)/sigma(btc.garch21t.fit)
fitdist(distribution = "std", btc.res, control = list())$pars## mu sigma shape
## -0.0004689593 1.1224293088 2.8131536722 v <- pdist(distribution = "std", q = btc.res, mu = -0.0004689593 , sigma = 1.1224293088, shape = 2.8131536722)GARCH ETH
###GARCH 11
#NORM
eth.garch11n.spec <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(1, 1)), mean.model = list(armaOrder = c(2, 1), include.mean = TRUE), distribution.model = "norm")
eth.garch11n.fit <- ugarchfit(spec = eth.garch11n.spec, data = data$ETH)
#STD
eth.garch11t.spec <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(1, 1)), mean.model = list(armaOrder = c(2, 1), include.mean = TRUE), distribution.model = "std")
eth.garch11t.fit <- ugarchfit(spec = eth.garch11t.spec, data= data$ETH)
##sstd
eth.garch11st.spec <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(1, 1)), mean.model = list(armaOrder = c(2, 1), include.mean = TRUE), distribution.model = "sstd")
eth.garch11st.fit <- ugarchfit(spec = eth.garch11st.spec, data = data$ETH)
##ged
eth.garch11g.spec <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(1, 1)), mean.model = list(armaOrder = c(2, 1), include.mean = TRUE), distribution.model = "ged")
eth.garch11g.fit <- ugarchfit(spec = eth.garch11g.spec, data = data$ETH)
#sged
eth.garch11sg.spec <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(1, 1)), mean.model = list(armaOrder = c(2, 1), include.mean = TRUE), distribution.model = "sged")
eth.garch11sg.fit <- ugarchfit(spec = eth.garch11sg.spec, data = data$ETH)##garch(1,2)
# GARCH(1,2) with NORM distribution
eth.garch12n.spec <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(1, 2)),
mean.model = list(armaOrder = c(2, 1), include.mean = TRUE),
distribution.model = "norm")
eth.garch12n.fit <- ugarchfit(spec = eth.garch12n.spec, data = data$ETH)
# GARCH(1,2) with STD distribution
eth.garch12t.spec <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(1, 2)),
mean.model = list(armaOrder = c(2, 1), include.mean = TRUE),
distribution.model = "std")
eth.garch12t.fit <- ugarchfit(spec = eth.garch12t.spec, data = data$ETH)
# GARCH(1,2) with SSTD distribution
eth.garch12st.spec <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(1, 2)),
mean.model = list(armaOrder = c(2, 1), include.mean = TRUE),
distribution.model = "sstd")
eth.garch12st.fit <- ugarchfit(spec = eth.garch12st.spec, data = data$ETH)
# GARCH(1,2) with GED distribution
eth.garch12g.spec <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(1, 2)),
mean.model = list(armaOrder = c(2, 1), include.mean = TRUE),
distribution.model = "ged")
eth.garch12g.fit <- ugarchfit(spec = eth.garch12g.spec, data = data$ETH)
# GARCH(1,2) with SGED distribution
eth.garch12sg.spec <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(1, 2)),
mean.model = list(armaOrder = c(2, 1), include.mean = TRUE),
distribution.model = "sged")
eth.garch12sg.fit <- ugarchfit(spec = eth.garch12sg.spec, data = data$ETH)# GARCH(2,1) with NORM distribution
eth.garch21n.spec <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(2, 1)),
mean.model = list(armaOrder = c(2, 1), include.mean = TRUE),
distribution.model = "norm")
eth.garch21n.fit <- ugarchfit(spec = eth.garch21n.spec, data = data$ETH)
# GARCH(2,1) with STD distribution
eth.garch21t.spec <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(2, 1)),
