  Multivariate (or vector-valued) processes are important for modeling multiple
variables. The fractal indices of the components of the underlying multivariate
process play a key role in characterizing the dependence structures and
statistical properties of the multivariate process.
  In this paper, under the infill asymptotics framework, we establish joint
asymptotic results for the increment-based estimators of bivariate fractal
indices. Our main results quantitatively describe the effect of the
cross-dependence structure on the performance of the estimators.
