[R] ARMA and ARIMA modeling

[Dirk Eddelbuettel]

On Sat, Mar 09, 2002 at 07:18:17AM +0000, Prof Brian D Ripley wrote:
> Only ts has full handling of ARIMA models.  It's changed a lot in R-devel.
> It also provides basic function on which all the others rely.
> 
> tseries contains other models primarily of interest in economics, and
> GARCH models (which are better models of stock prices).  It also has

Hm, "better" sounds odd here. 

They cannot be compared directly: Garch models are different from Arma
models in the sense of being "arma-type models in the variance". They model
second moments (variance, and thus volatility), not first moments. Both have
benn combined by using AR(F)(I)MA for the first moment and Garch-type models
for the second moment.  Doing that estimation jointly is tricky. It is also
tricky to fit the Ar(f)(i)ma model "well" to financial markets return.
Low-hanging fruits like this get picked up in the markets the earliest...

"Better" is of course correct in a less-narrow sense of Garch models being
considered a generally more valid fit in the variance space than arma models
in the mean space.

> arma, which is subsumed by arima (and arima0) in R-devel.
> 
> fracdiff handles fractionally differenced models, a very specialized topic.

A generalisation of ARIMA by relaxing the d=1 restriction. I never had much
luck with the package -- the covariance matrix estimator seems very broken
(some elements are in the order of 1e-28, others 1e+20 which cannot be
sensible; try "example(fracdiff)".) I always meant to debug that but
haven't.

Another somewhat important distinction is that David (or I) are not supposed
to use fracdiff or tseries at work -- fracdiff and some parts of tseries are
not free for commerical use.

Dirk

-- 
Good judgement comes from experience; experience comes from bad judgement. 
							    -- Fred Brooks
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