In response to Sven's request not so long ago I enabled
specification of particular lags of the y variables in VARs (e.g.
you could have a VAR with lags 1 and 3, skipping 2).
I said I'd follow up by allowing that sort of thing for VECMs too,
but unless I'm getting mixed up (quite possible) this seems
substantially more difficult.
Consider the gappy VAR (deterministic terms and error omitted for
simplicity):
y_t = A_1 y_{t-1} + A_3 y_{t-3}
The VECM representation is, I think,
\delta y_t = \Pi y_{t-1} + G_1 \delta y_{t-1}
+ G_2 \delta y_{t-2}
where \Pi = A_1 + A_3 - I
G_1 = -A_3
G_2 = -A_3
That, not only have we "dropped a lag" (as per usual), but now
there's an implied restriction on the G_i matrices. First
question: have I gone off the rails here? Second Q: if not, how
would we handle this and would it be worth the trouble?
Allin.