LRD spectral analysis of multifractional functional time series on manifolds
Metadatos
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Springer Nature
Materia
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
Date
2024-01-12Referencia bibliográfica
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
Patrocinador
MCIN/ AEI/PID2022-142900NB-I00; CEX2020-001105-M MCIN/ AEI/10.13039/501100011033; Universidad de Granada/CBUARésumé
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.