论文标题
图形Ornstein-Uhlenbeck过程的可能性理论
Likelihood theory for the Graph Ornstein-Uhlenbeck process
论文作者
论文摘要
我们考虑了通过已知的静态图（或网络）结构给出的连续观察时间序列之间建模限制相互作用的问题。为此，我们定义了一个参数多元图Ornstein-uhlenbeck（grou）过程，该过程由一般的lévy过程驱动，以研究节点之间的动量和网络效应，这些效应分别量化了节点对自身及其邻居的影响。我们得出了最大似然估计器（MLE）及其通常的特性（存在，独特性和效率），以及它们的渐近正态性和一致性。此外，一种自适应拉索方法或受惩罚的似然方案同时渗透了图形结构，并同时呈现GROU参数，并显示出满足相似属性。最后，我们表明，渐近理论扩展到考虑驱动Lévy过程的随机波动率调节时。
We consider the problem of modelling restricted interactions between continuously-observed time series as given by a known static graph (or network) structure. For this purpose, we define a parametric multivariate Graph Ornstein-Uhlenbeck (GrOU) process driven by a general Lévy process to study the momentum and network effects amongst nodes, effects that quantify the impact of a node on itself and that of its neighbours, respectively. We derive the maximum likelihood estimators (MLEs) and their usual properties (existence, uniqueness and efficiency) along with their asymptotic normality and consistency. Additionally, an Adaptive Lasso approach, or a penalised likelihood scheme, infers both the graph structure along with the GrOU parameters concurrently and is shown to satisfy similar properties. Finally, we show that the asymptotic theory extends to the case when stochastic volatility modulation of the driving Lévy process is considered.
