Re: [Gretl-users] New plot for arma models

On Mon, 27 Mar 2017, Sven Schreiber wrote: I thought that the sample periodogram is better for the purpose I had in mind, which is to provide a basic visual "mis-specification test". Maybe I'm wrong, but the whole idea was to provide a sort-of "actual-vs-fitted" plot. If the model is correctly specified, you should see the spectrum nicely going through the periodogram points. Otherwise... try this: <hansl> nulldata 128 setobs 1 1 --special-time-series series y = 0 series y = 1.8 * y(-1) - 0.9 * y(-1) + normal() # simulate an ar(2) arima 0 2 ; y --window # estimate a ma(2) - bleah </hansl> That said, of course you have to be aware that 1) sample periodogram ordinates are negative exponentials if the process is Gaussian, so when you take their logs the distribution you get is left-skewed and you shouldn't expect the spectrum to go through the paeriodogram "halfway", so to speak. You should get lots of small positive "errors" and some large negative ones. 2) You could actually come up with arma parameters which give you a marginally better "fit", if you maximised the "Whittle likelihood" instead of the familiar one. But then, who cares? ------------------------------------------------------- Riccardo (Jack) Lucchetti Dipartimento di Scienze Economiche e Sociali (DiSES) Università Politecnica delle Marche (formerly known as Università di Ancona) r.lucchetti(a)univpm.it http://www2.econ.univpm.it/servizi/hpp/lucchetti -------------------------------------------------------