  We construct estimators for the parameters of a parabolic SPDE with one
spatial dimension based on discrete observations of a solution in time and
space on a bounded domain. We establish central limit theorems for a
high-frequency asymptotic regime. The asymptotic variances are shown to be
substantially smaller compared to existing estimation methods. Moreover,
asymptotic confidence intervals are directly feasible. Our approach builds upon
realized volatilities and their asymptotic illustration as response of a
log-linear model with spatial explanatory variable. This yields efficient
estimators based on realized volatilities with optimal rates of convergence and
minimal variances. We demonstrate efficiency gains compared to previous
estimation methods numerically and in Monte Carlo simulations.
