R语言基于ARMA-GARCH-VaR模型拟合和预

nu <- 3
fixed.p <- list(mu = 0, #   mu (intercept)
ar1 = 0.5, #   phi_1 (AR(1) 参数 of mu_t)
ma1 = 0.3, #   theta_1 (MA(1) 参数 of mu_t)
omega = 4, #   alpha_0 (intercept)
alpha1 = 0.4, #   alpha_1 (GARCH(1) 参数 of sigma_t^2)
beta1 = 0.2, #   beta_1 (GARCH(1) 参数 of sigma_t^2)
shape = nu) #
armaOrder <- c(1,1) # ARMA 参数
garchOrder <- c(1,1) # GARCH 参数
varModel <- list(model = "sGARCH", garchOrder = garchOrder)
spec <- ugarchspec(varModel, mean.model = list(armaOrder = armaOrder),
fixed.pars = fixed.p, distribution.model = "std") # t 标准残差

plot(X,   type = "l", xlab = "t", ylab = expression(X[t]))
plot(sig, type = "h", xlab = "t", ylab = expression(sigma[t]))

plot(eps, type = "l", xlab = "t", ylab = expression(epsilon[t]))

## 拟合 an ARMA(1,1)-GARCH(1,1) model
spec <- ugarchspec(varModel, mean.model = list(armaOrder = armaOrder),
distribution.model = "std") #
fit <- ugarchfit(spec, data = X) # fit


##
mu. <- fitted(fit) # 拟合 hat{mu}_t (= hat{X}_t)
sig. <- sigma(fit) # 拟合 hat{sigma}_t


##
stopifnot(all.equal(as.numeric(mu.),  fit@fit$fitted.values),
all.equal(as.numeric(sig.), fit@fit$sigma))

## [1] 10
## [1] 12
## [1] "Correct Exceedances"
## [1] "Fail to Reject H0"
## [1] "Correct Exceedances & Independent"
## [1] "Fail to Reject H0"