1. V ar(X n ) = 0 for any n 1 implies that X i = 0 a.s., where X n := n 1 P n i=1 X i : (iii) in (10.27), the second implication holds by Lemma 25.2 (with X i = 0 g i ) and the fourth implication holds by Assumption SR-V 2 (c), SR-V 2 -CS(c), SR-V 1 (c), SR-V 1 -CS(c), SR-(c), or SR--CS(c), and (iv) the result of Lemma 6.2, which is used in the proof of Lemma 10.6, holds using the equivariance condition in Assumption SR-V 2 (b), SR-V 2 -CS(b);:g is a strictly stationary sequence of mean zero, square integrable, strong mixing random variables. Then
2. Brie ?y, these modi?cations involve: (i) the de?nition of 5;F ; (ii) justifying the convergence in probability of b n and the positive de?niteness of its limit by;AG1, which is given in Section 19 in the SM to AG1
3. Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimation;D W K Andrews;Econometrica,1991