Guaranteed Multidimensional Time Series Prediction via Deterministic Tensor Completion Theory

TL;DR

This paper introduces a deterministic tensor completion framework for multidimensional time series prediction, leveraging a novel TCTNN model to improve accuracy and efficiency over existing methods across various real-world datasets.

Contribution

It proposes a new theoretical approach and the TCTNN model that precisely predicts the maximum forecast horizon for multidimensional time series data.

Findings

TCTNN outperforms existing methods in prediction accuracy.

TCTNN offers better computational efficiency.

The approach is validated on diverse real-world datasets.

Abstract

In recent years, the prediction of multidimensional time series data has become increasingly important due to its wide-ranging applications. Tensor-based prediction methods have gained attention for their ability to preserve the inherent structure of such data. However, existing approaches, such as tensor autoregression and tensor decomposition, often have consistently failed to provide clear assertions regarding the number of samples that can be exactly predicted. While matrix-based methods using nuclear norms address this limitation, their reliance on matrices limits accuracy and increases computational costs when handling multidimensional data. To overcome these challenges, we reformulate multidimensional time series prediction as a deterministic tensor completion problem and propose a novel theoretical framework. Specifically, we develop a deterministic tensor completion theory and introduce the Temporal Convolutional Tensor Nuclear Norm (TCTNN) model. By convolving the multidimensional time series along the temporal dimension and applying the tensor nuclear norm, our approach identifies the maximum forecast horizon for exact predictions. Additionally, TCTNN achieves superior performance in prediction accuracy and computational efficiency compared to existing methods across diverse real-world datasets, including climate temperature, network flow, and traffic ride data. Our implementation is publicly available at https://github.com/HaoShu2000/TCTNN.