  In this paper, we show that the mixed Hodge structures of character varieties
are of Hodge--Tate type and that the mixed Hodge polynomials are independent of
the choice of generic eigenvalues, which is a conjecture due to Hausel,
Letellier and Rodriguez-Villegas. Moreover, we investigate the mixed Hodge
structures of the moduli space of semistable parabolic Higgs bundles and the
moduli space of semistable regular singular parabolic connections. We show that
the mixed Hodge structures of these moduli spaces are pure.
