2025/04/08 by Tinio, Jan Nino G., Alaya, Mokhtar Z., Bouzebda, Salim
#FOS: Computer and information sciences #FOS: Mathematics #Machine Learning (stat.ML) #Statistics Theory (math.ST)
paper · doi:10.48550/arxiv.2504.06453
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.