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The recursive nature of the GARCH variance

Under the GARCH(1,1) equation the predicted variance is determined by the squared surprise in return and the previous variance prediction:

You can implement this using a loop (refer to the slides if you don't remember the loop structure from the video).

Let's do this for the S&P 500 daily returns. The variables omega, alpha, beta, nobs, e2 and predvar are already loaded in your R environment.

Diese Übung ist Teil des Kurses

GARCH Models in R

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Anleitung zur Übung

  • Compute the predicted variances.
  • Use predvar to define the series of predicted annualized volatility ann_predvol .
  • Plot the predicted annualized volatility for the years 2008-2009 to see the dynamics around the financial crisis.

Interaktive Übung

Vervollständige den Beispielcode, um diese Übung erfolgreich abzuschließen.

# Compute the predicted variances
predvar[1] <- var(sp500ret) 
for(t in 2:nobs){
   predvar[t] <- ___ + ___ * e2[t-1] + ___ * predvar[___]
}

# Create annualized predicted volatility
ann_predvol <- xts(___(252) * sqrt(___), order.by = time(sp500ret))

# Plot the annual predicted volatility in 2008 and 2009
___(___["2008::2009"], main = "Ann. S&P 500 vol in 2008-2009")
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