Discussion of “ High - dimensional autocovariance matrices and optimal linear prediction ” ∗ , †

First, we would like to congratulate Prof. McMurry and Prof. Politis for their thought-provoking paper on the optimal linear prediction based on full time series sample (hereafter, referred as [MP15]). [MP15] considered the one-step optimal linear predictor X∗ n+1 = ∑n i=1 φi(n)Xn+1−i of a univariate time series X1, . . . , Xn in the ` 2 sense which is given by the solution of the Yule-Walker equations φ(n) = Γ−1 n γ(n).