LRD spectral analysis of multifractional functional time series on manifolds Ovalle Muñoz, Diana Paola Ruiz Medina, María Dolores Connected and compact two--point homogeneous spaces Ibragimov contrast function LRD multifractionally integrated functional time series Manifold cross-time RFs Multifractional spherical stochastic partial differential equations Multivariate functional regression and asymptotic theory on manifold. Applications in medicine environment and astrophysics MCIN/AEI/PID2022-142900NB-I00. IMAG Excellence Seal “María de Maeztu” with reference CEX2020-001105-M MCIN/AEI/10.13039/501100011033. Funding for open access publishing: Universidad de Granada/CBUA. 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. 2024-04-29T10:57:46Z 2024-04-29T10:57:46Z 2024-01-12 journal article Ovalle–Muñoz, D.P., Ruiz–Medina, M.D. LRD spectral analysis of multifractional functional time series on manifolds. TEST (2024). https://doi.org/10.1007/s11749-023-00913-7 https://hdl.handle.net/10481/91256 10.1007/s11749-023-00913-7 eng open access Springer Nature