Re: [Gretl-users] New plot for arma models
Am 27.03.2017 um 08:47 schrieb Riccardo (Jack) Lucchetti:
On Mon, 27 Mar 2017, Sven Schreiber wrote:
> When you say "sample periodogram", I guess you're
using the smoothed
> periodogram? (As the raw periodogram isn't a consistent estimator.)
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.
I think it depends on how you define "through".
Intuitively I'd say that if you are using the correct model (an
estimated version of the DGP), then asymptotically the parametrically
estimated spectrum and the non-parametrically estimated one (for
example, using the smoothed periodogram) will converge on each other. I
don't think that the same result would hold for the raw sample
periodogram, because it is not a consistent estimator of the spectrum.
In that sense the periodogram ordinates are not "actuals" like
datapoints are, I think.
Graphically I would expect the sample periodogram to "wiggle" around,
and the parametric spectrum estimate will be comparably smooth and go
"through" the periodogram in a common-sense way. I think that would
basically mean that the user is doing the smoothing of the periodogram
herself mentally, in her imagination.
(Smoothing is of course not the only way to obtain a consistent estimator.)
cheers,
sven