Weak-consistent dynamic correlation estimators for Brownian motion pairs and for Geometric Brownian motion pairs

TL;DR

This paper introduces new estimators for dynamic correlation between pairs of Brownian motions and Geometric Brownian motions, demonstrating their convergence to true correlation as sample size grows.

Contribution

It proposes novel estimators for dynamic correlation in Brownian motion pairs and proves their consistency with increasing sample size.

Findings

Estimators converge in probability to true dynamic correlation.

Applicable to both Brownian and Geometric Brownian motion pairs.

Enhances accuracy of correlation estimation in stochastic processes.

Abstract

Estimating dynamic correlation between a pair of time series is of importance in many applications. We present new estimators for the dynamic correlation between a pair of correlated Brownian motions and separately for dynamic correlation between a pair of correlated Geometric Brownian motions. We show that, as the sample size increases, all estimators presented in this paper converge in probability to the underlying true dynamic correlation.