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Exercise

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.

Instructions
100 XP
  • 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.