Time-series prediction has drawn considerable attention during the past decades fueled by the emerging advances of deep learning methods. However, most neural network based methods lack interpretability and fail in extracting the hidden mechanism of the targeted physical system. To overcome these shortcomings, an interpretable sparse system identification method without any prior knowledge is proposed in this study. This method adopts the Fourier transform to reduces the irrelevant items in the dictionary matrix, instead of indiscriminate usage of polynomial functions in most system identification methods. It shows an interpretable system representation and greatly reduces computing cost. With the adoption of $l_1$ norm in regularizing the parameter matrix, a sparse description of the system model can be achieved. Moreover, Three data sets including the water conservancy data, global temperature data and financial data are used to test the performance of the proposed method. Although no prior knowledge was known about the physical background, experimental results show that our method can achieve long-term prediction regardless of the noise and incompleteness in the original data more accurately than the widely-used baseline data-driven methods. This study may provide some insight into time-series prediction investigations, and suggests that an white-box system identification method may extract the easily overlooked yet inherent periodical features and may beat neural-network based black-box methods on long-term prediction tasks.

翻译：时间序列预测在过去几十年中因深度学习方法的兴起而受到广泛关注。然而，大多数基于神经网络的方法缺乏可解释性，无法提取目标物理系统的内在机制。为克服这些缺陷，本研究提出了一种无需先验知识的可解释稀疏系统辨识方法。该方法利用傅里叶变换减少字典矩阵中的无关项，而非像大多数系统辨识方法那样不加区分地使用多项式函数。它展示了可解释的系统表示形式，并大幅降低了计算成本。通过采用 $l_1$ 范数对参数矩阵进行正则化，可获得系统模型的稀疏描述。此外，本研究使用包括水利数据、全球温度数据和金融数据在内的三个数据集来测试所提方法的性能。尽管对物理背景一无所知，实验结果表明，无论原始数据中存在噪声和不完整性，我们的方法都能比广泛使用的基线数据驱动方法更准确地实现长期预测。本研究可能为时间序列预测研究提供一些见解，并表明白盒系统辨识方法能够提取容易被忽略但固有的周期性特征，并在长期预测任务上可能超越基于神经网络的黑盒方法。