论文标题
Lévy驱动的图形Ornstein-Uhlenbeck过程的高频估计
High-frequency Estimation of the Lévy-driven Graph Ornstein-Uhlenbeck process
论文作者
论文摘要
我们考虑在不均匀离散的时间网格上观察到的图形Ornstein-uhlenbeck（grou）过程，并引入具有特定于整个图形或特定于每个组件或节点的参数的离散的最大似然估计器。在高频采样方案下，我们研究了这些估计值的渐近行为，因为观察网的网格大小为零。在有限和无限跳跃活动下，我们证明了两个稳定的中央限制定理与连续观察的情况相同的分布。当图形结构未明确可用时，稳定的收敛允许考虑特定目的的稀疏推理过程，即在边缘本身上与GROU推理并行保留其渐近性能。我们将新的估计量应用于风能因子测量值，即与其额定峰值功率相比，在西班牙北部和葡萄牙的五十个位置，本地生产的风能之间的比率。通过模拟研究，我们显示了这些估计量的优势，该研究扩展了跨图构型，噪声类型和振幅的已知单变量结果。
We consider the Graph Ornstein-Uhlenbeck (GrOU) process observed on a non-uniform discrete time grid and introduce discretised maximum likelihood estimators with parameters specific to the whole graph or specific to each component, or node. Under a high-frequency sampling scheme, we study the asymptotic behaviour of those estimators as the mesh size of the observation grid goes to zero. We prove two stable central limit theorems to the same distribution as in the continuously-observed case under both finite and infinite jump activity for the Lévy driving noise. When a graph structure is not explicitly available, the stable convergence allows to consider purpose-specific sparse inference procedures, i.e. pruning, on the edges themselves in parallel to the GrOU inference and preserve its asymptotic properties. We apply the new estimators to wind capacity factor measurements, i.e. the ratio between the wind power produced locally compared to its rated peak power, across fifty locations in Northern Spain and Portugal. We show the superiority of those estimators compared to the standard least squares estimator through a simulation study extending known univariate results across graph configurations, noise types and amplitudes.
