LRD spectral analysis of multifractional functional time series on manifolds

Diana P. Ovalle–Muñoz and M. Dolores Ruiz–Medina ()
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Diana P. Ovalle–Muñoz: University of Granada
M. Dolores Ruiz–Medina: University of Granada

TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, 2024, vol. 33, issue 2, No 9, 564-588

Abstract: 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 (Fract Calc Appl Anal 25:1426–1458, 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.

Keywords: 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; 60G10; 60G12; 60G18; 60G20; 60G22 (primary); 60G60 (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s11749-023-00913-7

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