13.1 The Box–Jenkins approach

The methods of the last three sections fit together into a procedure, due to Box and Jenkins, for building an ARIMA model. Its main stages are:

1.: Identification: examining the data, its plot and its sample ac.f. and partial ac.f., to identify a model (after transforming or differencing if necessary);
2.: Estimation: estimating the parameters of the model;
3.: Diagnostic checking: examining the residuals from the fitted model to see whether the model is adequate;
4.: Consideration of an alternative model: done when the first model appears to be inadequate, after which the cycle is repeated.

Only when a model passes the checks is it used for forecasting (Figure 11). The emphasis on checking is the heart of the approach: identification from correlograms is a judgement, and the residuals are where a wrong judgement shows itself.

1Ip2Ele3Cre4FSaindlosahsoecdaettsteidrteqdn,icueiouet acmsqkacnaqui.aulateafyf.ta as14t,erec.te pasf.:c,, cof M QnL∗sider an alternative model — Figure 11: The Box–Jenkins cycle. A model is identified, estimated and checked; if the checks fail, a different model is identified and the cycle is repeated. Only a model that passes is used for forecasting.

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