# Estimating the confidence interval for the volatility of a GARCH model

This question is a followup of my previous question Forecasting with ARIMA and GARCH: does my plan look alright?

I have a times series $r_t$ and I am trying to estimate its volatility with a GARCH model as in the referred question.

You can for example consider the following time series:

  -0.008230499 -0.025105921 -0.025752496  0.025752496
 -0.008510690  0.041847110 -0.033336420  0.041499731
 -0.008163311  0.024292693 -0.032523192 -0.008298803
  0.080042708  0.000000000  0.088292607  0.041385216
 -0.013605652  0.046831300  0.006514681 -0.019672766
  0.013158085 -0.006557401  0.019544596  0.092373320
  0.116474991  0.020726131  0.169418152  0.167054085
 -0.128832872  0.056695344 -0.032002731 -0.016393810
 -0.151399646  0.104879631  0.159701110 -0.029964789
 -0.003809528 -0.034955015 -0.011928571 -0.016129382
  0.012121361 -0.004024150 -0.004040410 -0.008130126
 -0.033198069 -0.065382759  0.017857617  0.034786116
 -0.017241806 -0.026433257  0.013303966  0.000000000
 -0.045052664  0.013730193 -0.009132484 -0.013857035
 -0.023530497 -0.019231362 -0.070380797 -0.005221944
  0.015584731 -0.010362787 -0.048009219 -0.005479466
>


the elements of which are not autocorrelated.

The volatility is then estimated using a GARCH(1,1) model and predicted from it as follows:

G.A = garchFit(formula = A~garch(1, 1), data = diff_log_close_price, trace = F)
G.A.est = predict(G.A, 30, plot=T, nx=nrow(closing_price))