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Prediction errors

Under the GARCH model, the variance is driven by the square of the prediction errors \(e = R - \mu\). In order to calculate a GARCH variance, you thus need to first compute the prediction errors. For daily returns, it is common practice to set \(\mu\) equal to the sample average.

You're going to implement this and then verify that there is a large positive autocorrelation in the absolute value of the prediction errors. Positive autocorrelation reflects the presence of volatility clusters. When volatility is above average, it stays above average for some time. When volatility is low, it stays low for some time.

Diese Übung ist Teil des Kurses

GARCH Models in R

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Anleitung zur Übung

  • Set m to the mean of the daily S&P 500 returns in sp500ret.
  • Compute the prediction errors.
  • Plot the time series of absolute value of the prediction errors.
  • Use the function acf to plot the autocorrelation function of the absolute value of the prediction errors.

Interaktive Übung

Versuche dich an dieser Übung, indem du diesen Beispielcode vervollständigst.

# Compute the mean daily return
m <- ___(___)

# Define the series of prediction errors
e <- ___ - ___

# Plot the absolute value of the prediction errors
par(mfrow = c(2,1),mar = c(3, 2, 2, 2))
___(___(___))

# Plot the acf of the absolute prediction errors
___
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