Bounds in Wasserstein Distance for Locally Stationary Functional Time Series

Functional time series (FTS) extend traditional methodologies to accommodate data observed as functions/curves. A significant challenge in FTS consists of accurately capturing the time-dependence structure, especially with the presence of time-varying covariates. When analyzing time series with time-varying statistical properties, locally stationary time series (LSTS) provide a robust framework that allows smooth changes in mean and variance over time. This work investigates Nadaraya-Watson (NW) estimation procedure for the conditional distribution of locally stationary functional time series (LSFTS), where the covariates reside in a semi-metric space endowed with a semi-metric. Under small ball probability and mixing condition, we establish convergence rates of NW estimator for LSFTS with respect to Wasserstein distance. The finite-sample performances of the model and the estimation method are illustrated through extensive numerical experiments both on functional simulated and real data.

@article{tinio2025_2504.06453,
  title={ Bounds in Wasserstein Distance for Locally Stationary Functional Time Series },
  author={ Jan Nino G. Tinio and Mokhtar Z. Alaya and Salim Bouzebda },
  journal={arXiv preprint arXiv:2504.06453},
  year={ 2025 }
}