Title: Bounds in Wasserstein Distance for Locally Stationary Functional Time Series Show Chinese title

Title: Wasserstein 距离下的局部平稳函数时间序列的界

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. Show Chinese abstract

Abstract: 函数时间序列（FTS）扩展了传统方法以适应作为函数/曲线观察的数据。 FTS 中的一个重大挑战在于准确捕捉时间依赖结构，尤其是在存在时变协变量的情况下。 在分析具有时变统计特性的时序数据时，局部平稳时间序列（LSTS）提供了一个稳健的框架，允许均值和方差随时间平滑变化。 本文研究了局部平稳函数时间序列（LSFTS）条件分布的 Nadaraya-Watson (NW) 估计程序，其中协变量位于带有半度量的半度量空间中。 在小球概率和混合条件下，我们针对 Wasserstein 距离建立了 LSFTS 的 NW 估计量的收敛速度。 通过广泛的数值实验，包括对函数模拟数据和真实数据的实验，展示了模型和估计方法的有限样本性能。