IS SEASONAL ADJUSTMENT A LINEAR OR NONLINEAR DATA-FILTERING PROCESS

We investigate whether seasonal-adjustment procedures are, at least ap proximately, linear data transformations. This question was initially addressed by Young and is important with respect to many issues includ ing estimation of regression models with seasonally adjusted data. We focus on the X-11 program and rely on simulation evidence, involving l inear unobserved component autoregressive integrated moving average mo dels. We define a set of properties for the adequacy of a linear appro ximation to a seasonal-adjustment filter. These properties are examine d through statistical tests. Next, we study the effect of X-11 seasona l adjustment on regression statistics assessing the statistical signif icance of the relationship between economic variables. Several empiric al results involving economic data are also reported.