What are the assumptions of ARIMA/Box-Jenkins modeling for forecasting time series?
- 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.
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").