Suppose the process 5 1xt

, yt 2: t 5 0, 1, 2, p6 satisfies the equations yt 5 bxt 1 ut and Dxt 5 gDxt21 1 vt

, where E1ut 0It21 2 5 E1vt 0It21 2 5 0, It21 contains information on x and y dated at time t 2 1 and earlier, b 2 0, and 0g0 , 1 [so that xt

, and therefore yt

, is I(1)]. Show that these two equations imply an error correction model of the form Dyt 5 g1Dxt21 1 d1yt21 2 bxt21 2 1 et

, where g1 5 bg, d 5 21, and et 5 ut 1 bvt

. (Hint: First subtract yt21 from both sides of the first equation. Then, add and subtract bxt21 from the right-hand side and rearrange. Finally, use the second equation to get the error correction model that contains Dxt21.)