  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.
