Lévy驱动图Ornstein-Uhlenbeck过程的高频估计
High-frequency Estimation of the Lévy-driven Graph Ornstein-Uhlenbeck process
摘要：
我们认为，图Ornstein-Uhlenbeck（Gravity）过程中观察到的非均匀离散时间网格，并引入离散化的极大似然估计的参数特定于整个图或特定于每个组件，或节点。在高频抽样方案下，我们研究了这些估计的渐近行为的网格尺寸的观察网格趋于零。我们证明了两个稳定的中心极限定理相同的分布，在连续观测的情况下，有限和无限的跳跃活动的Lévy驱动噪声。当一个图形结构是不明确的，稳定的收敛允许考虑特定目的的稀疏推理过程，即修剪，在边缘本身并行的Gravity推理，并保持其渐近性质。我们将新的估计量应用于风力容量因子测量，即在西班牙北部和葡萄牙的50个地点，当地生产的风力发电与其额定峰值功率之间的比率。我们显示了这些估计的优越性相比，标准的最小二乘估计通过模拟研究扩展已知的单变量结果跨图形配置，噪声类型和幅度。
英文摘要：
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.
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