Re: [Gretl-users] AR roots?

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.