On Sat, 31 Mar 2012, Daniel Bencik wrote: There's no such a thing as an "inverted roots" problem. The problem I mentioned in my earlier message was the common roots problem, which may arise when you have both an AR part and an MA part. A classic reference is Mcleod (1999), "Necessary and Sufficient Condition for Nonsingular Fisher Information Matrix in ARMA and Fractional ARIMA Models", The American Statistician, although the problem was known long before that. In short: suppose you have a difference equation A(L) y_t = C(L) x_t (of which an arma model is a special case, with x_t a white noise process), where the order of A() is p and the order of C() is q. Of course the above equality still holds if you apply the polynomial (1-bL) on both sides of the equation, whatever the value of b. This means that, for each value of b, you have an equivalent representation P(L) y_t = Q(L) x_t where P(L) = A(L) (1-bL) and Q(L) (1-bL). In turn, this means that for every ARMA(p,q) process there exists an uncountable infinity of equivalent ARMA(p+1, q+1) representations. These representations are called "redundant". If you read the argument backwards, when you apply an ARMA(p,q) model to a data series, you may have common factors between the A() and C() polynomials: if so, then your representation is just one of the possible equivalent redundant representations and you'll be much better of with an ARMA(p-1, q-1) model. Of course, all this does not apply, for obvious reasons, to pure AR or MA models (like in your case). Hope this helps, Riccardo (Jack) Lucchetti Dipartimento di Economia Università Politecnica delle Marche (formerly known as Università di Ancona) r.lucchetti(a)univpm.it http://www2.econ.univpm.it/servizi/hpp/lucchetti