Auto.arima vs autobox do they differ? From reading posts on this site I know there is an R function auto.arima (in the forecast package).  I also know that IrishStat, a member of of this site built the commercial package autobox in the early 1980s.  As these two packages exist today and automatically select arima models for given data sets what do they do differently?  Will they possibly produce different models for the same data set?
 A: michael/wayne 
AUTOBOX would definitely deliver/identify a different model if one or more of the following conditions is met 
1) there are pulses in the data 
2) there is 1 or more level/step shift in the data 
3) if there are seasonal pulses in the data 
4) there are 1 or more local time trends in the data that are not simply remedied 
5) if the parameters of the model change over time 
6) if the variance of the errors change over time and no power transformation is adequate. 
In terms of a specific example, I would suggest that both of you select/make a time series and post both of them to the web. I will use AUTOBOX to analyse the data in an unattended mode and I will post the models to the list. You then run the R program and then each of you make a separate objective analysis of both results, pointing out similarities and differences. Send those two models complete with all available supporting material including the final error terms to me for my comments. Summarize and presents these results to the list and then ask readers of the list to VOTE for which procedure seems best to them.
A: They represent two different approaches to two similar but different problems. I wrote auto.arima and @IrishStat is the author of Autobox. 
auto.arima() fits (seasonal) ARIMA models including drift terms. Autobox fits transfer function models to handle level shifts and outliers. An ARIMA model is a special case of a transfer function model.
Even if you turned off the level shifts and outlier detection in Autobox, you would get a different ARIMA model from auto.arima() due to different choices in how to identify the ARIMA parameters.
In my testing on the M3 and M-competition data, auto.arima() produces more accurate forecasts than Autobox for these data. However, Autobox will do better with data containing major outliers and level shifts.
A: EDIT: Per your comment, I believe that if you turn off many of autobox's options, you'd probably get a similar answer to auto.arima. But if you do not, and in the presence of outliers there will definitely be a difference: auto.arima doesn't care about outliers, while autobox will detect them and handle them appropriately, which would give a better model. There may be other differences as well, and I"m sure IrishStat can describe those.

I believe autobox detects outliers and other things beyond just searching for the best AR, I, and MA coefficients. If that's correct, it would require more analysis and a couple of other R functions to have similar functionality. And IrishStats is a valuable member of this community, and quite friendly.
Of course, R is free and can do a bazillion things beyond ARIMA.
Another choice that's free for economics-style ARIMA is X13-ARIMA SEATS, from the US Census Bureau, which is open source. There are binaries for Windows and Linux, but it compiled straightforwardly on my Mac, given that I'd already loaded gnu's gfortran compiler. It's the successor to X12-ARIMA, and was just released in the last few days, after years of development and testing. (It updates X12 and also adds in SEATS/TRAMO features. X12 is the official US tool, while SEATS/TRAMO is from the Bank of Spain and is the "European tool".)
I really like X12 (and now X13) a lot. If you output a fair amount of diagnostics and read through them and learn what they mean, they are actually a fairly good education in ARIMA and time series. I've developed my own workflow, but there's an R package x12 for doing most work from within R (you still have to create the input model (".spc") file for X12).
I say X12 is good at "economics style" ARIMA to mean monthly data with more than 3 years of data. (You need 5+ years of data to use some diagnostic features.) It has an outlier identification feature, can handle all kinds of outlier specifications, and can handle holidays, floating holidays, trading day effects, and a host of economic things. It's the tool that the US government uses to create seasonally-adjusted data.
