The AR(1)-GJR GARCH dynamics of MSFT returns
You have seen in the video that the sign of the autoregressive parameter in the AR(1) model depends on the market reaction to news
A positive value of \(\rho \) is consistent with the interpretation that markets under-react to news leading to a momentum in returns. A negative value of \(\rho \) is consistent with the interpretation that markets over-react to news leading to a reversion in returns.
Are the daily Microsoft returns characterized by a momentum or a reversal effect in their AR(1) dynamics? Let's find this out by estimating the parameters of the AR(1)-GJR GARCH model using the daily Microsoft returns in msftret
.
This exercise is part of the course
GARCH Models in R
Exercise instructions
armaOrder = c(1,2)
corresponds to an ARMA(1,2) model. An AR(1) model is the same as ARMA(1,0).- Complete the
mean.model
argument inugarchspec
to specify the AR(1) model to be used. - Estimate the model.
- Print the first two coefficients of the estimated GARCH model.
Hands-on interactive exercise
Have a go at this exercise by completing this sample code.
# Specify AR(1)-GJR GARCH model
garchspec <- ugarchspec(mean.model = list(armaOrder = ___ ),
variance.model = list(model = "gjrGARCH"),
distribution.model = "sstd")
# Estimate the model
garchfit <- ___
# Print the first two coefficients
___(___)[c(1:2)]