时齐扩散过程在金融领域具有重要作用，它被广泛应用于描述基础资产变量的随机波动。研究时齐扩散过程的漂移系数和扩散系数的非参数估计问题，在高阶近似的基础上给出新的非参数估计方法——B样条估计。该方法通过对B样条拟合系数加以非负约束来保证扩散系数的非负性。模拟结果验证了该方法在对扩散系数的估计上优于局部多项式估计方法。
Time-homogeneous diffusion process plays an important role in the financial market, and it is widely used for describing the stochastic dynamics of the underlying economic variables. In this work, we study nonparametric estimation of the drift and diffusion functions for the time-homogeneous diffusion process, and propose a new nonparametric regression technique based on higher-order approximations, which is called B-spline approach. The nonnegativity of the diffusion function is guaranteed by the restricted B-spline method. Our simulation results show that our method indeed outperforms the local polynomial method.
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