The R-code procedure in the GARCH-EVT-Copula model estimation

I have been able to do the following steps in R:

  1. Fit GARCH models to each series.
  2. Extract standardized returns.
  3. Transform standardized returns to uniform marginals using the parametric IFM method by Joe.
  4. Fit the copulas and estimate the parameters.
  5. Generate 100 1-day ahead forecasts from the copulas.
  6. Reverse transform the simulated values.
  7. Use these transformed forecasts in ugarchsim (using custom.dist)
  8. Extract forecasted mu and sigma.
  9. Calculate 95% and 99% VaR equally weighted portfolio of 2 assets with weights 1/5

My question is, how to do the 9th step?


Use ugarchpath instead of ugarchsim and take the empirical 5% quantile (across the different simulation runs) of the simulated return $\hat x_{t+1}$ as a forecast of the 95% VaR and the 1% quantile for 99% VaR.

Alternatively, skip steps 7. and 8. and feed in the reverse-transformed simulated values $z_{t+1}$ into the estimated model equations (first insert $z_{t+1}$ into the model for $\sigma$, thus obtain the forecasted $\hat\sigma_{t+1}$, then insert $\hat\sigma_{t+1} z_{t+1}$ in place of $\varepsilon_{t+1}$ into the conditional mean equation to obtain the forecasted return $\hat x_{t+1}$) and take the empirical 5% quantile of $\hat x_{t+1}$ as a forecast of the 95% VaR and the 1% quantile for 99% VaR.

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