Variance inequalities for quadratic forms with applications

TL;DR

This paper derives variance inequalities for quadratic forms of weakly dependent random variables with bounded fourth moments and applies these results to spectral distribution of random matrices and long-run variance estimation.

Contribution

It introduces new variance inequalities for quadratic forms of dependent variables and demonstrates their applications in spectral analysis and time series variance estimation.

Findings

Variance inequalities for quadratic forms of dependent variables.

Application to limiting spectral distribution of random matrices.

Application to long-run variance estimation in time series.

Abstract

We obtain variance inequalities for quadratic forms of weakly dependent random variables with bounded fourth moments. We also discuss two application. Namely, we use these inequalities for deriving the limiting spectral distribution of a random matrix and estimating the long-run variance of a stationary time series.