1. Suppose that a list contains the values 20 44 48 55 62 66 74 88 93 99 at index positions 0 through 9. Trace the values of the variables….

## explain what would happen to the forecasts in this case.

(g) Suppose now that the researcher had estimated the above GARCH model for a series of returns on a stock index and obtained the following parameter estimates: µˆ = 0.0023, aˆ 0 = 0.0172,

ˆß = 0.9811, ˆa1 = 0.1251. If the researcher has data available up to and including time T , write down a set of equations in s2 t and u2t their lagged values, which could be employed to produce one-, two-,

and three-step-ahead forecasts for the conditional variance of yt .

(h) Suppose now that the coefficient estimate of ˆß for this model is 0.98 instead. By re-considering the forecast expressions you derived in part (g), explain what would happen to the forecasts in this case.