Control charts to check yearly predictions by monthly observations

In many cases an organization makes predictions of a variable on a yearly scale although the variable is actually observed at shorter time intervals. Given such a yearly prediction, the question will arise as to under which conditions one can say that the actual development of the variable at shorter time intervals deviates so much from the year estimate as to render the latter implausible. Policy makers confronted with such a problem tend to use rather primitive statistical methods of inference. In this paper the situation is judged from a statistical point of view and placed in the context of the ‘significance test’ approach to control chart theory. It is assumed that the variables are generated by a multivariate autoregressive moving average model. Thus the paper derives an approximate distribution of the future observations of the series given the values of some linear compounds of the variables. With this, three control charts can be constructed. The approach is illustrated by an example on the monthly tax returns of the Dutch central government. The example suggests the usefulness of the approach in many practical situations of forecasting and planning.