Encompassing the VAR: A Formalization of Seasonal Encompassing with an Application on a German Macromodel

In this paper we apply the encompassing principle to test whether a model that has been estimated with seasonally adjusted data (SA) can encompass a model that is based on non-seasonllay adjusted (NSA) data. Building upon and extending the work på Ericsson, Hendry and Tran (1994) who analyze this question in a single equation framework we will suggest how to test whethet a SA model which is estimated as a system of simultaneous equations can "seasonally encompass" a NSA model. This paper formalizes the test procedure and provides an application to a German macromodel.