The effect of seasonal adjustment filters on tests for a unit root

Abstract

We consider the effect of seasonal adjustment filters in univariate dynamic models. We concentrate our analysis on the behavior of the least-squares estimator of the sum of the autoregressive coefficients in a regression. We show the existence of a limiting upward bias with the X-11 filter when the process does not contain a unit root. We quantify the extent of this bias for a range of models and filtering procedures. The asymptotic bias has interesting implications with respect to the power of tests for a unit root. In order to assess the importance of this effect we present an extensive simulation study of both the size and power of the usual Dickey-Fuller (1979) and Phillips-Perron (1988) statistics. We show that, in many cases, there is considerable reduction in power compared to the benchmark cases where the data is unfiltered. Finally some practical implications of our study are addressed with respect to tests for unit roots with seasonally adjusted data.