Multi-target forecasting in univariate time series via embedding-based target space

This work examines the multi-step (multi-horizon) forecasting problem in univariate time series. Conventional methods usually depend on direct or iterative approaches, where the direct approach trains a separate model for every forecast horizon while the iterative approach uses past forecasts as inputs for upcoming steps. A novel multi-target regression framework is suggested as a solution to this problem. This method uses a time series embedding technique (e.g., PCA and ICA) first to project the prediction target vector, which consists of forecasts for the next \textit{H} time steps, into a lower-dimensional, uncorrelated, and informative target space. This lower-dimensional space is used to perform predictions, which are then inverse-transformed and translated back to the original space. Based on their demonstrated performance on multi-output prediction tasks, tree-based machine learning algorithms are employed during the modeling process. Tree-based models are used to produce forecasts for all horizons in a single pipeline. The Random Forest algorithm trained on these tasks as true multi-target tasks. As for XGBoost, LightGBM and CatBoost, multi-output regressor wrapper was used and this results in one independent model being trained per horizon. An embedding-based target space showed encouraging forecasting performance on some datasets. However, while the results of the multi-target regressions based on embeddings were promising, the non-embedded baselines in the form of the tree models were, in general, the strongest models and target space embedding did not result in statistically significant improvements over the baselines when measured over all series.