Time series analysis by state-space models is widely used in forecasting and extracting unobservable components like level, slope, and seasonality, along with explanatory variables. However, their reliance on traditional Kalman filtering frequently hampers their effectiveness, primarily due to Gaussian assumptions and the absence of efficient subset selection methods to accommodate the multitude of potential explanatory variables in today's big-data applications. Our research introduces the State Space Learning (SSL), a novel framework and paradigm that leverages the capabilities of statistical learning to construct a comprehensive framework for time series modeling and forecasting. By utilizing a regularized high-dimensional regression framework, our approach jointly extracts typical time series unobservable components, detects and addresses outliers, and selects the influence of exogenous variables within a high-dimensional space in polynomial time and global optimality guarantees. Through a controlled numerical experiment, we demonstrate the superiority of our approach in terms of subset selection of explanatory variables accuracy compared to relevant benchmarks. We also present an intuitive forecasting scheme and showcase superior performances relative to traditional time series models using a dataset of 48,000 monthly time series from the M4 competition. We extend the applicability of our approach to reformulate any linear state space formulation featuring time-varying coefficients into high-dimensional regularized regressions, expanding the impact of our research to other engineering applications beyond time series analysis. Finally, our proposed methodology is implemented within the Julia open-source package, ``StateSpaceLearning.jl".

本研究解决了传统卡尔曼滤波在时间序列分析中面临的高斯假设和变量选择效率低下的问题。我们提出了一种新颖的状态空间学习（SSL）框架，利用正则化的高维回归来提取时间序列的隐含成分并优化变量选择。实验结果表明，该方法在变量选择的准确性和预测性能上优于传统模型，扩展了其在其他工程领域的应用潜力。

通过状态空间学习进行时间序列分析