mean.model = list(armaOrder = c(2, 1), include.mean = TRUE),
distribution.model = "std")
eth.garch21t.fit <- ugarchfit(spec = eth.garch21t.spec, data = data$ETH)
# GARCH(2,1) with SSTD distribution
eth.garch21st.spec <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(2, 1)),
mean.model = list(armaOrder = c(2, 1), include.mean = TRUE),
distribution.model = "sstd")
eth.garch21st.fit <- ugarchfit(spec = eth.garch21st.spec, data = data$ETH)
# GARCH(2,1) with GED distribution
eth.garch21g.spec <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(2, 1)),
mean.model = list(armaOrder = c(2, 1), include.mean = TRUE),
distribution.model = "ged")
eth.garch21g.fit <- ugarchfit(spec = eth.garch21g.spec, data = data$ETH)
# GARCH(2,1) with SGED distribution
eth.garch21sg.spec <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(2, 1)),
mean.model = list(armaOrder = c(2, 1), include.mean = TRUE),
distribution.model = "sged")
eth.garch21sg.fit <- ugarchfit(spec = eth.garch21sg.spec, data = data$ETH)
##GARCH 22
# GARCH(2,2) with NORM distribution
eth.garch22n.spec <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(2, 2)),
mean.model = list(armaOrder = c(2, 1), include.mean = TRUE),
distribution.model = "norm")
eth.garch22n.fit <- ugarchfit(spec = eth.garch22n.spec, data = data$ETH)
# GARCH(2,2) with STD distribution
eth.garch22t.spec <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(2, 2)),
mean.model = list(armaOrder = c(2, 1), include.mean = TRUE),
distribution.model = "std")
eth.garch22t.fit <- ugarchfit(spec = eth.garch22t.spec, data = data$ETH)
# GARCH(2,2) with SSTD distribution
eth.garch22st.spec <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(2, 2)),
mean.model = list(armaOrder = c(2, 1), include.mean = TRUE),
distribution.model = "sstd")
eth.garch22st.fit <- ugarchfit(spec = eth.garch22st.spec, data = data$ETH)
# GARCH(2,2) with GED distribution
eth.garch22g.spec <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(2, 2)),
mean.model = list(armaOrder = c(2, 1), include.mean = TRUE),
distribution.model = "ged")
eth.garch22g.fit <- ugarchfit(spec = eth.garch22g.spec, data = data$ETH)
# GARCH(2,2) with SGED distribution
eth.garch22sg.spec <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(2, 2)),
mean.model = list(armaOrder = c(2, 1), include.mean = TRUE),
distribution.model = "sged")
eth.garch22sg.fit <- ugarchfit(spec = eth.garch22sg.spec, data = data$ETH)CHỌN MÔ HÌNH ETH
eth.model.list <- list(garch11n = eth.garch11n.fit, garch11t = eth.garch11t.fit, garch11st = eth.garch11st.fit, garch11g = eth.garch11g.fit, garch11sg = eth.garch11sg.fit,
garch12n = eth.garch12n.fit, garch12t = eth.garch12t.fit, garch12st = eth.garch12st.fit, garch12g = eth.garch12g.fit, garch12sg = eth.garch12sg.fit,
garch21n = eth.garch21n.fit, garch21t = eth.garch21t.fit, garch21st = eth.garch21st.fit, garch21g = eth.garch21g.fit, garch21sg = eth.garch21sg.fit,
garch22n = eth.garch22n.fit, garch22t = eth.garch22t.fit, garch22st = eth.garch22st.fit, garch22g = eth.garch22g.fit, garch22sg = eth.garch22sg.fit)
eth.info.mat <- sapply(eth.model.list, infocriteria)
rownames(eth.info.mat) <- rownames(infocriteria(eth.garch11n.fit))
eth.info.mat## garch11n garch11t garch11st garch11g garch11sg garch12n garch12t
