# Bounds in Wasserstein Distance for Locally Stationary Functional Time Series

arXiv: https://arxiv.org/abs/2504.06453 · HTML: https://mlsanity.com/paper/2504.06453/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 7 of its 75 references that are in the map.
- First posted on arXiv 8 Apr 2025.

## Builds on (most cited first, 7 of 7)

- [Computational Optimal Transport](https://mlsanity.com/paper/1803.00567/) (2018)
- [Minimax Confidence Intervals for the Sliced Wasserstein Distance](https://mlsanity.com/paper/1909.07862/) (2019)
- [Smooth p-Wasserstein Distance: Structure, Empirical Approximation, and Statistical Applications](https://mlsanity.com/paper/2101.04039/) (2021)
- [Testing for stationarity of functional time series in the frequency domain](https://mlsanity.com/paper/1701.01741/) (2017)
- [Locally Stationary Functional Time Series](https://mlsanity.com/paper/1602.05125/) (2016)
- [A general framework to quantify deviations from structural assumptions in the analysis of nonstationary function-valued processes](https://mlsanity.com/paper/2208.10158/) (2022)
- [Bounds in Wasserstein Distance for Locally Stationary Processes](https://mlsanity.com/paper/2412.03414/) (2024)

## Abstract (arXiv)

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.