(b). the sequence of matrices rs so is absolutely summable (a). By definition TS=EO T。=E[t+业1et-1+业2Et-2+…+业Et-s++1et-8-1+… et-s+亚1Et-8-1+亚2Et-s-2+ 业92亚+重+9v1+更+2亚2 y。y fo 0,1,2 The row i, column j element of Is is therefore the autocovariance between the ith variable at time t and the jth variable s period earlier, E(yit -ui(,t-s -ui)(b). the sequence of matrices {Γs} ∞ s=0 is absolutely summable. Proof: (a). By definition Γs = E(yt − µ)(yt−s − µ) 0 or Γs = E [εt + Ψ1εt−1 + Ψ2εt−2 + ... + Ψsεt−s + Ψs+1εt−s−1 + ....] [εt−s + Ψ1εt−s−1 + Ψ2εt−s−2 + ....] 0 = ΨsΩΨ0 0 + Ψs+1ΩΨ0 1 + Ψs+2ΩΨ0 2 + ... = X∞ v=0 Ψs+vΩΨ0 v for s = 0, 1, 2, ... The row i, column j element of Γs is therefore the autocovariance between the ith variable at time t and the jth variable s period earlier, E(yit −µi)(yj,t−s−µj ). (b). 4