非时齐扩散模型中时变参数的局部线性估计

Local Linear Estimations of Time-Varying Parameters for Time-Inhomogeneous Diffusion Models

  • 摘要: 本文主要研究非时齐扩散模型中时变的漂移参数和扩散参数的局部线性估计. 基于非时齐扩散模型的离散观测样本, 首先得到了漂移参数的局部线性估计及其标准误差. 然后, 考虑到扩散参数的非负性, 本文利用局部对数线性拟合的方法得到了扩散参数的核函数加权估计, 并讨论了扩散项估计的渐近偏差、渐近方差和渐近正态性. 最后, 通过模拟研究表明所得局部估计有很好的拟合效果.

     

    Abstract: This paper studies the local linear estimations of the time-varying parameters for time-inhomogeneous diffusion models. Based on discretely observed sample of time-inhomogeneous diffusion models, the local linear estimations of the drift parameters are proposed and their standard errors are discussed. Considering the volatility parameter being positive, we obtain the kernel weighted estimation of the diffusion parameter by using locally log-linear fitting, and discuss asymptotic bias, asymptotic variance and asymptotic normal distribution of volatility function. It is shown that the local estimations proposed perform well through simulation studies.

     

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