Optimal Reconciliation of Seasonally Adjusted Disaggregates Taking Into Account the Difference Between Direct and Indirect Adjustment of the Aggregate

This article presents a new method to reconcile direct and indirect deseasonalized economic time series. The proposed technique uses a Combining Rule to merge, in an optimal manner, the directly deseasonalized aggregated series with its indirectly deseasonalized counterpart. The lastmentioned series is obtained by aggregating the seasonally adjusted disaggregates that compose the aggregated series. This procedure leads to adjusted disaggregates that verify Denton’s movement preservation principle relative to the originally deseasonalized disaggregates. First, we use as preliminary estimates the directly deseasonalized economic time series obtained with the X-13ARIMA-SEATS program applied to all the disaggregation levels. Second, we contemporaneously reconcile the aforementioned seasonally adjusted disaggregates with its seasonally adjusted aggregate, using Vector Autoregressive models. Then, we evaluate the finite sample performance of our solution via a Monte Carlo experiment that considers six Data Generating Processes that may occur in practice, when users apply seasonal adjustment techniques. Finally, we present an empirical application to the Mexican Global Economic Indicator and its components. The results allow us to conclude that the suggested technique is appropriate to indirectly deseasonalize economic time series, mainly because we impose the movement preservation condition to the preliminary estimates produced by a reliable seasonal adjustment procedure.