## Akaike 6.032872 5.872167 5.873086 5.872511 5.871646 6.033950 5.873245
## Bayes 6.056702 5.898976 5.902874 5.899320 5.901433 6.060759 5.903033
## Shibata 6.032835 5.872120 5.873028 5.872464 5.871588 6.033903 5.873187
## Hannan-Quinn 6.041655 5.882048 5.884065 5.882392 5.882625 6.043831 5.884224
## garch12st garch12g garch12sg garch21n garch21t garch21st garch21g
## Akaike 5.874164 5.873590 5.872723 6.031311 5.871234 5.872232 5.871492
## Bayes 5.906931 5.903377 5.905490 6.061098 5.904001 5.907977 5.904259
## Shibata 5.874095 5.873532 5.872654 6.031253 5.871164 5.872149 5.871422
## Hannan-Quinn 5.886241 5.884569 5.884800 6.042290 5.883311 5.885407 5.883569
## garch21sg garch22n garch22t garch22st garch22g garch22sg
## Akaike 5.871993 6.032389 5.872312 5.873310 5.872570 5.873071
## Bayes 5.907738 6.065155 5.908058 5.912034 5.908315 5.911795
## Shibata 5.871910 6.032319 5.872229 5.873213 5.872487 5.872974
## Hannan-Quinn 5.885168 6.044466 5.885487 5.887583 5.885745 5.887344eth.inds <- which(eth.info.mat == min(eth.info.mat), arr.ind=TRUE)
model.eth <- colnames(eth.info.mat)[eth.inds[,2]]
model.eth## [1] "garch21t"eth.garch21t.fit##
## *---------------------------------*
## * GARCH Model Fit *
## *---------------------------------*
##
## Conditional Variance Dynamics
## -----------------------------------
## GARCH Model : gjrGARCH(2,1)
## Mean Model : ARFIMA(2,0,1)
## Distribution : std
##
## Optimal Parameters
## ------------------------------------
## Estimate Std. Error t value Pr(>|t|)
## mu 0.143356 0.097159 1.47548 0.140084
## ar1 0.839171 0.007515 111.66816 0.000000
## ar2 0.099756 0.021141 4.71854 0.000002
## ma1 -0.932963 0.022409 -41.63254 0.000000
## omega 1.919940 0.738241 2.60070 0.009303
## alpha1 0.013148 0.037572 0.34995 0.726378
## alpha2 0.115818 0.047854 2.42022 0.015511
## beta1 0.823755 0.044177 18.64658 0.000000
## gamma1 0.148043 0.075247 1.96741 0.049136
## gamma2 -0.147651 0.076393 -1.93279 0.053262
## shape 3.461593 0.317580 10.89991 0.000000
##
## Robust Standard Errors:
## Estimate Std. Error t value Pr(>|t|)
## mu 0.143356 0.101173 1.41695 0.156498
## ar1 0.839171 0.020649 40.63889 0.000000
## ar2 0.099756 0.018985 5.25460 0.000000
## ma1 -0.932963 0.007313 -127.58436 0.000000
## omega 1.919940 0.945342 2.03095 0.042260
## alpha1 0.013148 0.037180 0.35364 0.723608
## alpha2 0.115818 0.045601 2.53982 0.011091
## beta1 0.823755 0.054225 15.19137 0.000000
## gamma1 0.148043 0.084448 1.75307 0.079590
## gamma2 -0.147651 0.090231 -1.63637 0.101762
## shape 3.461593 0.324129 10.67969 0.000000
##
## LogLikelihood : -5434.569
##
## Information Criteria
## ------------------------------------
##
## Akaike 5.8712
## Bayes 5.9040
## Shibata 5.8712
## Hannan-Quinn 5.8833
##
## Weighted Ljung-Box Test on Standardized Residuals
## ------------------------------------
## statistic p-value
## Lag[1] 9.72 1.823e-03
## Lag[2*(p+q)+(p+q)-1][8] 16.63 0.000e+00
## Lag[4*(p+q)+(p+q)-1][14] 19.98 9.020e-06
## d.o.f=3
## H0 : No serial correlation
##
## Weighted Ljung-Box Test on Standardized Squared Residuals
## ------------------------------------
## statistic p-value
## Lag[1] 0.2313 0.6306
## Lag[2*(p+q)+(p+q)-1][8] 5.3799 0.3038
## Lag[4*(p+q)+(p+q)-1][14] 7.2364 0.4756
## d.o.f=3
##
## Weighted ARCH LM Tests
## ------------------------------------
## Statistic Shape Scale P-Value
## ARCH Lag[4] 5.786 0.500 2.000 0.01616
## ARCH Lag[6] 5.941 1.461 