We identify Melrose’s suspended algebra of pseudodifferential operators with a subalgebra of the algebra of parametric pseudodifferential operators with parameter space ; ; ; ; R; ; mathbb {R}; ; ; . For a general algebra of parametric pseudodifferential operators, where the parameter space may now be a cone ; ; ; ; Γ; ⊂; ; ; R; ; p; ; ; Gamma subset mathbb {R}^p; ; ; , we construct a unique “symbol valued trace”, which extends the ; ; ; ; L; 2; ; L^2; ; ; –trace on operators of small order. This construction is in the spirit of a trace due to Kontsevich and Vishik in the nonparametric case. Our trace allows us to construct various trace functionals in a systematic way. Furthermore, we study the higher–dimensional eta–invariants on algebras with parameter space ; ; ; ; ; R; ; ; 2; k; −; 1; ; ; mathbb {R}^{2k-1}; ; ; . Using Clifford representations we construct for each first order elliptic differential operator a natural family of parametric pseudodifferential operators over ; ; ; ; ; R; ; ; 2; k; −; 1; ; ; mathbb {R}^{2k-1}; ; ; . The eta–invariant of this family coincides with the spectral eta–invariant of the operator.