We develop a method to construct distribution-free prediction intervals for dynamic time-series, called EnbPI that wraps around any bootstrap ensemble estimator to construct sequential prediction intervals. EnbPI is closely related to the conformal prediction (CP) framework but does not require data exchangeability. Theoretically, these intervals attain asymptotically valid marginal coverage for broad classes of regression functions and time-series with certain dependencies. Intervals also converge in width to the oracle lower bound asymptotically. Computationally, EnbPI avoids overfitting and requires neither data-splitting nor training multiple ensemble estimators; it efficiently aggregates bootstrap estimators that have been trained. In general, 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 simulation and real-data analyses to demonstrate its effectiveness and applicability beyond predictive inference.

翻译：我们为动态时间序列(称为EnbPI)制定了一种构建无分配的预测间隔的方法,它环绕着任何靴杆组合估计值来构建连续预测间隔。EnbPI与符合的预测框架密切相关,但并不要求数据互换。理论上,这些间隔对于具有某些依赖性的广泛类别的回归函数和时间序列来说是无实际作用的边际覆盖。两个间隔也以宽度和角宽度相交,不附带任何约束。比较而言,EnbPI避免过配,也不要求数据分离或培训多个共同估计值;它有效地综合了受过培训的靴杆估计值。一般来说,EnbPI很容易实施,可以任意地按顺序生成许多预测间隔,而且完全适合广泛的回归函数。我们进行了广泛的模拟和真实数据分析,以证明其效力和适用性,超出了预测性。