We develop methodology to detect structural breaks in the slope function of a concurrent functional linear regression model for functional time series in $C[0,1]$. Our test is based on a CUSUM process of regressor-weighted OLS residual functions. To accommodate both global and local changes, we propose $L^2$- and sup-norm versions, with the sup-norm particularly sensitive to spike-like changes. Under Hölder regularity and weak dependence conditions, we establish a functional strong invariance principle, derive the asymptotic null distribution, and show that the resulting tests are consistent against a broad class of alternatives with breaks in the slope function. Simulation studies illustrate finite-sample size and power. We apply the method to sports data obtained via body-worn sensors from running athletes, focusing on hip and knee joint-angle trajectories recorded during a fatiguing run. As fatigue accumulates, runners adapt their movement patterns, and sufficiently pronounced adjustments are expected to appear as a change point in the regression relationship. In this manner, we illustrate how the proposed tests support interpretable inference for biomechanical functional time series.

翻译：我们开发了一种方法来检测$C[0,1]$空间中函数时间序列的并发函数线性回归模型斜率函数的结构性突变。我们的检验基于回归量加权OLS残差函数的CUSUM过程。为兼顾全局变化与局部变化，我们提出了$L^2$范数与上确界范数两种版本，其中上确界范数检验对尖峰状变化尤为敏感。在Hölder正则性与弱依赖性条件下，我们建立了函数型强不变原理，推导了渐近零分布，并证明所得检验对斜率函数存在突变的广泛备择假设具有一致性。模拟研究展示了有限样本下的检验水平与功效。我们将该方法应用于通过可穿戴传感器从跑步运动员获取的运动数据，重点关注疲劳跑过程中记录的髋关节与膝关节角度轨迹。随着疲劳累积，跑者会调整其运动模式，足够显著的调整预计会表现为回归关系中的变点。通过这种方式，我们阐释了所提出的检验如何为生物力学函数时间序列提供可解释的推断支持。