The Box-Jenkins methodology is a strategy or procedure that can be used to build an ARIMA model. The methodology is outlined in the book Time Series Analysis: Forecasting and Control by George E. P. Box and Gwilym M. Jenkins, originally published in 1970 - more recent editions exist.
By opening up SAS, calling proc ARIMA, and supply numbers for p, d, and q, you have merely estimated an ARIMA model. Doing this blindly, that is, by not using any particular recognized methodology to identify the ARIMA model itself, is a bit like playing with matches - the dangers of software!
If you keep repeating this process - estimating lots and lots of ARIMA models - you will eventually be able to select a model with the lowest Akaike Information criterion (from the set of models that you have estimated). In this context, a more systematic approach would be to use an algorithm based on comparing AIC values for a variety of different models to automatically select an ARIMA model for you, such as the one provided by the forecast package in R - the relevant function name is
In any event, the procedure you outlined involved selecting an ARIMA model based on minimizing some information criterion (in this case, AIC, but there are other measures). This is one particular methodology, but it's not the Box-Jenkins methodology; an alternative.
The Box-Jenkins methodology comprises five stages (although sometimes said to involve just three stages):
- Checking for stationarity or non-stationarity and transforming the data, if necessary;
- Identification of a suitable ARMA model;
- Estimation of the parameters of the chosen model;
- Diagnostic checking of model adequacy; and
- Forecasting, or repetition of steps two to five.
Notably, it is an iterative process that involves the model builder exercising some judgement - and this is one aspect of the methodology that has been considered a shortcoming. The judgemental part comes into play particularly when interpreting two tools; namely, the (estimated) autocorrelation function (ACF) and partial autocorrelation function (PACF).
If you'd like to become a practitioner of the Box-Jenkins methodology, I'd recommended consulting the original text (you'd be surprised what modern textbooks omit!) alongside whatever modern variations you can find. Alan Pankratz has a couple of excellent textbooks, which I'd highly recommend, too; for example, Forecasting with Univariate Box-Jenkins Models: Concepts and Cases.
Experience suggests to me that the term "Box-Jenkins methodology" is used in a loose manner because I've heard some people use it to simply refer to building ARIMA models in general - and not to the actual process involved in building an ARIMA model - while others use it to refer to a modified version of what was published in 1970. As @Glen_b has pointed out, "there are numerous documents that describe the Box-Jenkins methodology these days that would include the use of AIC or similar quantities".
Q: Are you supposed to use Box-Jenkins methodology to come up with initial estimates of p,d,q?
As already mentioned, there are different model selection strategies so the answer is no it's not necessarily the case that you need to employ the Box-Jenkins methodology, but you could if you wanted to.
Q: Did SAS use it internally somehow?
Highly unlikely unless that software offers a quite sophisticated function! Consult the official SAS documentation for details of what the software does or is capable of doing. If it was R, you could look at the source code, but I doubt that's an option with SAS.