Seasonal adjustment subject to accounting constraints

Abstract

The indirect seasonal adjustment obtained by aggregating component seasonal adjustments may be inadequate, whereas the direct adjustment of the aggregate can typically be ensured to be adequate by adjusting the statistical model. Reconciliation techniques can be used to allocate the discrepancies between the direct and indirect adjustments of the aggregate unto the various component series, essentially enforcing that the indirect procedure yields the same outcome as the adequate direct procedure. This paper proposes utilizing adequacy of the component seasonal adjustments—given the modifications entailed by reconciliation—as an additional constraint to the accounting problem. We focus on seasonal adjustments arising from X‐13ARIMA‐SEATS and apply this constrained reconciliation procedure to copper imports, a component of gross domestic product.