Suppose the process [(xt, yt): t = 0, 1, 2, ...} satisfies the equations yt = xt + ut and xt = xt-1, + vt,

Suppose the process [(xt, yt): t = 0, 1, 2, ...} satisfies the equations
yt = βxt + ut
and
Δxt = γΔxt-1, + vt,
where E(ut | It-1) = E(vt | It-1) = 0, It-1, contains information on x and y dated at time t - 1 and earlier, β ≠ 0, and |γ| < 1 [so that xt, and therefore yt, is I(1)]. Show that these two equations imply an error correction model of the form
Δyt = γ1 Δxt-1 + δ(yt-1 - βxt-1) + et,
where y, = βγ, δ = - 1, and et = ut + Bvt.