System Identification With Fourier Transformation for Long-Term Time Series Forecasting

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 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 visible 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 a 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.