1.711 0.06957
## ARCH Lag[8] 6.097 2.368 1.583 0.15315
##
## Nyblom stability test
## ------------------------------------
## Joint Statistic: 2.6243
## Individual Statistics:
## mu 0.42614
## ar1 0.09409
## ar2 0.22568
## ma1 0.11586
## omega 0.22336
## alpha1 0.27720
## alpha2 0.28511
## beta1 0.28792
## gamma1 0.38098
## gamma2 0.35243
## shape 0.55476
##
## 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 1.42811 0.1534
## Negative Sign Bias 0.91458 0.3605
## Positive Sign Bias 0.04783 0.9619
## Joint Effect 2.97648 0.3953
##
##
## Adjusted Pearson Goodness-of-Fit Test:
## ------------------------------------
## group statistic p-value(g-1)
## 1 20 32.71 0.02597
## 2 30 40.92 0.06999
## 3 40 53.89 0.05669
## 4 50 61.68 0.10546
##
##
## Elapsed time : 1.580666eth.res <- residuals(eth.garch21t.fit)/sigma(eth.garch21t.fit)
fitdist(distribution = "std", eth.res, control = list())$pars## mu sigma shape
## 0.0009551004 1.0110046149 3.3988135082 u <- pdist(distribution = "std", q = eth.res, mu = 0.0009551004 , sigma = 1.0110046149, shape = 3.3988135082)ad.test(u, "punif")##
## Anderson-Darling test of goodness-of-fit
## Null hypothesis: uniform distribution
## Parameters assumed to be fixed
##
## data: u
## An = 0.64479, p-value = 0.6067ad.test(v, "punif")##
## Anderson-Darling test of goodness-of-fit
## Null hypothesis: uniform distribution
## Parameters assumed to be fixed
##
## data: v
## An = 0.67779, p-value = 0.5776cvm.test(v, "punif")##
## Cramer-von Mises test of goodness-of-fit
## Null hypothesis: uniform distribution
## Parameters assumed to be fixed
##
## data: v
## omega2 = 0.1085, p-value = 0.5448cvm.test(u, "punif")##
## Cramer-von Mises test of goodness-of-fit
## Null hypothesis: uniform distribution
## Parameters assumed to be fixed
##
## data: u
## omega2 = 0.083103, p-value = 0.6742 ks.test(v, "punif")##
## Asymptotic one-sample Kolmogorov-Smirnov test
##
## data: v
## D = 0.017586, p-value = 0.6147
## alternative hypothesis: two-sided ks.test(u, "punif")##
## Asymptotic one-sample Kolmogorov-Smirnov test
##
## data: u
## D = 0.016902, p-value = 0.6643
## alternative hypothesis: two-sided#CHẠY COPULA
## phù hợp nhất
BiCopSelect(u, v, familyset= 1:9, selectioncrit="AIC",indeptest = FALSE, level = 0.05)## Bivariate copula: Survival BB1 (par = 0.08, par2 = 2.72, tau = 0.65)Stu <- BiCopEst(u, v, family = 7, method = "mle", se = T, max.df = 10)
summary(Stu)## Family
## ------
## No: 7
## Name: BB1
##
## Parameter(s)
## ------------
## par: 1.26 (SE = 0.09)
## par2: 1.68 (SE = 0.06)
## Dependence measures
## -------------------
## Kendall's tau: 0.64 (empirical = 0.65, p value < 0.01)
## Upper TD: 0.49
## Lower TD: 0.72
##
## Fit statistics
## --------------
## logLik: 1210.84
## AIC: -2417.69
## BIC: -2406.64# gau
gaus <- BiCopEst(u, v, family = 1, method = "mle", se = T, max.df = 10)
summary(gaus)## Family
## ------
## No: 1
## Name: Gaussian
##
## Parameter(s)
## ------------
## par: 0.83 (SE = 0.01)
##
## Dependence measures
## -------------------
## Kendall's tau: 0.63 (empirical = 0.65, p value < 0.01)
## Upper TD: 0
## Lower TD: 0
##
## Fit statistics
## --------------
## logLik: 1104.56
## AIC: -2207.12
## BIC: -2201.59stud <- BiCopEst(u, v, family = 2, method = "mle", se = T, max.df = 10)
summary(stud)## Family
