多變量時間序列預測任務相對於單變量預測需要更謹慎地去思考變量與變量之間的關聯性。以常見的幾項預測模型為例，如 CNN-based、Transformer-based 等模型，雖然能夠很好的處理時域間的潛在關係，但對於特徵之間的關聯性捕捉仍有待加強。而 GNN-based 模型卻恰好可以補足這點，除了時域特徵的捕捉外，圖形結構可以對各個變量之間的潛在依賴關係進行建模來獲取空域上的特徵，加強預測的準確性。本文將延續圖神經網路模型優點，加強模型對於時域特徵的處理，除了改善常見的資料不平穩問題外，還採取了多尺度整合局部與全域訊息做為資料前處理步驟，並配合時域資料本身特性，在保留時間關聯性的前提上進行特徵建模與預測，最後在單步預測與多步預測兩項任務上驗證了所提出方法的有效性。

In multivariate time series prediction tasks, careful consideration of the interrelationships between variables is essential compared to univariate prediction. Popular prediction models such as CNN-based and Transformer-based models excel at capturing the temporal relationships between time steps. However, they still have room for improvement in capturing the correlations between features. In contrast, GNN-based models precisely address this issue by not only capturing temporal features but also leveraging the graph structure to model the underlying dependencies among variables, thereby enhancing prediction accuracy in the spatial domain.
Building upon the advantages of GNN models, this study enhances the handling of temporal features. In addition to addressing common issues related to data non-stationarity, it incorporates a multi-scale integration of local and global information as a data preprocessing step. Furthermore, it leverages the inherent characteristics of temporal data to perform feature modeling and prediction while preserving the temporal correlations. Finally, the effectiveness of the proposed approach is validated through experiments on both single-step and multi-step prediction tasks.

[1] M. Nabipour, P. Nayyeri, H. Jabani, A. Mosavi, and E. Salwana, “Deep learning
for stock market prediction,” Entropy, vol. 22, no. 8, p. 840, 2020.
[2] W. Jiang, “Applications of deep learning in stock market prediction: recent
progress,” Expert Systems with Applications, vol. 184, p. 115537, 2021.
[3] D. P. Gandhmal and K. Kumar, “Systematic analysis and review of stock market prediction techniques,” Computer Science Review, vol. 34, p. 100190, 2019.
[4] L. Jiang and G. Hu, “Day-ahead price forecasting for electricity market using
long-short term memory recurrent neural network,” in 2018 15th International
Conference on Control, Automation, Robotics and Vision (ICARCV). IEEE,
2018, pp. 949–954.
[5] S. Liu, C. Wu, and H. Zhu, “Graph neural networks for learning real-time prices
in electricity market,” arXiv preprint arXiv:2106.10529, 2021.
[6] H. Tampubolon, C.-L. Yang, A. S. Chan, H. Sutrisno, and K.-L. Hua, “Optimized capsnet for traffic jam speed prediction using mobile sensor data under
urban swarming transportation,” Sensors, vol. 19, no. 23, p. 5277, 2019.
[7] C. Gu, G. Wang, Y. Li, T. Inoue, and C. Li, “A hybrid radar-camera sensing system with phase compensation for random body movement cancellation
in doppler vital sign detection,” IEEE transactions on microwave theory and
techniques, vol. 61, no. 12, pp. 4678–4688, 2013.
[8] J.-Y. Kim, J.-H. Park, S.-Y. Jang, and J.-R. Yang, “Peak detection algorithm
for vital sign detection using doppler radar sensors,” Sensors, vol. 19, no. 7, p.
1575, 2019.
[9] C. Gu, J. Wang, and J. Lien, “Deep neural network based body movement
cancellation for doppler radar vital sign detection,” in 2019 IEEE MTT-S International Wireless Symposium (IWS). IEEE, 2019, pp. 1–3.
[10] K.-L. Hua, T.-T. Ho, K.-A. Jangtjik, Y.-J. Chen, and M.-C. Yeh, “Artist-based
painting classification using markov random fields with convolution neural network,” Multimedia Tools and Applications, vol. 79, pp. 12 635–12 658, 2020.
