It looks like the forecast server is picking a factored ARIMA models. For example, P((1)(7)) = (1-ar1*B)*(1-ar7*B**7), not (1-ar1*B - ar7*B**7).
Below is some more info about the factored ARIMA models.
Subset, Seasonal, and Factored ARMA Models
Factored Models
A factored model (also referred to as a multiplicative model) represents the ARIMA model as a product of simpler ARIMA models. For example, you might model SALES as a combination of an AR(1) process that reflects short term dependencies and an AR(12) model that reflects the seasonal pattern.
It might seem that the way to do this is with the option P=(1 12), but the AR(1) process also operates in past years; you really need autoregressive parameters at lags 1, 12, and 13. You can specify a subset model with separate parameters at these lags, or you can specify a factored model that represents the model as the product of an AR(1) model and an AR(12) model. Consider the following two ESTIMATE statements:
identify var=sales;
estimate p=(1 12 13);
estimate p=(1)(12);
The mathematical form of the autoregressive models produced by these two specifications are shown in Table 8.2.
Table 8.2: Subset versus Factored Models
Option
Autoregressive Operator
P=(1 12 13)
P=(1)(12)
Both models fit by these two ESTIMATE statements predict SALES from its values 1, 12, and 13 periods ago, but they use different parameterizations. The first model has three parameters, whose meanings may be hard to interpret.
The factored specification P=(1)(12) represents the model as the product of two different AR models. It has only two parameters: one that corresponds to recent effects and one that represents seasonal effects. Thus the factored model is more parsimonious, and its parameter estimates are more clearly interpretable.
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