Abstract: With the continuous advancement of neural network methodologies, time series prediction has attracted substantial interest over the past decades. Nonetheless, the interpretability of neural networks is insufficient and the utilization of deep learning techniques for prediction necessitates significant computational expenditures, rendering its application arduous in numerous scenarios. In order to tackle this challenge, an interpretable sparse system identification method which does not require a time-consuming training through back-propagation is proposed in this study. This method integrates advantages from both knowledge-based and data-driven approaches, and constructs dictionary functions by leveraging Fourier basis and taking into account both the long-term trends and the short-term fluctuations behind data. By using the $l_1$ norm for sparse optimization, prediction results can be gained with an explicit sparse expression function and an extremely high accuracy. The performance evaluation of the proposed method is conducted on comprehensive benchmark datasets, including ETT, Exchange, and ILI. Results reveal that our proposed method attains a significant overall improvement of more than 20\% in accordance with the most recent state-of-the-art deep learning methodologies. Additionally, our method demonstrates the efficient training capability on only CPUs. Therefore, this study may shed some light onto the realm of time series reconstruction and prediction.