Benchmarking by State Space Models

Summary We have a monthly series of observations which are obtained from sample surveys and are therefore subject to survey errors. We also have a series of annual values, called benchmarks, which are either exact or are substantially more accurate than the survey observations; these can be either annual totals or accurate values of the underlying variable at a particular month. The benchmarking problem is the problem of adjusting the monthly series to be consistent with the annual values. We provide two solutions to this problem. The first of these is a two‐stage method in which we first fit a state space model to the monthly data alone and then combine the results obtained at this stage with the benchmark data. In the second solution we construct a single series from the monthly and annual values together and fit a state space model to this series in a single stage. The treatment is extended to series which behave multiplicatively. The methods are illustrated by applying them to Canadian retail sales sereis.