[11] M. Tanveer, A. H. Rashid, M. Ganaie, M. Reza, I. Razzak, and K.-L. Hua,
“Classification of alzheimer＇s disease using ensemble of deep neural networks
trained through transfer learning,” IEEE Journal of Biomedical and Health
Informatics, vol. 26, no. 4, pp. 1453–1463, 2021.
[12] K. A. Jangtjik, T.-T. Ho, M.-C. Yeh, and K.-L. Hua, “A cnn-lstm framework for
authorship classification of paintings,” in 2017 IEEE International Conference
on Image Processing (ICIP). IEEE, 2017, pp. 2866–2870.
[13] Y.-X. Lin, D. S. Tan, W.-H. Cheng, Y.-Y. Chen, and K.-L. Hua, “Spatiallyaware domain adaptation for semantic segmentation of urban scenes,” in 2019
IEEE International Conference on Image Processing (ICIP). IEEE, 2019, pp.
1870–1874.
[14] M. Shahid, I.-F. Chien, W. Sarapugdi, L. Miao, and K.-L. Hua, “Deep spatialtemporal networks for flame detection,” Multimedia Tools and Applications,
vol. 80, pp. 35 297–35 318, 2021.
[15] C.-L. Yang, A. Setyoko, H. Tampubolon, and K.-L. Hua, “Pairwise adjacency
matrix on spatial temporal graph convolution network for skeleton-based twoperson interaction recognition,” in 2020 IEEE International Conference on
Image Processing (ICIP). IEEE, 2020, pp. 2166–2170.
[16] H.-H. Lin, J.-D. Lin, J. J. M. Ople, J.-C. Chen, and K.-L. Hua, “Social media
popularity prediction based on multi-modal self-attention mechanisms,” IEEE
Access, vol. 10, pp. 4448–4455, 2021.
[17] Z. Wu, S. Pan, G. Long, J. Jiang, X. Chang, and C. Zhang, “Connecting
the dots: Multivariate time series forecasting with graph neural networks,” in
Proceedings of the 26th ACM SIGKDD international conference on knowledge
discovery & data mining, 2020, pp. 753–763.
[18] G. E. Box, G. M. Jenkins, and J. F. MacGregor, “Some recent advances in
forecasting and control,” Journal of the Royal Statistical Society: Series C
(Applied Statistics), vol. 23, no. 2, pp. 158–179, 1974.
[19] C. C. Holt, “Forecasting seasonals and trends by exponentially weighted moving
averages,” International journal of forecasting, vol. 20, no. 1, pp. 5–10, 2004.
[20] S. Hochreiter and J. Schmidhuber, “Long short-term memory,” Neural computation, vol. 9, no. 8, pp. 1735–1780, 1997.
[21] A. Vaswani, N. Shazeer, N. Parmar, J. Uszkoreit, L. Jones, A. N. Gomez,
Ł. Kaiser, and I. Polosukhin, “Attention is all you need,” Advances in neural
information processing systems, vol. 30, 2017.
[22] S. Bai, J. Z. Kolter, and V. Koltun, “An empirical evaluation of generic
convolutional and recurrent networks for sequence modeling,” arXiv preprint
arXiv:1803.01271, 2018.
[23] Y.-C. Yeh, J. Dy, T.-M. Huang, Y.-Y. Chen, and K.-L. Hua, “Vdnet: video
deinterlacing network based on coarse adaptive module and deformable recurrent residual network,” Neural Computing and Applications, vol. 34, no. 15, pp.
12 861–12 874, 2022.
[24] J. Zhou, G. Cui, S. Hu, Z. Zhang, C. Yang, Z. Liu, L. Wang, C. Li, and
M. Sun, “Graph neural networks: A review of methods and applications,” AI
open, vol. 1, pp. 57–81, 2020.
[25] J. J. M. Ople, P.-Y. Yeh, S.-W. Sun, I.-T. Tsai, and K.-L. Hua, “Multi-scale
neural network with dilated convolutions for image deblurring,” IEEE Access,
vol. 8, pp. 53 942–53 952, 2020.
[26] Y. Liu, H. Wu, J. Wang, and M. Long, “Non-stationary transformers: Exploring
the stationarity in time series forecasting,” Advances in Neural Information
Processing Systems, vol. 35, pp. 9881–9893, 2022.
