Title: Statistics for stochastic PDEs based on high-frequency observations
Authors: Markus Bibinger - Philipps University of Marburg (Germany) [presenting]
Mathias Trabs - University of Hamburg (Germany)
Abstract: Parameter estimation is discussed for a parabolic, linear stochastic partial differential equation (SPDE) from observations of a solution on a discrete grid in time and space. We consider SPDEs with one spatial dimension and a bounded spatial domain with Dirichlet boundary conditions. Focusing first on volatility estimation and assuming a high-frequency regime in time, we provide an explicit and easy to implement method of moments estimator based on squared time increments. Our estimator is consistent and admits a central limit theorem. The asymptotic theory is developed based on a representation of the solution of the SPDE as an infinite SDE-factor model and exploiting central limit theorems for time series which satisfy some mixing-type properties. This is established moreover for the joint estimation of the integrated volatility and parameters in the differential operator in a semi-parametric framework.