ACF of the errors For revision, I am working out a multiplicative model for sales data, and then conducting a simple error analysis (actual sales - forecasted). I understand the process but in my lecturer's mark scheme he has put 'You should mention the usefulness of the ACF of the errors'. How would I go about this? My error results are:
Errors: -7.75 1.67 -2.26 0.776 3.88 4.61 6.024 3.112 -0.49 -1.44 -7.688 2.448 

 A: Presumably this is a time-series model.
What does the auto-correlation function show in general?

 The sample auto-correlation function of a variable shows the correlation of the variable with itself at various time lags. If you calculate it for the residuals it shows the correlation of the residuals with themselves at various lags. (It's not a correlation with the time period—that would be a trend.)

What assumption that you make about the errors in your model is relevant?

 That the errors are uncorrelated. The residuals from your model are estimates of these errors, so should be (more or less) uncorrelated—as you say in your comment, there should be no clear patterns in the ACF of the residuals.

A: In general, the residual autocorrelation function (acf) is a tool used at the diagnostic-checking stage of the Box-Jenkins methodology. The residual acf is just like any other estimated acf except for the fact that it's the residuals from an estimated model that are used to calculate the autocorrelation coefficients rather than observations from the time-series under investigation - sales data in this particular case.
The residual acf helps the model builder answer the following question: has the estimated model been properly formulated? If the model is said to be adequate then the estimated residuals should be uncorrelated on average. So, by inspecting the residual acf, the model builder can find out whether or not the autocorrelation coefficients are all statistically zero. If they are, the model has been properly constructed. If not, the residual acf signals that perhaps there exists a more appropriate model for the time-series.
The residual acf actually plays a dual role in this regard. Not only does the residual acf help with deciding whether or not the model has been properly built (that is, statistically adequate), but it can also be used to reformulate the model. Remember, the Box-Jenkin's methodology is an iterative process. 
To reformulate the model based on information obtained from the residual acf, one adds the coefficient implied by the residual acf to the model from which the residuals have been derived. For example, let's say we build an AR(1) model and estimate the residual acf. If the residual acf contains a single significant spike at lag one, then this pattern suggests adding an MA(1) term to the model. This results in a reformulation of the model as an ARMA(1,1) instead of an AR(1). 
In conclusion, the residual acf is a very useful tool for providing diagnostic checks, and, in addition, it can prove useful even at the identification stage (or reformulation stage) of the model building process.
Note: if you need it, the residual acf based on the errors provided is shown below. Maybe as an exercise you could try to calculate the residual autocorrelation coefficients and the confidence interval shown in the plot. Then, provide an interpretation of the graph bearing in mind what it allows you to infer about the model (that is, mention its usefulness).

