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

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.