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.
Use
to calculate and store differences. Then, to examine the ACF and PACF of the differenced series, use and .The identification of adequate autoregressive and moving average orders in an ARIMA model is difficult and time-consuming. Use Forecast with Best ARIMA Model to significantly speed up the model identification process by automatically selecting the best model from a candidate set.
In addition to comparing different models, you can examine the ACF and PACF of your stationary data in order to identify what autoregressive or moving average models terms are suggested.
For most data, no more than two autoregressive parameters or two moving average parameters are required in ARIMA models.