  We define a hierarchy of Hamiltonian PDEs associated to an arbitrary
tau-function in the semi-simple orbit of the Givental group action on genus
expansions of Frobenius manifolds. We prove that the equations, the
Hamiltonians, and the bracket are weighted-homogeneous polynomials in the
derivatives of the dependent variables with respect to the space variable.
  In the particular case of a conformal (homogeneous) Frobenius structure, our
hierarchy coincides with the Dubrovin-Zhang hierarchy that is canonically
associated to the underlying Frobenius structure. Therefore, our approach
allows to prove the polynomiality of the equations, Hamiltonians and one of the
Poisson brackets of these hierarchies, as conjectured by Dubrovin and Zhang.
