A Basic Step-by-Step Weighted X-11 Algorithm and the Cascade Filters

Abstract The X-11 family of programs in official statistics consists of non-parametric seasonal adjustment methods that smooth the original series using sequentially applied linear filters, adding and removing one observation at a time. This paper provides a detailed description of the algorithm used in the additive decomposition model for the central observations of the series, particularly when a down-weighting procedure is applied to the irregular component. The main contribution of this work is the derivation of the cascade filters for the three types of decompositions available in X-13ARIMA-SEATS, along with a detailed algorithm that enables practitioners to accurately replicate its implementation.