Multivariate Time-Series Forecasting Model: Predictability Analysis and Empirical Study

Multivariate time series forecasting has wide applications such as traffic flow prediction, supermarket commodity demand forecasting and etc., and a large number of forecasting models have been developed. Given these models, a natural question has been raised: what theoretical limits of forecasting accuracy can these models achieve? Recent works of urban human mobility prediction have made progress on the maximum predictability that any algorithm can achieve. However, existing approaches on maximum predictability on the multivariate time series fully ignore the interrelationship between multiple variables. In this article, we propose a methodology to measure the upper limit of predictability for multivariate time series with multivariate constraint relations. The key of the proposed methodology is a novel entropy, named Multivariate Constraint Sample Entropy (McSE), to incorporate the multivariate constraint relations for better predictability. We conduct a systematic evaluation over eight datasets and compare existing methods with our proposed predictability and find that we get a higher predictability. We also find that the forecasting algorithms that capture the multivariate constraint relation information, such as GNN, can achieve higher accuracy, confirming the importance of multivariate constraint relations for predictability.