Nonlinear and delayed effects of covariates often render time series forecasting challenging. To this end, we propose a novel forecasting framework based on ridge regression with signature features calculated on sliding windows. These features capture complex temporal dynamics without relying on learned or hand-crafted representations. Focusing on the discrete-time setting, we establish theoretical guarantees, namely universality of approximation and stationarity of signatures. We introduce an efficient sequential algorithm for computing signatures on sliding windows. The method is evaluated on both synthetic and real electricity demand data. Results show that signature features effectively encode temporal and nonlinear dependencies, yielding accurate forecasts competitive with those based on expert knowledge.

翻译：协变量的非线性与滞后效应常使时间序列预测面临挑战。为此，我们提出一种基于岭回归与滑动窗口特征计算的新型预测框架。该框架通过滑动窗口计算的特征能捕捉复杂的时序动态，且无需依赖学习所得或人工构建的表征。聚焦于离散时间场景，我们建立了理论保证，即特征的普适逼近性与平稳性。同时提出一种高效的滑动窗口特征序列计算算法。该方法在合成数据与真实电力需求数据上均进行了评估。结果表明，特征能有效编码时序与非线性的依赖关系，其预测精度可与基于专家知识的预测方法相媲美。