  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.
