We provide a functional central limit theorem for a broad class of smooth functions for possibly noncausal multivariate linear processes with time-varying coefficients. Since the limiting processes depend on unknown quantities, we propose a local block bootstrap procedure to circumvent this inconvenience in practical applications. In particular, we prove bootstrap validity for a very broad class of processes. Our results are illustrated by some numerical examples.

翻译：我们为可能具有时间变化系数的非因果多变线性进程提供了一个广泛的顺利功能类别功能的功能中心限制理论。由于限制过程取决于未知数量,我们提议了一个本地块式靴子陷阱程序,以避免在实际应用中出现这种不便。特别是,我们证明,对于非常广泛的程序类别来说,靴子陷阱是有效的。我们的结果可以用数字例子来说明。