Is Seasonal Adjustment a Linear or Nonlinear Data-Filtering Process?

The authors investigate whether seasonal adjustment procedures are linear data transformations. This question was addressed by A. H. Young (1968) and is important for the estimation of regression models with seasonally adjustment data. The authors focus on the X-11 program and rely on simulation evidence, involving linear unobserved component autorgressive integrated moving average models. They define and test a set of properties for the adequacy of a linear approximation to a seasonal adjustment filter. Next, the authors study the effect of X-11 on regression statistics assessing the statistical significance between economic variables. Several empirical results involving economic data are also reported.