  In this article, the existence of ghost classes for the Shimura varieties
associated to algebraic groups of orthogonal similitudes of signature (2, n) is
investigated. We make use of the study of the weights in the mixed Hodge
structures associated to the corresponding cohomology spaces and results on the
Eisenstein cohomology of the algebraic group of orthogonal similitudes of
signature (1, n-1). For the values of n = 4, 5 we prove the non-existence of
ghost classes for most of the irreducible representations (including most of
those with an irregular highest weight). For the rest of the cases, we prove
strong restrictions on the possible weights in the space of ghost classes and,
in particular, we show that they satisfy the weak middle weight property.
