1. Suppose that 5 yt 6 and 5 zt 6 are I(1) series, but yt 2 b zt is I(0) for some b 2 0. Show that for any d 2 b, yt 2 d zt must be I(1). 2. Consider the error correction model in equation...

1. Suppose that 5yt6 and 5zt6 are I(1) series, but
yt
2 bzt
is I(0) for some b 2 0. Show that for any

d 2 b,
yt
2 dzt
must be I(1).

2. Consider the error correction model in equation (18.37). Show that if you add another lag of the error correction term,
yt22 2 bxt22, the equation suffers from perfect collinearity. (Hint: Show that
yt22 2 bxt22 is a perfect linear function of
yt21 2 bxt21, Dxt21, and Dyt21.)