# Block Hankel Tensor ARIMA for Multiple Short Time Series Forecasting

arXiv: https://arxiv.org/abs/2002.12135 · HTML: https://mlsanity.com/paper/2002.12135/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 25 Feb 2020.

## Built on by (most cited first, 12 of 12)

- [Generative Time Series Forecasting with Diffusion, Denoise, and Disentanglement](https://mlsanity.com/paper/2301.03028/) (2023)
- [Low-Rank Hankel Tensor Completion for Traffic Speed Estimation](https://mlsanity.com/paper/2105.11335/) (2021)
- [Correlating sparse sensing for large-scale traffic speed estimation: A Laplacian-enhanced low-rank tensor kriging approach](https://mlsanity.com/paper/2210.11780/) (2022)
- [Learning Informative Representation for Fairness-aware Multivariate Time-series Forecasting: A Group-based Perspective](https://mlsanity.com/paper/2301.11535/) (2023)
- [SGDP: A Stream-Graph Neural Network Based Data Prefetcher](https://mlsanity.com/paper/2304.03864/) (2023)
- [Modeling Time-evolving Causality over Data Streams](https://mlsanity.com/paper/2502.08963/) (2025)
- [Towards Foundation Time Series Model: To Synthesize Or Not To Synthesize?](https://mlsanity.com/paper/2403.02534/) (2024)
- [Spatiotemporal Regularized Tucker Decomposition Approach for Traffic Data Imputation](https://mlsanity.com/paper/2305.06563/) (2023)
- [Guaranteed Multidimensional Time Series Prediction via Deterministic Tensor Completion Theory](https://mlsanity.com/paper/2501.15388/) (2025)
- [Soft Smoothness for Audio Inpainting Using a Latent Matrix Model in Delay-embedded Space](https://mlsanity.com/paper/2203.09746/) (2022)
- [Evaluating Short-Term Forecasting of Multiple Time Series in IoT Environments](https://mlsanity.com/paper/2206.07784/) (2022)
- [Optical Coherence Tomography Image Enhancement via Block Hankelization and Low Rank Tensor Network Approximation](https://mlsanity.com/paper/2306.11750/) (2023)

## Abstract (arXiv)

This work proposes a novel approach for multiple time series forecasting. At first, multi-way delay embedding transform (MDT) is employed to represent time series as low-rank block Hankel tensors (BHT). Then, the higher-order tensors are projected to compressed core tensors by applying Tucker decomposition. At the same time, the generalized tensor Autoregressive Integrated Moving Average (ARIMA) is explicitly used on consecutive core tensors to predict future samples. In this manner, the proposed approach tactically incorporates the unique advantages of MDT tensorization (to exploit mutual correlations) and tensor ARIMA coupled with low-rank Tucker decomposition into a unified framework. This framework exploits the low-rank structure of block Hankel tensors in the embedded space and captures the intrinsic correlations among multiple TS, which thus can improve the forecasting results, especially for multiple short time series. Experiments conducted on three public datasets and two industrial datasets verify that the proposed BHT-ARIMA effectively improves forecasting accuracy and reduces computational cost compared with the state-of-the-art methods.