Block Hankel Tensor ARIMA for Multiple Short Time Series Forecasting

TL;DR

This paper introduces a tensor-based forecasting method combining MDT, Tucker decomposition, and tensor ARIMA to improve accuracy and efficiency in predicting multiple short time series.

Contribution

It presents a novel unified framework that leverages low-rank block Hankel tensors and tensor ARIMA for enhanced multi-series forecasting.

Findings

Improves forecasting accuracy over state-of-the-art methods

Reduces computational cost in multi-series prediction

Effective on both public and industrial datasets

Abstract

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.