  We consider the problem of estimating stochastic volatility for a class of
second-order parabolic stochastic PDEs. Assuming that the solution is observed
at a high temporal frequency, we use limit theorems for multipower variations
and related functionals to construct consistent nonparametric estimators and
asymptotic confidence bounds for the integrated volatility process. As a
byproduct of our analysis, we also obtain feasible estimators for the
regularity of the spatial covariance function of the noise.
