The multivariate adaptive regression splines (MARS) model is a flexible non-parametric sparse regression algorithm and provides an excellent promise to data fitting through nonlinear basis functions. During the last decades, it is employed in many fields of control design, finance, technology, and science. It can be regarded as an extension of linear models that automatically model interactions and nonlinearities. The least absolute shrinkage and selection operator (LASSO) analysis is a variable selection and shrinkage method to linear regression models. It proposes to construct the subset of explanatory variables which minimizes estimation error to a quantitative dependent variable. LASSO is applied to choose the variables and perform the regularization to improve the interpretability and robustness of the model. In this paper, we examine MARS and LASSO to generate natural gas demand forecasts of residential users for the distribution system operators who need both short- and long-term forecasts. We also compare the performance of MARS and LASSO with a simple multiple-linear regression (LR) commonly used in practice. Our analysis reveals that MARS outperforms LASSO and LR in both the average measures and in the worst-case analysis. For 1 day-ahead forecast, MARS provides a MAPE of around 4.8% while the same figure under LASSO and LR reaches 8.3 and 8.5% respectively. However, as the forecasting horizon increases, we observe that the performance of these proposed methods gets worse and for 1 year-ahead forecast, the MAPE values for MARS, LASSO, and LR are 13.4%, 24.8% and 26.3% respectively.

多元自适应回归样条 (MARS) 模型是一种灵活的非参数稀疏回归算法，通过非线性基函数为数据拟合提供了极好的前景。在过去的几十年里，它被用于控制设计、金融、技术和科学的许多领域。它可以被视为线性模型的扩展，可以自动对相互作用和非线性进行建模。最小绝对收缩和选择算子（LASSO）分析是线性回归模型的一种变量选择和收缩方法。它建议构建解释变量的子集，以最大限度地减少对定量因变量的估计误差。LASSO 用于选择变量并执行正则化以提高模型的可解释性和鲁棒性。在本文中，我们检查了 MARS 和 LASSO，以便为需要短期和长期预测的配电系统运营商生成住宅用户的天然气需求预测。我们还将 MARS 和 LASSO 的性能与实践中常用的简单多元线性回归 (LR) 进行了比较。我们的分析表明，MARS 在平均测量和最坏情况分析中均优于 LASSO 和 LR。对于提前 1 天的预测，MARS 提供的 MAPE 约为 4.8%，而 LASSO 和 LR 下的相同数字分别达到 8.3 和 8.5%。然而，随着预测范围的增加，我们观察到这些方法的性能变得更差，对于 1 年前的预测，MARS、LASSO 和 LR 的 MAPE 值分别为 13.4%、24.8% 和 26.3%。