[Gretl-devel] ARIMA output

I think there is something slightly incorrect in the second part of the ARIMA output. Look for example to the output generated by a pure seasonal model as the one in this script: <hansl> nulldata 500 setobs 4 1:1 --time-series set seed 1234 eps=randgen(N,0,1) Yt=0*const Yt=0.8*Yt(-4)+eps arma 0 0 ; 1 0 ; Yt --nc </hansl> with this seed I obtain here an estimated coefficient of 0.75, and the second part of the gretl output table reports the roots as: <output> Real Imaginary Modulus Frequency ----------------------------------------------------------- AR (seasonal) Root 1 1.3223 0.0000 1.3223 0.0000 ----------------------------------------------------------- </output> but this is not exactly correct. The estimated AR polynomial is (1-0.75 L^4) which has four roots in 1.32, -1.32, 1.32i and -1.32i, all of them with the same modulus, 1.32, and being their frequencies 0, 0.5, and 0.25 (the two complex roots with the same observed frequency because of the aliasing problem). I think for the non-seasonal part it is interesting to report the roots as we are doing now, but for the seasonal part I think that showing all the roots and frequencies may be excessive (imagine in the weekly case, 52 roots), but for not inducing the user to something incorrect we should report only the modulus. -- Ignacio Diaz-Emparanza DEPARTAMENTO DE ECONOMÍA APLICADA III (ECONOMETRÍA Y ESTADÍSTICA) UPV/EHU Avda. Lehendakari Aguirre, 83 | 48015 BILBAO T.: +34 946013732 | F.: +34 946013754 www.ea3.ehu.es