Time series forecasting has been a quintessential topic in data science, but traditionally, forecasting models have relied on extensive historical data. In this paper, we address a practical question: How much recent historical data is required to attain a targeted percentage of statistical prediction efficiency compared to the full time series? We propose the Pareto-Efficient Backsubsampling (PaEBack) method to estimate the percentage of the most recent data needed to achieve the desired level of prediction accuracy. We provide a theoretical justification based on asymptotic prediction theory for the AutoRegressive (AR) models. In particular, through several numerical illustrations, we show the application of the PaEBack for some recently developed machine learning forecasting methods even when the models might be misspecified. The main conclusion is that only a fraction of the most recent historical data provides near-optimal or even better relative predictive accuracy for a broad class of forecasting methods.

翻译：时间序列预测历来是数据科学中的经典课题，但传统上预测模型依赖于大量历史数据。本文探讨一个实际问题：与完整时间序列相比，需要多少近期历史数据才能达到特定统计预测效率百分比？我们提出帕累托高效回溯子采样（PaEBack）方法，用于估计实现目标预测精度所需的最远数据百分比。基于自回归（AR）模型的渐近预测理论，我们给出了理论支撑。特别地，通过多项数值示例，我们展示了PaEBack在若干近期发展的机器学习预测方法中的应用，即使模型可能被误设。主要结论是：对于广泛的预测方法类别，仅需采用部分近期历史数据即可提供接近最优甚至更优的相对预测精度。