[27] H. Wang, J. Peng, F. Huang, J. Wang, J. Chen, and Y. Xiao, “Micn: Multiscale local and global context modeling for long-term series forecasting,” in The
Eleventh International Conference on Learning Representations, 2022.
[28] M. Liu, A. Zeng, M. Chen, Z. Xu, Q. Lai, L. Ma, and Q. Xu, “Scinet: Time
series modeling and forecasting with sample convolution and interaction,” Advances in Neural Information Processing Systems, vol. 35, pp. 5816–5828, 2022.
[29] G. P. Zhang, “Time series forecasting using a hybrid arima and neural network
model,” Neurocomputing, vol. 50, pp. 159–175, 2003.
[30] S. Roberts, M. Osborne, M. Ebden, S. Reece, N. Gibson, and S. Aigrain,
“Gaussian processes for time-series modelling,” Philosophical Transactions of
the Royal Society A: Mathematical, Physical and Engineering Sciences, vol.
371, no. 1984, p. 20110550, 2013.
[31] R. Frigola, “Bayesian time series learning with gaussian processes,” Ph.D. dissertation, University of Cambridge, 2015.
[32] G. Lai, W.-C. Chang, Y. Yang, and H. Liu, “Modeling long-and short-term
temporal patterns with deep neural networks,” in The 41st international ACM
SIGIR conference on research & development in information retrieval, 2018,
pp. 95–104.
[33] S.-Y. Shih, F.-K. Sun, and H.-y. Lee, “Temporal pattern attention for multivariate time series forecasting,” Machine Learning, vol. 108, pp. 1421–1441,
2019.
[34] H. Zhou, S. Zhang, J. Peng, S. Zhang, J. Li, H. Xiong, and W. Zhang, “Informer: Beyond efficient transformer for long sequence time-series forecasting,”
in Proceedings of the AAAI conference on artificial intelligence, vol. 35, no. 12,
2021, pp. 11 106–11 115.
[35] H. Wu, J. Xu, J. Wang, and M. Long, “Autoformer: Decomposition transformers with auto-correlation for long-term series forecasting,” Advances in Neural
Information Processing Systems, vol. 34, pp. 22 419–22 430, 2021.
[36] Y. Li, R. Yu, C. Shahabi, and Y. Liu, “Diffusion convolutional recurrent neural network: Data-driven traffic forecasting,” arXiv preprint arXiv:1707.01926,
2017.
[37] B. Yu, H. Yin, and Z. Zhu, “Spatio-temporal graph convolutional networks: A deep learning framework for traffic forecasting,” arXiv preprint
arXiv:1709.04875, 2017.
[38] Z. Wu, S. Pan, G. Long, J. Jiang, and C. Zhang, “Graph wavenet for deep
spatial-temporal graph modeling,” arXiv preprint arXiv:1906.00121, 2019.
[39] Z. Pan, Y. Liang, W. Wang, Y. Yu, Y. Zheng, and J. Zhang, “Urban traffic
prediction from spatio-temporal data using deep meta learning,” in Proceedings
of the 25th ACM SIGKDD international conference on knowledge discovery &
data mining, 2019, pp. 1720–1730.
[40] C. Zheng, X. Fan, C. Wang, and J. Qi, “Gman: A graph multi-attention network for traffic prediction,” in Proceedings of the AAAI conference on artificial
intelligence, vol. 34, no. 01, 2020, pp. 1234–1241.
[41] W. Chen, L. Chen, Y. Xie, W. Cao, Y. Gao, and X. Feng, “Multi-range attentive
bicomponent graph convolutional network for traffic forecasting,” in Proceedings
of the AAAI conference on artificial intelligence, vol. 34, no. 04, 2020, pp. 3529–
3536.
[42] D. Jin, J. Shi, R. Wang, Y. Li, Y. Huang, and Y.-B. Yang, “Trafformer: Unify
time and space in traffic prediction,” in Proceedings of the AAAI Conference
on Artificial Intelligence, vol. 37, no. 7, 2023, pp. 8114–8122.
[43] Z. Shao, Z. Zhang, F. Wang, and Y. Xu, “Pre-training enhanced spatialtemporal graph neural network for multivariate time series forecasting,” in
Proceedings of the 28th ACM SIGKDD Conference on Knowledge Discovery
and Data Mining, 2022, pp. 1567–1577.