(i) Use NYSE.RAW to estimate equation (12.48). Let t be the fitted values from this equation (the estimates of the conditional variance). How many t are negative?
(ii) Add return2t-1 to (12.48) and again compute the fitted values, t. Are any t negative?
(iii) Use the t from part (ii) to estimate (12.47) by weighted least squares (as in Section 8.4). Compare your estimate of (1 with that in equation (11.16). Test H0: (1 = 0 and compare the outcome when OLS is used.
(iv) Now, estimate (12.47) by WLS, using the estimated ARCH model in (12.51) to obtain the t. Does this change your findings from part (iii)?