Scientists and statisticians often want to learn about the complex relationships that connect two variables that vary over time. 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 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 relax 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 four simulation studies, justified by two real sets of hydrological data.

翻译：科学家和统计学家经常希望了解随时间变化的两个变量之间的复杂关系。近期关于稀疏函数历史线性模型的研究证实了其在这一目标上的潜力，但仍存在若干显著局限。最重要的是，先前研究对系数函数施加了稀疏性，但未能允许稀疏性（即滞后性）随时间变化。我们通过使用矩形系数结构结合Whittaker平滑方法简化了稀疏函数历史线性模型框架，并进一步通过从分层系数结构中估计动态时间滞后突破了先前框架的限制。本研究以从水文数据中提取隐含的物理降雨-径流过程为动机，通过四次仿真研究验证了方法的有效性，并利用两组真实水文数据进行了实证分析。