An LRD spectral test for irregularly discretely observed contaminated functional time series in manifolds

TL;DR

This paper extends a spectral test for long-range dependence in functional time series on manifolds to scenarios where data are irregularly observed and contaminated, analyzing its asymptotic properties under these challenging conditions.

Contribution

It provides an analysis of the asymptotic behavior of the spectral LRD test when applied to discretely observed, contaminated functional data on manifolds.

Findings

Asymptotic properties of the test are characterized under irregular sampling.

The test maintains consistency despite data contamination.

The spectral approach is robust to discretization and noise.

Abstract

A statistical hypothesis test for long range dependence (LRD) in functional time series in manifolds has been formulated in Ruiz-Medina and Crujeiras (2025) in the spectral domain for fully observed functional data. The asymptotic Gaussian distribution of the proposed test statistics, based on the weighted periodogram operator, under the null hypothesis, and the consistency of the test have been derived. In this paper, we analyze the asymptotic properties of this spectral LRD testing procedure, when functional data are contaminated, and discretely observed through random uniform spatial sampling.