Efficient parameter estimation for parabolic SPDEs based on a log-linear model
Conference
64th ISI World Statistics Congress
Format: IPS Abstract
Keywords: high-frequency, stochastic process
Session: IPS 150 - Statistical inference for stochastic ordinary and partial differential equations
Monday 17 July 2 p.m. - 3:40 p.m. (Canada/Eastern)
Abstract
We present statistical methods to calibrate dynamic models based on stochastic partial differential equations (SPDEs). We construct estimators for the parameters of parabolic SPDEs based on discrete observations in time and space of a solution on a bounded domain. We point out the relation of power variation statistics to the response variable of a log-linear model. This allows to conclude about efficiency and minimal variances. We establish central limit theorems under high-frequency asymptotics. The asymptotic variances are smaller compared to existing estimation methods and asymptotic confidence intervals are directly feasible. We demonstrate the efficiency gains numerically and in Monte Carlo simulations.