[R] good procedure to estimate ARMA(p, q)?

[Gad Abraham]

Michael wrote:
> Hi all,
> 
> I have some residuals from regression, and i suspect they have correlations
> in them...
> 
> I am willing to cast the correlation into a ARMA(p, q) framework,
> 
> what's the best way to identify the most suitable p, and q, and fit ARMA(p,
> q) model and then correct for the correlations in regression?
> 
> I know there are functions in R, I have used them before, but I just want to
> see if I can do the whole procedure myself, just to improve my understanding
> ...
> 
> Please give me some pointers! Thanks a lot

I'm assuming the data is a time series, otherwise ARIMA models might not 
be applicable here.

I think identifying the order of ARIMA models is something of an art, 
because most real world models aren't as clean and simple as textbook 
examples. When you have several similar models, each with its own 
strengths and weaknesses, which one is "best"?

In short, you want to make sure your series is stationary, look at its 
ACF and PACF, then try different values of p and q based on that, and 
finally look at the residuals (autocorrelation, distribution, etc).

This is basically the Box-Jenkins methodology. The most accessible 
descriptions I've seen are in "Forecasting: Methods and Applications" by 
Makridakis, Wheelwright and Hyndman (chapter 7), and "Forecasting with 
Univariate Box-Jenkins Models" by Pankratz.

Cheers,
Gad

-- 
Gad Abraham
Department of Mathematics and Statistics
The University of Melbourne
Parkville 3010, Victoria, Australia
email: g.abraham at ms.unimelb.edu.au
web: http://www.ms.unimelb.edu.au/~gabraham