4. Using QMLE, estimate the GARCH(1,1)-˜t

(d) model. Fix the variance parameters at their values from question 3. Set the starting value of d equal to 10.

(Excel Hint: Use the GAMMALN function for the log-likelihood function of the standardized t

(d) distribution.)

Construct a QQ plot for the standardized returns using the standardized t

(d) distribution. Compare your result with Figure 4.3. (Hint: Excel contains a two-sided quantile from the t

(d) distribution. To compute one-sided quantiles from the standardized t

(d) distribution, we use the relationship

˜t

−1 p

(d) =

−|tinv(2p, d)|

√

(d − 2)/d, if p ≤ 0.5

|tinv(2(1 − p), d)|

√

(d − 2)/d ifp > 0.5 where TINV is the function in Excel, and where ˜t

−1 p

(d) is the standardized one-sided quantile we need for the QQ plot.)