Effect of mean model on volatility predictions

Modelling the mean dynamics typically has a major effect on the obtained predicted returns, but only a minor effect on the volatility predictions. The effect on volatility predictions is so small that, if the interest is only in the volatility dynamics, usually one can ignore the mean dynamics and just assume the most simple specification, namely the constant mean model.

Let's test this for the daily returns of Microsoft. The predicted mean and volatility of the GARCH estimation under the assumption of constant mean and AR(1) are already available in the console as the variables constmean_mean, ar1_mean, constmean_vol and ar1_vol.

Complete the code to estimate the GARCH-in-mean model.
Compute the predicted mean and volatility.
Complete the code to compute the correlation between the AR(1) and GARCH-in-mean return predictions.
Complete the code to compute the correlation of all three volatility predictions.

Take Hint (-30 XP)

Exercise

Effect of mean model on volatility predictions

Instructions