Estimating the Copula of a class of Time-Changed Brownian Motions: A non-parametric Approach

TL;DR

This paper introduces a non-parametric method for estimating copulas linked to time-changed Brownian motions within a high-frequency setting, demonstrating consistency and asymptotic properties through theoretical analysis and Monte Carlo testing.

Contribution

It presents a novel non-parametric estimator for copulas of time-changed Brownian motions, with proven consistency and asymptotic mixed-Gaussian behavior.

Findings

Estimator is consistent and asymptotically mixed-Gaussian.

Finite-sample accuracy confirmed via Monte Carlo simulations.

Applicable to high-frequency financial data analysis.

Abstract

Within a high-frequency framework, we propose a non-parametric approach to estimate a family of copulas associated to a time-changed Brownian motion. We show that our estimator is consistent and asymptotically mixed-Gaussian. Furthermore, we test its finite-sample accuracy via Monte Carlo.