An AutoRegressive Integrated Moving Average (ARIMA) model predicts future values of a time series by a linear combination of its past values and a series of errors (also known as random shocks or innovations). The ARIMA command performs a maximum likelihood fit of the specified ARIMA model to the time series.
, the general form for the ARIMA model is:
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 
, respectively, the autoregressive operator and the moving average operator and are written
and
are the sequence of random shocks.
are assumed to be independent and normally distributed with mean zero and constant variance.
where the constant estimate 
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An ARIMA model is commonly denoted ARIMA(p,d,q). If any of p,d, or q are zero, the corresponding letters are often dropped. For example, if p and d are zero, then model would be denoted MA(q).
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The Confidence Intervals box allows you to set the confidence level between 0 and 1 for the forecast confidence bands. The Intercept check box determines whether the intercept term μ will be part of the model. If the Constrain fit check box is checked, the fitting procedure will constrain the autoregressive parameters to always remain within the stable region and the moving average parameters within the invertible region. You might want to uncheck this box if the fitter is having difficulty finding the true optimum or if you want to speed up the fit. You can check the Model Summary table to see if the resulting fitted model is stable and invertible.