论文标题
多相功能时间序列的LRD光谱分析
LRD spectral analysis of multifractional functional time series on manifolds
论文作者
论文摘要
本文介绍了显示在空间变化的远距离依赖性（LRD）的歧管跨时随机场（RF）的二阶结构的估计，该结构采用了Ruiz-Medina中引入的功能时间序列框架（2022）。希尔伯特 - 施密特操作员规范中综合期刊操作员渐近算子的渐近无偏见的条件超出了结构假设。在高斯环境中，在半摩托功能频谱框架下实现了长期内存运算符的弱一致估计。还分析了在不同的歧管尺度上显示短距离依赖性（SRD）和LRD的情况。在仿真研究中，在多种集成的球形功能自动回归平均值（SPHARMA（P，Q））过程的背景下，两种估计程序的性能都在说明。
This paper addresses the estimation of the second-order structure of a manifold cross-time random field (RF) displaying spatially varying Long Range Dependence (LRD), adopting the functional time series framework introduced in Ruiz-Medina (2022). Conditions for the asymptotic unbiasedness of the integrated periodogram operator in the Hilbert-Schmidt operator norm are derived beyond structural assumptions. Weak-consistent estimation of the long-memory operator is achieved under a semiparametric functional spectral framework in the Gaussian context. The case where the projected manifold process can display Short Range Dependence (SRD) and LRD at different manifold scales is also analyzed. The performance of both estimation procedures is illustrated in the simulation study, in the context of multifractionally integrated spherical functional autoregressive-moving average (SPHARMA(p,q)) processes.
