Estimation of correlation for continuous semimartingales

Abstract

In this paper we are concerned with inference on the correlation parameter rho of two Brownian motions, when only high-frequency observations from two one-dimensional continuous It^o semimartingales, driven by these particular Brownian motions, are available. Estimators for rho are constructed in two situations: Either when both components are observed (at the same time), or when only one component is observed and the other one represents its volatility process and thus has to be estimated from the data as well. In the first case it is shown that our estimator has the same asymptotic behaviour as the standard one for i.i.d. observations, whereas a feasible estimator can still be defined in the second framework, but with a slower rate of convergence.