Unit root, prespecified S.s., large deviation less accuracy?

[bingye]

I am facing a problem when thinking about the case where a unit root is present. E.g., a=a(-1)+u.
I am told that a value has to be given for a to pin down the STEADY STATE and linearization is then possible. But the problem is, a may drift far from the prespecified value, so are other endogenous variables. As a result, the linear approximation (first order approximation)around the prespecified steady state may be inaccuracy.
Is it true?

[jpfeifer]

Yes, this is true as the approximation is always only local. It is typically not an issue for e.g. IRF analysis at the initially specified point, but might be a problem when doing long simulations where the variable drifts away from the initial approximation point.