标题： 多元非平稳函数时间序列的滞后数增加时的综合检验 显示英文标题

标题： A portmanteau test for multivariate non-stationary functional time series with an increasing number of lags

摘要： 多元局部平稳函数时间序列提供了一个灵活的框架，用于建模同时具有时间和空间依赖性的复杂数据结构，并且允许数据生成机制随时间变化。 本文提出了一种专门针对多元局部平稳函数时间序列的白噪声假设检验的端口型检验方法，无需降维。 由于极限分布可能是非标准的甚至不存在，因此我们提出了一个简单的自助程序来实施该检验。 我们的方法基于一个新的关于二阶函数时间序列退化$U$-统计量最大值的高斯近似结果，这一结果本身也有独立的研究价值。 通过理论分析和模拟研究，我们展示了所提出的方法在检测多元局部平稳函数时间序列中偏离白噪声假设方面的有效性和适应性。 显示英文摘要

摘要： Multivariate locally stationary functional time series provide a flexible framework for modeling complex data structures exhibiting both temporal and spatial dependencies while allowing for time-varying data generating mechanism. In this paper, we introduce a specialized portmanteau-type test tailored for assessing white noise assumptions for multivariate locally stationary functional time series without dimension reduction. A simple bootstrap procedure is proposed to implement the test because the limiting distribution can be non-standard or even does not exist. Our approach is based on a new Gaussian approximation result for a maximum of degenerate $U$-statistics of second-order functional time series, which is of independent interest. Through theoretical analysis and simulation studies, we demonstrate the efficacy and adaptability of the proposed method in detecting departures from white noise assumptions in multivariate locally stationary functional time series.