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3.5. TESTING MONETARY MODEL PREDICTIONS 93To simplify computations of the conditional expectations of futurefundamentals growth, reformulate the VAR in (3.20) in the VAR(1)companion formY t = BY t−1 + u t , (3.22)whereB =⎛⎜⎝Y t =⎛⎜⎝∆f t∆f t−1.∆f t−p+1ζ tζ t−1.ζ t−p+1⎞⎟⎠, u t =⎛⎜⎝² t0.0v t0.0⎞⎟⎠a 11,1 a 11,2 ··· a 11,p a 12,1 a 12,2 ··· a 12,p1 0 ··· 0 0 0 ··· 00 1 0··· 0 0 0 ··· 0. ··· ··· . . . . .0 ··· ···1 0 0 ··· ··· 0a 21,1 a 21,2 ··· a 21,p a 22,1 a 22,2 ··· a 22,p0 ··· ··· 0 1 0 ··· 00 ··· ··· 0 0 1 0··· 0. ··· ··· . . . . .0 ··· ··· 0 0 ··· ···1 0Now let e 1 be a (1 × 2p) row vector with a 1 in the Þrst element andzeros elsewhere and let e 2 be a (1 × 2p) rowvectorwitha1asthep +1−th element and zeros elsewheree 1 =(1, 0,...,0), e 2 =(0,...,0, 1, 0,...,0).,⎞⎟⎠These are selection vectors that give⇐(65)e 1 Y t = ∆f t , e 2 Y t = ζ t .Now the k-step ahead forecast of f t is conveniently expressed asE(∆f t+j |H t )=e 1 E(Y t+j |H t )=e 1 B j Y t . (3.23)