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.
Data matrices were not correcty lagged for lags>1. This commit fixes the
inconsistencies (in terms of residuals) between Iterative OLS and NLS routines.
Stéphane Adjemia (Scylla)
Stéphane Adjemian(Charybdis)