## ------
## No: 2
## Name: t
##
## Parameter(s)
## ------------
## par: 0.85 (SE = 0.01)
## par2: 3.67 (SE = 0.41)
## Dependence measures
## -------------------
## Kendall's tau: 0.64 (empirical = 0.65, p value < 0.01)
## Upper TD: 0.56
## Lower TD: 0.56
##
## Fit statistics
## --------------
## logLik: 1190.49
## AIC: -2376.98
## BIC: -2365.93clay <- BiCopEst(u, v, family = 3, method = "mle", se = T, max.df = 10)
summary(clay)## Family
## ------
## No: 3
## Name: Clayton
##
## Parameter(s)
## ------------
## par: 2.8 (SE = 0.08)
##
## Dependence measures
## -------------------
## Kendall's tau: 0.58 (empirical = 0.65, p value < 0.01)
## Upper TD: 0
## Lower TD: 0.78
##
## Fit statistics
## --------------
## logLik: 1109.16
## AIC: -2216.31
## BIC: -2210.79rotclay <- BiCopEst(u, v, family = 23, method = "mle", se = T, max.df = 10)
summary(rotclay)## Family
## ------
## No: 23
## Name: Rotated Clayton 90 degrees
##
## Parameter(s)
## ------------
## par: 0 (SE = 0.07)
##
## Dependence measures
## -------------------
## Kendall's tau: 0 (empirical = 0.65, p value < 0.01)
## Upper TD: 0
## Lower TD: 0
##
## Fit statistics
## --------------
## logLik: -0.17
## AIC: 2.33
## BIC: 7.86gum <- BiCopEst(u, v, family = 4, method = "mle", se = T, max.df = 10)
summary(gum)## Family
## ------
## No: 4
## Name: Gumbel
##
## Parameter(s)
## ------------
## par: 2.53 (SE = 0.05)
##
## Dependence measures
## -------------------
## Kendall's tau: 0.6 (empirical = 0.65, p value < 0.01)
## Upper TD: 0.68
## Lower TD: 0
##
## Fit statistics
## --------------
## logLik: 1005.12
## AIC: -2008.24
## BIC: -2002.71rotgum <- BiCopEst(u, v, family = 24, method = "mle", se = T, max.df = 10)
summary(rotgum)## Family
## ------
## No: 24
## Name: Rotated Gumbel 90 degrees
##
## Parameter(s)
## ------------
## par: -1 (SE = 0.03)
##
## Dependence measures
## -------------------
## Kendall's tau: 0 (empirical = 0.65, p value < 0.01)
## Upper TD: 0
## Lower TD: 0
##
## Fit statistics
## --------------
## logLik: -0.29
## AIC: 2.59
## BIC: 8.11Frank <- BiCopEst(u, v, family = 5, method = "mle", se = T, max.df = 10)
summary(Frank)## Family
## ------
## No: 5
## Name: Frank
##
## Parameter(s)
## ------------
## par: 9.51 (SE = 0.24)
##
## Dependence measures
## -------------------
## Kendall's tau: 0.65 (empirical = 0.65, p value < 0.01)
## Upper TD: 0
## Lower TD: 0
##
## Fit statistics
## --------------
## logLik: 1092.75
## AIC: -2183.5
## BIC: -2177.98Joe <- BiCopEst(u, v, family = 6, method = "mle", se = T, max.df = 10)
summary(Joe)## Family
## ------
## No: 6
## Name: Joe
##
## Parameter(s)
## ------------
## par: 2.77 (SE = 0.06)
##
## Dependence measures
## -------------------
## Kendall's tau: 0.49 (empirical = 0.65, p value < 0.01)
## Upper TD: 0.72
## Lower TD: 0
##
## Fit statistics
## --------------
## logLik: 716.8
## AIC: -1431.6
## BIC: -1426.07RotJoe <- BiCopEst(u, v, family = 26, method = "mle", se = T, max.df = 10)
summary(RotJoe)## Family
## ------
## No: 26
## Name: Rotated Joe 90 degrees
##
## Parameter(s)
## ------------
## par: -1 (SE = 0.03)
##
## Dependence measures
## -------------------
## Kendall's tau: 0 (empirical = 0.65, p value < 0.01)
## Upper TD: 0
## Lower TD: 0
##
## Fit statistics
## --------------
## logLik: -0.17
## AIC: 2.33
## BIC: 7.86# cái bb1 là phù hợp nhất phần ở trên
rotbb1 <- BiCopEst(u, v, family = 27, method = "mle", se = T, max.df = 10)## [1] "The rotated BB1 copulas cannot be used for positively dependent data."summary(rotbb1)## Family
