SETAR_Trees

This repository contains the experiments related to a new and accurate tree-based global forecasting algorithm named, SETAR-Tree.

We use the underlying concept of a Self Exciting Threshold Autoregressive (SETAR) model to develop this new tree algorithm. In contrast to the traditional tree-based algorithms which consider the average of the training outputs in leaf nodes to forecast new instances, our algorithm trains separate global Pooled Regression (PR) models in each leaf node allowing the model to learn cross-series information during training. The depth of the tree is internally controlled by conducting a statistical linearity test and measuring the error reduction percentage at each node split. Thus, the proposed tree model requires minimal external hyperparameter tuning compared to the state-of-theart tree-based algorithms and provides decent results under its default configuration. We also use this tree algorithm to develop a forest where the forecasts provided by a collection of diverse SETAR-Trees are combined during the forecasting process. The proposed tree and forest models can also be trained with external covariates.

For more details on our proposed tree and forest models, please refer to our paper.

Instructions for execution

Executing the SETAR-Tree Model

You can directly execute the exepriments related to the proposed SETAR-Tree model using the "do_setar_forecasting" function implemented in ./experiments/setar_tree_experiments.R script. The function parameters are explained in detail in the script. The forecasts, errors, execution times and tree related information (tree depth, number of nodes in the leaf level and number of instances per each leaf node) related to the SETAR-Tree model will be stored into "./results/forecasts/setar_tree", "./results/errors", "./results/execution_times/setar_tree" and "./results/tree_info" folders, respectively. See the examples provided in ./experiments/setar_tree_experiments.R script for more details.

Executing the SETAR-Forest Model

You can directly execute the exepriments related to the proposed SETAR-Forest model using the "do_setar_forest_forecasting" function implemented in ./experiments/setar_forest_experiments.R script. The function parameters are explained in detail in the script. The forecasts, errors and execution times related to the SETAR-Forest model will be stored into "./results/forecasts/setar_forest", "./results/errors" and "./results/execution_times/setar_forest" folders, respectively. See the examples provided in ./experiments/setar_forest_experiments.R script for more details.

Executing the Benchmark Models

In our paper, we have compared the performance of our proposed SETAR-Tree and forest models against a number of benchmarks including 4 traditional univariate forecasting models: Exponential Smoothing (ETS), Auto-Regressive Integrated Moving Average (ARIMA), SETAR and Smooth Transition Autoregressive (STAR), and 8 global forecasting models: PR, Cubist, Feed-Forward Neural Network (FFNN), Regression Tree, LightGBM, CatBoost, eXtreme Gradient Boosting (XGBoost) and Random Forest.

The traditional univariate forecasting models can be executed using the "do_local_forecasting" function implemented in ./experiments/local_model_experiments.R script. The function parameters are explained in detail in the script. See the examples provided in ./experiments/local_model_experiments.R script for more details.

The global forecasting models can be executed using the "do_global_forecasting" function implemented in ./experiments/global_model_experiments.R script. The function parameters are explained in detail in the script. See the examples provided in ./experiments/global_model_experiments.R script for more details.

Experimental Datasets

The experimental datasets are available in the datasets folder.

Recreating the Results Tables

All results tables in our paper are reproducible.

For that, first run all the experiments including the SETAR-Tree experiments (./experiments/setar_tree_experiments.R), SETAR-Forest experiments (./experiments/setar_forest_experiments.R), local model benchmarking experiments (./experiments/local_model_experiments.R) and global model benchmarking experiments (./experiments/global_model_experiments.R).

The results tables can be then recreated using the scripts inside the tables folder. Please use the scripts recreate_table_2.R, recreate_table_3.R and recreate_table_4.R, respectively, to recreate Tables 2, 3 and 4 in our paper.

Citing Our Work

When using this repository, please cite:

@article{godahewa2023setar,
  title = {SETAR-Tree: A Novel and Accurate Tree Algorithm for Global Time Series Forecasting},
  author = {Godahewa, Rakshitha and Webb, Geoffrey I. and Schmidt, Daniel and Bergmeir, Christoph},
  journal = {Machine Learning},
  year = {2023},
  note = {forthcoming}
}