ChebyshevNet: a novel time series analysis model using Chebyshev polynomial

Time series analysis is a widely used technique which can be applied to many areas such as electricity usage, commodity sales, traffic flow, and linguistics. Regarding linguistic application, time series analysis is worth being used to word frequency which can predict the popularity of online buzzwords. The research on time series analysis models has seen significant expansion in recent years. Recent studies have shown that both deep learning models and conventional methods based solely on mathematical computations can be improved. Conversely, hybrid approaches that utilize the advantages of both tend to be more effective. This paper presents ChebyshevNet, a novel time series analysis model that combines Chebyshev polynomials with convolutional neural networks (CNNs). This integration marks the first application of Chebyshev polynomials within the architectural framework of CNNs to build generalized models for various time series analysis tasks. Inspired by the pioneering work of TimesNet, which integrates Fourier transforms into its network architecture, ChebyshevNet firstly embeds Chebyshev polynomials into the backbone of the CNN. The experimental results show that ChebyshevNet outperforms TimesNet in several analysis tasks, particularly in anomaly detection and imputation. These promising results not only highlight the excellent prediction capabilities of ChebyshevNet but also its potential for further improvements and applications, thereby providing a broad space for future research and development in the field of time series analysis. In future work, we will apply ChebyshevNet to word frequency prediction in linguistics, fine-tune the model and build a dataset for this specific application scenario.