On Mon, 19 Jul 2010, Skipper Seabold wrote:
All,
I was playing around and fitting an AR(2) model using the yearly
sunspots data provided by R data(sunspots), actually with more years
than in the R default dataset, and I was curious as to how the roots
of the AR coefficients are computed in gretl?
When I run
arima 2 0 0 ; SUNACTIVITY --conditional
I get a constant and phi_1 = 1.39181 and phi_2 = -.690287
IIUC, the roots to check for stability should be the solution to the
characteristic polynomial, which is in this case, X^2 - 1.39181 * X +
.690287. Using MATLAB's (or NumPy's) roots function, I find that the
roots of this equation are both
0.69590262389467661+0.45387935182766354j
But gretl says they are both 1.0081-.6575j, which is not a root of the
above. Am I misunderstanding something? If so, could someone point
to a reference?
The polynomial you want the roots for is the other way around, that is
1 - 1.39181 * X + 0.690287 * X^2: it is no coincidence that the roots you
found are the complex inverses of the ones that gretl shows.
Riccardo (Jack) Lucchetti
Dipartimento di Economia
Università Politecnica delle Marche
r.lucchetti(a)univpm.it
http://www.econ.univpm.it/lucchetti