  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.
