Scientists and statisticians often want to learn about the complex relationships that connect two time-varying variables. Recent work on sparse functional historical linear models confirms that they are promising for this purpose, but several notable limitations exist. Most importantly, previous works have imposed sparsity on the historical coefficient function, but have not allowed the sparsity, hence lag, to vary with time. We simplify the framework of sparse functional historical linear models by using a rectangular coefficient structure along with Whittaker smoothing, then reduce the assumptions of the previous frameworks by estimating the dynamic time lag from a hierarchical coefficient structure. We motivate our study by aiming to extract the physical rainfall-runoff processes hidden within hydrological data. We show the promise and accuracy of our method using eight simulation studies, further justified by two real sets of hydrological data.

翻译：科学家和统计学家常希望了解两个时变变量之间的复杂关系。近期关于稀疏泛函历史线性模型的研究虽已证实其在此方面的潜力，但仍存在若干显著局限。最核心的问题在于，已有研究均在历史系数函数上施加稀疏性约束，但未允许稀疏性（即时间滞后）随时间变化。我们通过采用矩形系数结构结合Whittaker平滑方法简化了稀疏泛函历史线性模型的框架，并基于层级系数结构估计动态时间滞后，从而减少了先前框架的假设条件。本研究以提取水文数据中隐藏的物理降雨-径流过程为动机，通过八组模拟研究验证了方法的有效性，并基于两组真实水文数据集进一步证实了其实用性与准确性。