, the general form for the ARIMA model is as follows:
t is the time index
B is the backshift operator defined as 
is the response series after differencingμ is the intercept or mean term
and 
are the autoregressive operator and the moving average operator, respectively, and are written as follows:
are the sequence of random shocks
are assumed to be independent and normally distributed with mean zero and constant variance.
The constant estimate δ is given by the relation:
In the case of Seasonal ARIMA modeling, the differencing, autoregressive, and moving average operators are the product of seasonal and nonseasonal polynomials:
where s is the number of observations per period. The first index on the coefficients is the factor number (1 indicates nonseasonal, 2 indicates seasonal) and the second is the lag of the term.