Abstract

The classic X-11 seasonal adjustment method for monthly and quarterly economic data is equipped with routines for a data-driven selection of Henderson trend filters and 3×k seasonal filters, where k∈{3,5,9}. Although these routines have a long-standing tradition that can be traced back as far as 1960, they have not been adopted in a recent JDemetra+ implementation of a modified X-11 method that is tailored to the specifics of infra-monthly time series, such as the coexistence of multiple seasonal patterns with potentially fractional periodicities. Focusing on seasonal filters, we seek to fill this gap by extending the legacy selection concept based upon the so-called moving seasonality ratio in multiple ways. In particular, we allow for picking from a broader family of 3×k seasonal filters and incorporate a common scheme for obtaining their asymmetric variants. A generalisation of the latter scheme then paves the way for a comprehensible derivation of certain indifference intervals in which the moving seasonality ratio needs to be recalculated from suitably shortened observations. Our resulting automatic selection routine is illustrated in three examples using quarterly, monthly and daily macroeconomic time series for Germany.