Climate change analysis from LRD manifold functional regression

Abstract: This work is motivated by the problem of predicting downward solar radiation flux spherical maps from the observation of atmospheric pressure at high cloud bottom. To this aim nonlinear functional regression is implemented under strong-correlated functional data. The link operator reflects the heat transfer in the atmosphere. A latent parametric linear functional regression model reduces uncertainty in the support of this operator. An additive long-memory manifold-supported functional time series error models persistence in time of random fluctuations observed in the response. Time is incorporated via the scalar covariates in the latent linear functional regression model. The functional regression parameters in this model are supported on a connected and compact two point homogeneous space. Its Generalized Least--Squares (GLS) parameter estimation is achieved. When the second-order structure of the functional error term is unknown, its minimum contrast estimation is obtained in the spectral domain. The performance of the theoretical and plug-in nonlinear functional regression predictors is illustrated in the simulation study undertaken in the sphere. The Supplementary Material provides a detailed empirical analysis in the one way ANOVA context. The real-data application extends the purely spatial statistical analysis of atmospheric pressure at high cloud bottom, and downward solar radiation flux in Alegria et al. (2021) to the spatiotemporal context.