When univariate model-free time series prediction is better than multivariate

Abstract The delay coordinate method is known to be a practically useful technique for reconstructing the states of an observed system. While this method is theoretically supported by Takens' embedding theorem concerning observations of a scalar time series, we can extend the method to include a multivariate time series. It is often assumed that a better prediction can be obtained using a multivariate time series than by using a scalar time series. However, multivariate time series contains various types of information, and it may be difficult to extract information that is useful for predicting the states. Thus, univariate prediction may sometimes be superior to multivariate prediction. Here, we compare univariate model-free time series predictions with multivariate ones, and demonstrate that univariate model-free prediction is better than multivariate one when the prediction steps are small, while multivariate prediction performs better when the prediction steps become larger. We show the validity of the former finding by using artificial datasets generated from the Lorenz 96 models and a real solar irradiance dataset. The results indicate that it is possible to determine which method is the best choice by considering how far into the future we want to predict.