n.ots <- 1000 #number of out of sample obsv
n.its <- 1500 #obsv in rolling windows
alpha <- 0.05

y.ots <- matrix(NA, nrow = n.ots, ncol = 1)
pred_vol_beta <- matrix(NA, nrow = n.ots, ncol = 1) #predicted volatility (cond. st. deviation)
pred_vol_beta_sk <- matrix(NA, nrow = n.ots, ncol = 1)

q_resid_beta <- matrix(NA, nrow = n.ots, ncol = 1)
q_resid_sk <- matrix(NA, nrow = n.ots, ncol = 1)

for (i in 1:n.ots) {
  y.its <- log_returns[i:(n.its + i - 1)]
  y.ots[i] <- log_returns[n.its + i]


  pred_vol_beta[i] <- predict(tegarch(y.its,skew = FALSE),n.ahead = 1)
  pred_vol_beta_sk[i] <- predict(tegarch(y.its,skew = TRUE),n.ahead = 1)

  q_resid_beta[i] <- quantile(residuals.tegarch(tegarch(y.its,skew = FALSE),standardized = TRUE),alpha) # quantile of the distribution applied to the standardized residuals
  q_resid_sk[i] <- quantile(residuals.tegarch(tegarch(y.its,skew = TRUE),standardized = TRUE),alpha)

}
toc()
pred_vol_beta <- unlist(pred_vol_beta)
pred_vol_beta_sk <- unlist(pred_vol_beta_sk)

VaR_beta <- q_resid_beta*pred_vol_beta
VaR_beta_sk <- q_resid_sk*pred_vol_beta_sk