  Given a Heath-Jarrow-Morton (HJM) interest rate model $\mathcal{M}$ and a
parametrized family of finite dimensional forward rate curves $\mathcal{G}$,
this paper provides a technique for projecting the infinite dimensional forward
rate curve $r_{t}$ given by $\mathcal{M}$ onto the finite dimensional manifold
$\mathcal{G}$.The Stratonovich dynamics of the projected finite dimensional
forward curve are derived and it is shown that, under the regularity
conditions, the given Stratonovich differential equation has a unique strong
solution. Moreover, this projection leads to an efficient algorithm for
implicit parametric estimation of the infinite dimensional HJM model. The
feasibility of this method is demonstrated by applying the generalized method
of moments.
