# AR(1) processes driven by second-chaos white noise: Berry-Ess\'een bounds for quadratic variation and parameter estimation

## TL;DR

This paper investigates the asymptotic properties of quadratic variation in AR(1) processes driven by second-chaos white noise, providing Berry-Esséen bounds and insights into parameter estimation.

## Contribution

It introduces new bounds on convergence rates for AR(1) processes driven by second-chaos noise and applies these to improve understanding of mean-reversion estimation.

## Key findings

- Established Berry-Esséen bounds for quadratic variation
- Demonstrated convergence rates to normal law
- Provided simulation validation of theoretical results

## Abstract

In this paper, we study the asymptotic behavior of the quadratic variation for the class of AR(1) processes driven by white noise in the second Wiener chaos. Using tools from the analysis on Wiener space, we give an upper bound for the total-variation speed of convergence to the normal law, which we apply to study the estimation of the model's mean-reversion. Simulations are performed to illustrate the theoretical results.