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.