论文标题
部分可观测时空混沌系统的无模型预测
Volatility density estimation by multiplicative deconvolution
论文作者
论文摘要
我们研究了未知的固定密度fv的非参数估计，即未观察到的严格固定波动率过程$（\ bm v_t）_ {t \ geq 0} $ on $ \ irp^2：=（0，\ infty）^2 $，基于离散的时间基于机构上的电流模型。我们确定了基本的乘法测量误差模型，并根据缩放，集成挥发率过程的梅林变换的估计以及梅林变换倒数的频谱截止正规化构建估计器。我们证明提出的估计器会导致一致的估计策略。提出了完全数据驱动的$ \ bm k \ in \ irp^2 $的选择，并提供了平均集成平方风险的上限。在我们的整个研究中，对于估计量的解剖学，挥发性过程的规律性特性是必需的。这些假设是通过在仿真研究中列出和使用的几个示例来实现的，以说明所提出的估计器的合理行为。
We study the non-parametric estimation of an unknown stationary density fV of an unobserved strictly stationary volatility process $(\bm V_t)_{t\geq 0}$ on $\IRp^2 := (0,\infty)^2$ based on discrete-time observations in a stochastic volatility model. We identify the underlying multiplicative measurement error model and build an estimator based on the estimation of the Mellin transform of the scaled, integrated volatility process and a spectral cut-off regularisation of the inverse of the Mellin transform. We prove that the proposed estimator leads to a consistent estimation strategy. A fully data-driven choice of $\bm k \in \IRp^2$ is proposed and upper bounds for the mean integrated squared risk are provided. Throughout our study, regularity properties of the volatility process are necessary for the analsysis of the estimator. These assumptions are fulfilled by several examples of volatility processes which are listed and used in a simulation study to illustrate a reasonable behaviour of the proposed estimator.
