Manuscript received July 13; accepted September 25, 2025; published November 28, 2025
Abstract—Accurate long-term time series forecasting is crucial for public resource allocation, industrial optimization, and epidemic prevention. Yet, the inherent non-stationarity and periodicity of time series make this task highly challenging. To address these issues, we propose a Conditional Variational Autoencoder (CVAE) framework tailored for non-stationary time series. By introducing noise, CVAE enhances adaptability to distribution shifts. A Mixture of Experts encodes features to capture periodic patterns, while the decoder incorporates seasonal-trend disentanglement, adaptive Nadaraya-Watson regression, difference–cumsum operations, and hypergraph convolution to model non-stationarity. Furthermore, sequence stabilization reintroduces non-stationary information into predictions to alleviate distribution drift. Extensive experiments on real-world industrial datasets and public benchmarks verify that our approach effectively improves long-term forecasting accuracy.
Keywords—long-term prediction, non-stationary, distribution drift, conditional variational autoencoder
Cite: Baowen Xu, Song Gao, and Hongxin Meng, "Long-Term Series Forecasting via Conditional Variational Autoencoder Modeling Non-Stationarity," International Journal of Machine Learning vol. 15, no. 4, pp. 83-91, 2025.
Copyright © 2025 by the authors. This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).