Equation for a p-th order autoregressive (AR) model — that is, AR(p) model:
Where {yt} is the data on which the ARMA model is to be applied. That means, the series is already power-transformed and differenced, in that order. The parameters φ1, φ2 and so on are AR coefficients.
Equation for a q-th order moving average (MA) model — that is, MA(q) model:
Where {yt} is as defined previously and θ1, θ2 and so on are MA coefficients.
Equation for an ARMA(p,q) model:
Where {yt}, φ1, φ2..., θ1, θ2... are as defined previously.
Equation for a SARMA(p,q)(P,Q) model (seasonal):
Where {yt}, {φ}, and {θ} are as defined previously, and {Φ} and {Θ} are the seasonal counterparts.