## Garch-in-Mean

The Garch-in-mean (MGARCH) model adds the equation’s variance to the regression function. This allows the average value of the dependent variable to depend on volatility of the underlying asset. In this way, more risk (volatility) can lead to higher average return. The equations are listed below:

yt = во + Oht + et (14.9)

ht = 5 + aief-1 + ydt-ie[81]-! + eiht-i (14.10)

Notice that in this formulation we left the threshold term in the model. The errors are normally distributed with zero mean and variance ht.

The parameters of this model can be estimated using gretl, though the recursive nature of the likelihood function makes it a bit more difficult. In the script below (Figure 14.9) you will notice that we’ve defined a function to compute the log-likelihood.2 The function is called g...

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