Trend Tests

Abstract

The following two major points, (a) and (b), have emerged in the previous chapter.

• (a) The principal components such that the unit root test statistic, UURT, diverges are either in Group 1, or in Group ⊥ where B_⊥η _⊥,i is a cointegration vector. Although the statistic in both groups diverges, principal components in Group 1 do not have a deterministic trend and those in Group ⊥ have a deterministic trend of order O(T^3/2).

• (b) The principal components such that either UURT or MURT has the limit distribution are either in Group 2, or in Group ⊥ where B_⊥η _⊥,i is not a cointegration vector. Although the statistics in both groups have the limit distributions, principal components in Group 2 do not have a deterministic trend and those in Group ⊥ have a deterministic trend of order O(T^3/2).