Bounds in Wasserstein Distance for Locally Stationary Functional Time Series

Jan Nino G. Tinio; Mokhtar Z. Alaya; Salim Bouzebda

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arXiv · 2504.06453

Bounds in Wasserstein Distance for Locally Stationary Functional Time Series

Jan Nino G. Tinio·Mokhtar Z. Alaya·Salim Bouzebda

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Abstract

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.

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Jan Nino G. Tinio, Mokhtar Z. Alaya, Salim Bouzebda. 2025-04-08. Bounds in Wasserstein Distance for Locally Stationary Functional Time Series. https://arxiv.org/abs/2504.06453

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