Effect of mean model on volatility predictions
Modeling 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.
This exercise is part of the course
GARCH Models in R
Exercise instructions
- 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.
Hands-on interactive exercise
Have a go at this exercise by completing this sample code.
# GARCH-in-Mean specification and estimation
gim_garchspec <- ___(
mean.model = list(armaOrder = c(0,0), archm = ___, archpow = ___),
variance.model = list(model = "gjrGARCH"), distribution.model = "sstd")
gim_garchfit <- ___(data = msftret , ___ = ___)
# Predicted mean returns and volatility of GARCH-in-mean
gim_mean <- ___(___)
gim_vol <- ___(___)
# Correlation between predicted return using AR(1) and GARCH-in-mean models
___(___, ___)
# Correlation between predicted volatilities across mean.models
___(merge(constmean_vol, ar1_vol, gim_vol))