Is Algorithmic Stability Necessary for Finite Sample Prediction from a Single Dependent Time Series?

Forecasting from a single dependent time series creates a tension between finite-sample predictive validity and data reuse. Split conformal prediction reserves observations for calibration, whereas Leave a Window Out (LWO) reuses nearly all historical observations but its existing finite-sample guarantee requires an algorithmic stability condition. We introduce Windowed Jackknife+ (WJ+), which removes a forward window beginning at each historical observation and uses the same window-deleted predictor for both the historical residual and the forecast prediction. Under the stated distributional and learning-rule conditions, this matched-predictor construction yields a finite-sample coverage guarantee without requiring an algorithmic stability assumption. The resulting miscoverage bound separates the contribution from unavailable score comparisons created by window removal from a term due to temporal dependence. We further show that the comparison contribution can persist even when removing observations does not change the predictor.