We introduce a novel class of nonlinear tests for serial dependence in functional time series, grounded in the functional quantile autocorrelation framework. Unlike traditional approaches based on the classical autocovariance kernel, the functional quantile autocorrelation framework leverages quantile-based excursion sets to robustly capture temporal dependence within infinite-dimensional functional data, accommodating potential outliers and complex nonlinear dependencies. We propose omnibus test statistics and study their asymptotic properties under both known and estimated quantile curves, establishing their asymptotic distribution and consistency under mild assumptions. In particular, no moment conditions are required for the validity of the tests. Extensive simulations and an application to high-frequency financial functional time series demonstrate the methodology's effectiveness, reliably detecting complex serial dependence with superior power relative to several existing tests. This work expands the toolkit for functional time series, providing a robust framework for inference in settings where traditional methods may fail.

翻译：本文提出了一类用于函数时间序列序列依赖性的新型非线性检验方法，其建立在函数分位数自相关框架之上。与基于经典自协方差核的传统方法不同，函数分位数自相关框架利用基于分位数的偏移集，以稳健地捕捉无限维函数数据中的时间依赖性，并能适应潜在的异常值和复杂的非线性依赖关系。我们提出了综合性检验统计量，并在已知和估计的分位数曲线两种情况下研究了它们的渐近性质，在温和的假设条件下建立了其渐近分布和一致性。特别地，检验的有效性不需要矩条件。大量的模拟实验以及对高频金融函数时间序列的应用表明，该方法能有效检测复杂的序列依赖性，相对于若干现有检验方法具有更优的检验功效。这项工作扩展了函数时间序列的分析工具，为传统方法可能失效的场景下的推断提供了一个稳健的框架。