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

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.

arXiv comment26 pages. The old version had dynamic correlation estimators (and corresponding consistency results) for Brownian motion pairs. Note that in the new version we added estimators and consistency results for Geometric Brownian motion pairs