PAC equation has to be written as
diff(x) = a0*(xstar(-1)-x(-1)) + a1*diff(x(-1)) + ... + ap*diff(x(-p)) + PAC_EXPECTATION(pacmodelname) + ...;
In the error correction term, a0*(xstar(-1)-x(-1)), we must have the difference
between the target (the trend xstar(-1)) and the level of the endogenous
variable (x(-1)). To ensure stability around the trend, the parameter a0 needs
to be positive.
REMARKS
[1] In the TREND_COMPONENT_MODEL the error correction terms are written in
reverse order, ie as the difference betwwen the level of the endogenous
variable and the trend variable.
[2] In the estimation routine we do not constrain a0 to be positive, but is
would surely help to satisfy this condition in the initial condition.
Stéphane Adjemia (Scylla)
Stéphane Adjemian(Charybdis)