Limit results in the spectral analysis of functional long-range dependence sequences

M. D. Ruiz Medina

Limit theorems in long-range dependence (LRD) functional sequences is a challenging topic. Central and functional central limit theorems under non-summability of the covariance operator norm sequence, and for the sample covariance operator have been recently derived in Düker (2018, 2020) in the time domain. On the other hand, in the functional spectral domain, Ruiz--Medina (2021) characterizes LRD in Hilbert-valued time series. Minimum contrast estimation is extended to this domain, under a Gaussian scenario, in a weak-consistent way. The present talk formulates reduction theorems in an infinite-dimensional framework to obtain some central and non-central limit results for stationary functional sequences displaying LRD.

Keywords: Central limit theorem, functional spectral analysis, non-central limit theorem, LRD functional sequences

Scheduled

GT17 Stochastic Processes and their Applications I
June 7, 2022  12:00 PM
A24

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