Bounds in Wasserstein Distance for Locally Stationary Functional Time Series
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866913784584470528 |
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| author | Tinio, Jan Nino G. Alaya, Mokhtar Z. Bouzebda, Salim |
| author_facet | Tinio, Jan Nino G. Alaya, Mokhtar Z. Bouzebda, Salim |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_06453 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Bounds in Wasserstein Distance for Locally Stationary Functional Time Series Tinio, Jan Nino G. Alaya, Mokhtar Z. Bouzebda, Salim Statistics Theory Machine Learning 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. |
| title | Bounds in Wasserstein Distance for Locally Stationary Functional Time Series |
| topic | Statistics Theory Machine Learning |
| url | https://arxiv.org/abs/2504.06453 |