论文标题
基于对数线性模型的抛物线SPDE的有效参数估计
Efficient parameter estimation for parabolic SPDEs based on a log-linear model for realized volatilities
论文作者
论文摘要
我们基于一个空间维度的抛物线SPDE参数构建估计器，基于一个空间维度，基于对界面域上时间和空间的离散观察结果。我们为高频渐近状态建立了中心限制定理。与现有的估计方法相比，渐近方差显示出明显小的。此外，渐近置信区间是直接可行的。我们的方法基于实现的波动及其渐近说明，作为具有空间解释变量的对数线性模型的响应。这将基于实现的波动性和最佳收敛速率和最小差异的有效估计器产生有效的估计器。与以前的估计方法相比，我们在数值和蒙特卡洛模拟中证明了效率提高。
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.
