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?

On Mon, Jul 19, 2010 at 6:01 PM, Riccardo (Jack) Lucchetti <r.lucchetti(a)univpm.it&gt; wrote: > 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. > Indeed, and I was just arriving at this conclusion. Thanks all. Then the stability condition is reversed I take it, so the equation is stable when all are greater than one in modulus? Forgive my ignorance, but are these referred to as the AR roots and the ones that I found as the inverted AR roots, or vice versa? Maybe a note about this in the docs is warranted?