Time series observations can be seen as realizations of an underlying dynamical system governed by rules that we typically do not know. For time series learning tasks, we need to understand that we fit our model on available data, which is a unique realized history. Training on a single realization often induces severe overfitting lacking generalization. To address this issue, we introduce a general recursive framework for time series augmentation, which we call Recursive Interpolation Method, denoted as RIM. New samples are generated using a recursive interpolation function of all previous values in such a way that the enhanced samples preserve the original inherent time series dynamics. We perform theoretical analysis to characterize the proposed RIM and to guarantee its test performance. We apply RIM to diverse real world time series cases to achieve strong performance over non-augmented data on regression, classification, and reinforcement learning tasks.

翻译：时间序列观测可以看作是由未知规则支配的底层动力系统的实现。对于时间序列学习任务，我们需要理解模型是在可用数据（即单一实现的历史记录）上进行拟合的。在单一实现上训练通常会导致严重的过拟合，缺乏泛化能力。为解决这一问题，我们提出了一种通用的递归时间序列增强框架，称为递归插值方法（Recursive Interpolation Method，简称RIM）。新样本通过使用所有先前值的递归插值函数生成，使得增强后的样本保留了原始内在的时间序列动态特性。我们进行了理论分析来描述所提出的RIM并保证其测试性能。我们将RIM应用于多个真实世界的时间序列场景，在回归、分类和强化学习任务上取得了优于未增强数据的强性能表现。