A bootstrap functional central limit theorem for time-varying linear processes

TL;DR

This paper establishes a functional central limit theorem for time-varying linear processes and introduces a local block bootstrap method to validate the theorem in practical scenarios.

Contribution

It provides a new functional CLT for noncausal multivariate processes with time-varying coefficients and proposes a bootstrap procedure for practical implementation.

Findings

Bootstrap validity is proven for a broad class of processes.

Numerical examples demonstrate the effectiveness of the bootstrap method.

Theoretical results extend existing CLT frameworks to nonstationary processes.

Abstract

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.