A functional nonlinear regression approach, incorporating time information in the covariates, is proposed for temporal strong correlated manifold map data sequence analysis. Specifically, the functional regression parameters are supported on a connected and compact two--point homogeneous space. The Generalized Least--Squares (GLS) parameter estimator is computed in the linearized model, having error term displaying manifold scale varying Long Range Dependence (LRD). The performance of the theoretical and plug--in nonlinear regression predictors is illustrated by simulations on sphere, in terms of the empirical mean of the computed spherical functional absolute errors. In the case where the second--order structure of the functional error term in the linearized model is unknown, its estimation is performed by minimum contrast in the functional spectral domain. The linear case is illustrated in the Supplementary Material, revealing the effect of the slow decay velocity in time of the trace norms of the covariance operator family of the regression LRD error term. The purely spatial statistical analysis of atmospheric pressure at high cloud bottom, and downward solar radiation flux in Alegria et al. (2021) is extended to the spatiotemporal context, illustrating the numerical results from a generated synthetic data set.

翻译：本文提出了一种将时间信息纳入协变量的函数非线性回归方法，用于分析时间强相关的流形映射数据序列。具体而言，函数回归参数定义在一个连通紧致的两点齐性空间上。在线性化模型中计算了广义最小二乘参数估计量，其误差项呈现流形尺度变化的长程依赖性。通过球面模拟，以计算出的球面函数绝对误差的经验均值为指标，说明了理论和插件式非线性回归预测器的性能。当线性化模型中函数误差项的二阶结构未知时，通过在函数谱域中进行最小对比度方法进行估计。补充材料中展示了线性情况，揭示了回归LRD误差项的协方差算子族迹范数随时间缓慢衰减速度的影响。将Alegria等人（2021）中对高云底部大气压和向下太阳辐射通量的纯空间统计分析扩展到时空背景，并通过生成的合成数据集说明了数值结果。