## ------
## No: 27
## Name: Rotated BB1 90 degrees
##
## Parameter(s)
## ------------
## par: 0 (SE = NaN)
## par2: -1 (SE = 0.03)
## Dependence measures
## -------------------
## Kendall's tau: 0 (empirical = 0.65, p value < 0.01)
## Upper TD: 0
## Lower TD: 0
##
## Fit statistics
## --------------
## logLik: -2.92
## AIC: 9.83
## BIC: 20.89BB6 <- BiCopEst(u, v, family = 8, method = "mle", se = T, max.df = 10)
summary(BB6)## Family
## ------
## No: 8
## Name: BB6
##
## Parameter(s)
## ------------
## par: 1 (SE = NaN)
## par2: 2.52 (SE = NaN)
## Dependence measures
## -------------------
## Kendall's tau: 0.6 (empirical = 0.65, p value < 0.01)
## Upper TD: 0.68
## Lower TD: 0
##
## Fit statistics
## --------------
## logLik: 1004.92
## AIC: -2005.84
## BIC: -1994.79rotbb6 <- BiCopEst(u, v, family = 28, method = "mle", se = T, max.df = 10)## [1] "The rotated BB6 copulas cannot be used for positively dependent data."summary(rotbb6)## Family
## ------
## No: 28
## Name: Rotated BB6 90 degrees
##
## Parameter(s)
## ------------
## par: -1 (SE = NaN)
## par2: -1 (SE = NaN)
## Dependence measures
## -------------------
## Kendall's tau: 0 (empirical = 0.65, p value < 0.01)
## Upper TD: 0
## Lower TD: 0
##
## Fit statistics
## --------------
## logLik: -2.91
## AIC: 9.82
## BIC: 20.87BB7 <- BiCopEst(u, v, family = 9, method = "mle", se = T, max.df = 10)
summary(BB7)## Family
## ------
## No: 9
## Name: BB7
##
## Parameter(s)
## ------------
## par: 1.84 (SE = 0.07)
## par2: 2.5 (SE = 0.1)
## Dependence measures
## -------------------
## Kendall's tau: 0.6 (empirical = 0.65, p value < 0.01)
## Upper TD: 0.54
## Lower TD: 0.76
##
## Fit statistics
## --------------
## logLik: 1176.67
## AIC: -2349.33
## BIC: -2338.28BB7r <- BiCopEst(u, v, family = 29, method = "mle", se = T, max.df = 10)## [1] "The rotated BB7 copulas cannot be used for positively dependent data."summary(BB7r)## Family
## ------
## No: 29
## Name: Rotated BB7 90 degrees
##
## Parameter(s)
## ------------
## par: -1 (SE = NaN)
## par2: 0 (SE = NaN)
## Dependence measures
## -------------------
## Kendall's tau: 0 (empirical = 0.65, p value < 0.01)
## Upper TD: 0
## Lower TD: 0
##
## Fit statistics
## --------------
## logLik: -2.02
## AIC: 8.04
## BIC: 19.1BB8 <- BiCopEst(u, v, family = 10, method = "mle", se = T, max.df = 10)
summary(BB8)## Family
## ------
## No: 10
## Name: BB8
##
## Parameter(s)
## ------------
## par: 6 (SE = 0.33)
## par2: 0.78 (SE = 0.02)
## Dependence measures
## -------------------
## Kendall's tau: 0.58 (empirical = 0.65, p value < 0.01)
## Upper TD: 0
## Lower TD: 0
##
## Fit statistics
## --------------
## logLik: 962.82
## AIC: -1921.64
## BIC: -1910.59RBB8 <- BiCopEst(u, v, family = 30, method = "mle", se = T, max.df = 10)## [1] "The rotated BB8 copulas cannot be used for positively dependent data."summary(RBB8)## Family
## ------
## No: 30
## Name: Rotated BB8 90 degrees
##
## Parameter(s)
## ------------
## par: -1 (SE = NaN)
## par2: 0 (SE = NaN)
## Dependence measures
## -------------------
## Kendall's tau: 0 (empirical = 0.65, p value < 0.01)
## Upper TD: 0
## Lower TD: 0
##
## Fit statistics
## --------------
## logLik: 0
## AIC: 4
## BIC: 15.05