Explainable boosted linear regression for time series forecasting

Abstract: Time series forecasting involves collecting and analyzing past observations to develop a model to extrapolate such observations into the future. Forecasting of future events is important in many fields to support decision making as it contributes to reducing the future uncertainty. We propose explainable boosted linear regression (EBLR) algorithm for time series forecasting, which is an iterative method that starts with a base model, and explains the model's errors through regression trees. At each iteration, the path leading to highest error is added as a new variable to the base model. In this regard, our approach can be considered as an improvement over general time series models since it enables incorporating nonlinear features by residuals explanation. More importantly, use of the single rule that contributes to the error most allows for interpretable results. The proposed approach extends to probabilistic forecasting through generating prediction intervals based on the empirical error distribution. We conduct a detailed numerical study with EBLR and compare against various other approaches. We observe that EBLR substantially improves the base model performance through extracted features, and provide a comparable performance to other well established approaches. The interpretability of the model predictions and high predictive accuracy of EBLR makes it a promising method for time series forecasting.