Beyond OLS: A Comparative Study of Regression Algorithms for Time Series Forecasting

Abstract

Recent time series forecasting developments indicated that simple linear models can be strong competitors to handle a vast majority of real-world datasets. However, the generality of such models can vary significantly between domains, not to mention between tasks. This paper extends the benchmark of Toner and Darlow Ordinary Least Squares (OLS) was investigated as a competitive baseline model for time series forecasting, to include a few more regression-based models. More specifically, we compare the performances of Gaussian Naive Bayes (NB), K-Nearest Neighbors (KNN), Decision Tree Regression (DT), and Random Forest Regression (RF) under the same experimental setup and datasets. Our experiments are performed using the ETTh1 benchmark dataset with fixed context horizon and forecasting horizon at 96-time intervals. Compared to the baseline OLS benchmark MSE of 0.376, and the corresponding Mean Absolute Error (MAE) of 0.399, our modified models clearly fare much better. Random Forest Regression does the best, at an MSE of 0.144, an MAE of 0.245, followed closely by Decision Tree Regression (MSE: 0.155, MAE: 0.262) and the KNN (MSE: 0.271, MAE: 0.369). Surprisingly, the modified version of the usual Gaussian Naive Bayes, which has been conditioned to regression using target binning , does an MSE of 1.053, with the corresponding MAE of 0.670, due to the probabilistic nature of the algorithm where the sample domain is not discrete but rather continuous. Our work highlights that Random Forests, which are tree models, are overwhelmingly powerful baselines, surpassing traditional linear methods. This demands a rethinking of the simplicity of definition of forecasting baselines and the use of more varied ML-based regressors as baselines. Source code and experimental configurations are released to facilitate reproduction and further extendibility of the code.