What are the assumptions of ARIMA/Box-Jenkins modeling for forecasting time series? What are the assumptions of ARIMA/Box-Jenkins modeling for forecasting time series?
 A: For the "pure" ARIMA models,


*

*That the time-series involved are weakly stationary or Integrated of some order (which implies restrictions on the values of the unknown coefficients, as well as their constancy).  

*That all observed time series are combinations of white noises only, and perhaps a constant.
Moreover, the very fact that you use the abbreviation "ARIMA", implies in itself that  


*There are no other predictors (in which case you would have an "ARIMA-X" model) and  

*The relations are exclusively linear (to indicate the possibility of non-linear modelling, you should abbreviate to "NARIMA").
A: *

*There are no known/suspected predictor variables

*There are no level shifts 

*There are no deterministic time trends of the form $1,2,3,...,t$ 

*There are no seasonal dummies

*There are no one time anomalies

*The model parameters are constant over time

*The error process is homoscedastic (constant) over time


Most software solutions proceed to ignore all of these assumptions. AUTOBOX a piece of software that I have helped develop identifies and tests and remedies any violations of the above (save 1) leading to a Robust ARIMA solution.
