We develop a method to construct distribution-free prediction intervals for dynamic time-series, called \Verb|EnbPI| that wraps around any bootstrap ensemble estimator to construct sequential prediction intervals. \Verb|EnbPI| is closely related to the conformal prediction (CP) framework but does not require data exchangeability. Theoretically, these intervals attain finite-sample, \textit{approximately valid} marginal coverage for broad classes of regression functions and time-series with strongly mixing stochastic errors. Computationally, \Verb|EnbPI| avoids overfitting and requires neither data-splitting nor training multiple ensemble estimators; it efficiently aggregates bootstrap estimators that have been trained. In general, \Verb|EnbPI| is easy to implement, scalable to producing arbitrarily many prediction intervals sequentially, and well-suited to a wide range of regression functions. We perform extensive real-data analyses to demonstrate its effectiveness.

翻译：我们开发了一种方法,用于构建动态时间序列的无分布式预测间隔,称为\Verb ⁇ EnbPI},环绕任何靴套共同估计值,以构建连续预测间隔。\Verb ⁇ EnbPI}}与符合的预测框架密切相关,但不需要数据互换。理论上,这些间隔可达到一定比例,\textit{约有效}边际覆盖广泛的回归函数和时间序列类别,并大力混合随机误差。比较,\Verb ⁇ EnbPI}避免了数据过度匹配,也不要求数据分离或培训多个共同估计值;它有效地综合了已经培训过的靴套测算器。一般来说,\Verb ⁇ EnbPI}易于执行,可以任意地按顺序生成许多预测间隔,并且非常适合广泛的回归功能。我们进行了广泛的真实数据分析,以证明其有效性。