  We consider parametric estimation for a parabolic linear second order
stochastic partial differential equation (SPDE) from high frequency data which
are observed in time and space. By using thinned data obtained from the high
frequency data, adaptive estimators of the coefficient parameters including the
volatility parameter of a parabolic linear SPDE model are proposed. Moreover,
we give some examples and simulation results of the adaptive estimators of the
SPDE model based on the high frequency data.
