Box and Jenkins present an interactive approach for fitting ARIMA models to time series. This iterative approach involves identifying the model, estimating the parameters, checking model adequacy, and forecasting. The model identification step usually requires judgment from the analyst.
A seasonal pattern that repeats each kth period of time indicates that you should take the kth difference to remove a portion of the pattern. Most series should not require more than two difference operations or orders. Be careful not to overdifference. If spikes in the ACF die out quickly, there is no need for more differencing. A sign of an overdifferenced series is the first autocorrelation close to -0.5 and small values elsewhere.
Useto calculate and store differences. Then, to examine the ACF and PACF of the differenced series, use and .
For most data, no more than two autoregressive parameters or two moving average parameters are required in ARIMA models.
The ARIMA algorithm will conduct up to 25 iterations to fit a specified model. If the solution does not converge, store the estimated parameters and use them as starting values for a second fit. You can store the estimated parameters and use them as starting values for a subsequent fit as often as necessary.