Time series prediction is challenging due to our limited understanding of the underlying dynamics. Conventional models such as ARIMA and Holt's linear trend model experience difficulty in identifying nonlinear patterns in time series. In contrast, machine learning models excel at learning complex patterns and handling high-dimensional data; however, they are unable to quantify the uncertainty associated with their predictions, as statistical models do. To overcome these drawbacks, we propose Random Feature Bayesian Lasso Takens (rfBLT) for forecasting time series data. This non-parametric model captures the underlying system via the Takens' theorem and measures the degree of uncertainty with credible intervals. This is achieved by projecting delay embeddings into a higher-dimensional space via random features and applying regularization within the Bayesian framework to identify relevant terms. Our results demonstrate that the rfBLT method is comparable to traditional statistical models on simulated data, while significantly outperforming both conventional and machine learning models when evaluated on real-world data. The proposed algorithm is implemented in an R package, rfBLT.

翻译：时间序列预测因对潜在动力学理解有限而具有挑战性。传统模型如ARIMA和Holt线性趋势模型在识别时间序列中的非线性模式方面存在困难。相比之下，机器学习模型擅长学习复杂模式并处理高维数据；然而，与统计模型不同，它们无法量化预测相关的不确定性。为克服这些缺陷，我们提出随机特征贝叶斯套索Takens（rfBLT）模型用于时间序列数据预测。该非参数模型通过Takens定理捕捉潜在系统，并利用可信区间度量不确定性程度。这是通过将延迟嵌入通过随机特征投影到高维空间，并在贝叶斯框架内应用正则化以识别相关项来实现的。我们的结果表明，rfBLT方法在模拟数据上与传统统计模型性能相当，而在真实世界数据评估中显著优于传统模型和机器学习模型。所提算法已在R软件包rfBLT中实现。