Seasonal arima forecast equation I need to compute a seasonal arima model, and make forecasts about vehicular traffic. My idea is to compute the model with R, and use the AR and MA coefficients in another application to predict future instances.
So, this is the question: given the (p,d,q)(P,D,Q)s model computed, which is the equation used to compute the forecasts?
I've found similar questions, but all of them are left unanswered. Thank you in advance.
 A: The problem using your approach is it lacks generability and would require the additional access to model errors and historical observations.
However all ARIMA models can be restated as a weighted average of the past. Some software actually presents/restates the equation in this form for a better understanding by the human that is involved in creating a narrative about the equation. The PI weights is the formal name for this re-expression. You can find out more about the pi weights by reviewing quality textbooks like http://www.amazon.co.uk/Time-Series-Analysis-Univariate-Multivariate/dp/0201159112  You might need to incorporate level shift or time trend variables into your equation or seasonal dummies. I would suggest that you try and duplicate the conversion of ARIMA models into PI weights. AUTOBOX, a piece of software that I have helped develop, performs this tour de force. You can download either a live unrestricted 30-day trial version or a pure demo version (data restricted) which allows you to use hundreds of delivered data sets.
edit:
I would like to repeat that all ARIMA model can also be represented as a pure AR model. These weights are referred to as the Pi weights as compared to the pure MA form (Psi weights) . In this way you can view (interpret) an ARIMA model as an optimized weighted average of the past values. In other words rather than assume a pre-specified length and values for a weighted average , an ARIMA model delivers both the length (n) of the weights and the actual weights (c1,c2,...cn).
Y(t) =c1*Y(t−1) + c2*Y(t-2) + c3*Y(t-3)+.... cn*Y(t-n) + a(t)
In this way an ARIMA model can be explained as the answer to the question
How many historical values should I use to compute a weighted sum of the past
Precisely what are those values.
A: Maybe ARMAtoMA function in R will help you? 
https://stat.ethz.ch/R-manual/R-devel/library/stats/html/ARMAtoMA.html
If you want to represent your model as a function of known historical values, switch the phi and the theta in the ARMAtoMA module to get the PIs of the infinite AR process: ARMAtoMA(ar=theta, ma=phi,n).
