Statistical Inference for High-Dimensional Vector Autoregression with Measurement Error

TL;DR

This paper develops new statistical inference methods for high-dimensional vector autoregression models with measurement error, enabling reliable testing of transition matrices in complex data scenarios.

Contribution

It introduces a novel sparse EM algorithm and asymptotic testing procedures for high-dimensional VAR models with measurement error, filling a gap in inference methods.

Findings

The proposed tests perform well in finite samples.

The methods are applicable to brain connectivity data.

Asymptotic guarantees are established for the tests.

Abstract

High-dimensional vector autoregression with measurement error is frequently encountered in a large variety of scientific and business applications. In this article, we study statistical inference of the transition matrix under this model. While there has been a large body of literature studying sparse estimation of the transition matrix, there is a paucity of inference solutions, especially in the high-dimensional scenario. We develop inferential procedures for both the global and simultaneous testing of the transition matrix. We first develop a new sparse expectation-maximization algorithm to estimate the model parameters, and carefully characterize their estimation precisions. We then construct a Gaussian matrix, after proper bias and variance corrections, from which we derive the test statistics. Finally, we develop the testing procedures and establish their asymptotic guarantees. We study the finite-sample performance of our tests through intensive simulations, and illustrate with a brain connectivity analysis example.