Derivation of Quarterly Figures from Annual Data

Quarterly figures may be required when only a series of annual data are available. If no assumption about the pattern of the quarterly figures can be made, so that merely a smooth trend must be obtained, a very simple procedure can be employed in order to obtain a fairly good adaptation of the quarterly figures to the annual totals. For each year t, the value of a quarterly figure is considered as a weighted average of the totals of the years t − 1, t and t + 1. After introduction of some quite natural conditions a system of equations is obtained, from which the weighting coefficients can be calculated. To a certain extent the solution contains some arbitrary aspects, but it has the advantage of simplicity, plausibility and practical usefulness.