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Exercise

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.

Instructions
100 XP
  • 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 in ugarchspec to specify the AR(1) model to be used.
  • Estimate the model.
  • Print the first two coefficients of the estimated GARCH model.