# On ARIMA and its implementation

I am interested in ARMA/ARIMA models. First off, is there any material online about how to identify such models? It is done via acf and pacf, but I find the material I found online somewhat misleading. I would like to have a set of rule of thumbs I can use for that.

Secondly, do you know of any C++ library, equivalent to R for time series?

Finally, is it possible to include dependency across different time series? For example, suppose we know that series $\{x\}_n$ depends upon series $\{y\}_n$. How would I include this when using ARIMA models?

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It seems that you are asking several independent questions at once in this post. I'd recommend that you move at least the last question to a separate post, as this keeps the site tidy and makes questions and answers easier to find in the future! –  MånsT Jul 24 '12 at 6:57

1. Yes. See http://otexts.com/fpp/8/ Using the ACF and PACF to identify models is very out-of-date and there are much better methods available. Use the AIC, for example.

2. The R function arima() uses C code and it is open-source.

3. If the dependency goes in both directions, you might consider a VAR or VARIMA model. If $x$ depends on $y$, but not vice-versa, you might use a regression with ARIMA errors, or a transfer-function model.

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could you possibly provide a reference for VAR and VARIMA? –  Bob Jul 27 '12 at 22:27
Try Reinsel's book: amazon.com/gp/product/0387406190/… –  Rob Hyndman Jul 28 '12 at 23:57

I found this reference online that I think is a good introduction that may be helpful but is not a full tutorial on how to identify them.

http://www.duke.edu/~rnau/411arim.htm

As I find common wikipedia gives a nice introduction with some useful links. I find the reference list too short. That could be improved a lot. Here is the link:

http://en.wikipedia.org/wiki/Autoregressive_integrated_moving_average

I found this presentation that I think is particularly good and meets most of your needs.

http://www.stats24x7.com/9ARIMAMODELINGOFTIMESERIES.pdf

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