For modeling multiple variables, the fractal indices of the components of the underlying multivariate process play a key role in characterizing the dependence structure among the components 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 for bivariate fractal indices. Our main results show the effect of the cross dependence structure on the performance of the estimators.
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