  A non-Euclidean generalization of conditional expectation is introduced and
characterized as the minimizer of expected intrinsic squared-distance from a
manifold-valued target. The computational tractable formulation expresses the
non-convex optimization problem as transformations of Euclidean conditional
expectation. This gives computationally tractable filtering equations for the
dynamics of the intrinsic conditional expectation of a manifold-valued signal
and is used to obtain accurate numerical forecasts of efficient portfolios by
incorporating their geometric structure into the estimates.
