Model-free Bootstrap Prediction Regions for Multivariate Time Series

TL;DR

This paper extends the model-free bootstrap method to multivariate time series, providing algorithms with theoretical guarantees and demonstrating their effectiveness through simulations.

Contribution

It introduces two new algorithms for multivariate time series prediction intervals, expanding the model-free bootstrap approach beyond univariate cases.

Findings

Algorithms are theoretically valid for multivariate series.

Simulation results show good coverage and accuracy.

Applicable to fixed and low-dimensional time series.

Abstract

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.