Exercise

# Parameter bounds and impact on forecasts

Let's take again the flexible GARCH model specification for which the estimated coefficients are printed in the console. Now assume that you believe that the GARCH parameter \(\alpha\) should be between 0.05 and 0.1, while the \(\beta\) parameter is between 0.8 and 0.95. You are asked here to re-estimate the model by imposing those bounds and see the effect on the volatility forecasts for the next ten days obtained using `ugarchforecast`

.

Instructions

**100 XP**

- Impose the
`c(0.05, 0.2)`

and`c(0.8, 0.95)`

bounds on`alpha1`

and`beta1`

. - Estimate the bounded model on the EURUSD returns.
- Note how coefficients have changed.
- Compare in a table the volatility predictions for the next 10 days using the unrestricted and restricted models.