@misc{10481/91256,
year = {2024},
month = {1},
url = {https://hdl.handle.net/10481/91256},
abstract = {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.},
organization = {MCIN/ AEI/PID2022-142900NB-I00},
organization = {CEX2020-001105-M MCIN/ AEI/10.13039/501100011033},
organization = {Universidad de Granada/CBUA},
publisher = {Springer Nature},
keywords = {Connected and compact two--point homogeneous spaces},
keywords = {Ibragimov contrast function},
keywords = {LRD  multifractionally integrated functional time series},
keywords = {Manifold cross-time RFs},
keywords = {Multifractional spherical stochastic partial differential equations},
title = {LRD spectral analysis of multifractional  functional time series on manifolds},
doi = {10.1007/s11749-023-00913-7},
author = {Ovalle Muñoz, Diana Paola and Ruiz Medina, María Dolores},
}