Common features and common I(2) trends in VAR systems

Abstract

This paper discusses serial correlation common features, CF, and integration of order 2, I(2), in VAR systems. The interplay of the CF restrictions and the I(2) conditions is discussed both for full VAR systems and for conditional systems with no levels and difference feedback, NF. Several notions of CF are introduced for I(2) systems; some of these are shown to be nested within the NF conditions. It is suggested to first test for I(2)-ness and next for CF. The test for I(2) can be conducted in the full system or under NF. It is shown that standard asymptotics apply once the integration indices, II, have been determined. The techinques are illustrated on the widely used UK money dataset.serial correlation common features, cointegration, common trends, VAR, I(2), 2SI2,RRR