In Das and Politis(2020), a model-free bootstrap(MFB) paradigm was proposed for generating prediction intervals of univariate, (locally) stationary time series. Theoretical guarantees for this algorithm was resolved in Wang and Politis(2019) under stationarity and weak dependence condition. Following this line of work, here we extend MFB for predictive inference under a multivariate time series setup. We describe two algorithms, the first one works for a particular class of time series under any fixed dimension d; the second one works for a more generalized class of time series under low-dimensional setting. We justify our procedure through theoretical validity and simulation performance.

翻译：在《Das and Politis》(2020年)中,提出了一种无模型的靴子陷阱(MFB)范式,用于生成单体(当地)固定时间序列的预测间隔。Wang和Politis(2019年)在静止和依赖性弱的条件下解决了这一算法的理论保障。根据这项工作,我们在此扩展MFB,用于在多变时间序列设置下预测推理。我们描述了两种算法,第一种算法在任何固定的维度下为某一类时间序列工作;第二种算法在低维度设置下为更普遍的时间序列工作。我们通过理论有效性和模拟性能来证明我们的程序是合理的。