Spectral analysis of long range dependence functional time series

Abstract

Long Range Dependence (LRD) in functional sequences is characterized in the spectral domain under suitable conditions. Particularly, multifractionally integrated functional autoregressive moving averages processes can be introduced in this framework. The convergence to zero in the Hilbert-Schmidt operator norm of the integrated bias of the periodogram operator is proved. Under a Gaussian scenario, a weak--consistent parametric estimator of the long--memory operator is then obtained by minimizing, in the norm of bounded linear operators, a divergence information functional loss.

36 pages

References in corpus (3)

• Weakly dependent functional data
• Operator self-similar processes and functional central limit theorems
• Spatial Cox processes in an infinite-dimensional framework

Cited by in corpus (1)

• Spectral Simulation of Functional Time Series