Daily multistep soil moisture forecasting by combining linear and nonlinear causality and attention-based encoder-decoder model

Traditional time series forecasting methods applied to long time series and multivariate data often ignore the importance of features and the causal relationships between predictors and predictands. Recent studies have shown that the Informer deep neural model, as one of the variants of the transformer, offers advantages in dealing with long sequence time-series forecasting (LSTF) problems. However, existing deep learning models for multivariate time series forecasting simply feed the dataset directly into the model and do not make good use of the interconnections between multivariate time series data. To address this issue, our study proposes the concept of Causal-Informer (C-Informer) by coupling Granger causality and Informer models, which can overcome the above problems with a significant improvement in forecasting accuracy. The C-Informer method first uses Granger linear and nonlinear causality to calculate the causality of all features and target variables, performs feature selection based on the results and then feeds the feature-selected dataset into the Informer model for forecasting. The experimental results from the FLUXNET soil moisture site dataset show that for prediction lengths of 1, 3, 6, 12, and 24 steps, the C-Informer method achieves average reductions in RMSE of 8.72%, 7.62%, 5.45%, 12.8%, and 11.1%, respectively, while R² increases by 2.75%, 7.88%, 2.09%, 6.86%, and 10.8% compared to the Informer method. Thus, C-Informer has an advantage over several Informer and transformer variants.