Construction of an ARIMA model
1. Stationarize the series, if necessary, by differencing (&
perhaps also logging, deflating, etc.)
2. Study the pattern of autocorrelations and partial
autocorrelations to determine if lags of the stationarized
series and/or lags of the forecast errors should be included
in the forecasting equation
3. Fit the model that is suggested and check its residual
diagnostics, particularly the residual ACF and PACF plots,
to see if all coefficients are significant and all of the pattern
has been explained.
4. Patterns that remain in the ACF and PACF may suggest the
need for additional AR or MA terms