Is seasonal adjustment a linear or nonlinear data-filtering process?

We investigate whether seasonal-adjustment procedures are, at least approximately, linear data transformations. This question was initially addressed by Young and is important with respect to many issues including estimation of regression models with seasonally adjusted data. We focus on the X-11 program and rely on simulation evidence, involving linear unobserved component autoregressive integrated moving average models. We define a set of properties for the adequacy of a linear approximation to a seasonal-adjustment filter. These properties are examined through statistical tests. Next, we study the effect of X-11 seasonal adjustment on regression statistics assessing the statistical significance of the relationship between economic variables. Several empirical results involving economic data are also reported.