from which we can deduce that X E(X,Xi++)=E out-i )(∑ out+T-j 02],T≥0. Hence, for lo| 1, the stochastic process Xt, tET')is both weakly-stationary and asymptotically uncorrelated since the autocovariance function →0.asT→∞ Therefore, if any finite subset of T*, say ti, t2,, tr of a Ar(1)process, (Xt, Xt, . Xtr) x has covariance matrix 1 where 1 It is straightforward to show by direct multiplication that PP=Q 10 0 0 0from which we can deduce that E(Xt) = 0, E(XtXt+τ ) = E ( X∞ i=0 φ iut−i ! X∞ j=0 φ iut+τ−j !) = σ 2 u X∞ i=0 φ iφ i+τ ! = σ 2 uφ τ X∞ i=0 φ 2i ! , τ ≥ 0. Hence, for |φ| < 1, the stochastic process {Xt , t ∈ T ∗} is both weakly-stationary and asymptotically uncorrelated since the autocovariance function γτ = σ 2 u (1 − φ 2 ) φ τ → 0, as τ → ∞. Therefore, if any finite subset of T ∗ , say t1,t2, ...,tT of a AR(1) process, (Xt1 , Xt2 , ..., XtT ) ≡ x 0 T has covariance matrix E(xTx 0 T) = σ 2 u 1 (1 − φ 2 )         1 φ . . . φ T −1 φ 1 φ . . φ T −2 . . . . . . . . . . . . . . . . . . φ T −1 . . . . 1         = σ 2 uΩ, where Ω = 1 (1 − φ 2 )         1 φ . . . φ T −1 φ 1 φ . . φ T −2 . . . . . . . . . . . . . . . . . . φ T −1 . . . . 1         . It is straightforward to show by direct multiplication that P 0P = Ω −1 , for P =         p 1 − φ 2 0 . . . 0 −φ 1 0 . . 0 0 −φ 1 0 . 0 . . . . . . . . . . . . 0 0 . . −φ 1         . 11