Estimating correlations among elliptically distributed random variables under any form of heteroskedasticity

Abstract

The paper introduces a semiparametric estimator of the correlations among elliptically distributed random variables invariant to any form of heteroscedasticity, robust to outliers, and asymptotically normal. Our estimator is particularly fit for financial applications as vectors of stock returns are generally well approximated by heteroskedastic processes with elliptical (conditional) distributions and heavy tails. The superiority of our estimator with respect to Pearson's sample correlation in financial applications is illustrated using simulated data and real high-frequency stock returns. Using simple exponentially weighted moving averages, we extend our estimator to the case of time-varying correlations and compare it to the popular GARCH-DCC model. We show that the two approaches have comparable performances through simulations and a simple application. However, our estimator is extremely fast to compute, computationally robust, and straightforward to implement.