On Statistical Inference for High-Dimensional Binary Time Series

TL;DR

This paper introduces a new statistical inference method for high-dimensional binary time series, including an estimator, Gaussian approximation, and bootstrap algorithm, with demonstrated effectiveness in simulations and real data.

Contribution

It proposes a novel post-selection estimator and bootstrap inference procedure tailored for high-dimensional binary vector autoregressive models.

Findings

The estimator performs well in finite samples.

The Gaussian approximation accurately captures the estimator's distribution.

The bootstrap method enables reliable inference on coefficients.

Abstract

The analysis of non-real-valued data, such as binary time series, has attracted great interest in recent years. This manuscript proposes a post-selection estimator for estimating the coefficient matrices of a high-dimensional generalized binary vector autoregressive process and establishes a Gaussian approximation theorem for the proposed estimator. Furthermore, it introduces a second-order wild bootstrap algorithm to enable statistical inference on the coefficient matrices. Numerical studies and empirical applications demonstrate the good finite-sample performance of the proposed method.