  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.
