[R-SIG-Finance] AIC and deeper insight into model comparison

[Gareth McEwan]

Dear all

Using reference paper "Ng, S. and Perron, P. (2005). A Note on the
Selection of Time Series Models. *Oxford Bulletin of Economics and *
*Statistics*, 67 (1):115-134."

In fitting ARMA(p,q)-GARCH(1,1), ARMA(p,q)-GJR-GARCH(1,1) and
ARMA(p,q)-EGARCH(1,1) models to a time series (p,q = 0,1,2) under the
available error specifications (norm, std, ged, ghyp, sstd, sged, jsu,
nig), I had in mind to choose the fit with the lowest AIC value.

The Ng and Perron paper, however, advise holding N (the number of
observations) *fixed* (bottom of p.8) if you want theoretically valid model
comparisons. I assume R fits all the data in ARMA(0,q) and would drop 1
observation in fitting ARMA(1,q) and, similarly, would drop 2 observations
in fitting ARMA(2,q).

Has anyone dealt with this model selection issue before? If so, could you
recommend an approach that would allow N to be fixed for all fittings.
Note: I think the way to address the problem is to use the whole dataset
for ARMA(2,q), then drop the first observation when fitting ARMA(1,q), and
drop the first 2 observations when fitting ARMA(2,q)...thinking that this
would use R in a way that leads to theoretically correct AIC values valid
in comparing models.

Any help or guidance would be appreciated.

Many thanks
Gareth McEwan

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