Joint Asymptotics for Estimating the Fractal Indices of Bivariate Gaussian Processes

TL;DR

This paper develops joint asymptotic results for estimators of fractal indices in bivariate Gaussian processes, highlighting how cross-dependence influences estimation accuracy under infill asymptotics.

Contribution

It provides the first joint asymptotic analysis of increment-based estimators for bivariate fractal indices, accounting for cross-dependence effects.

Findings

Quantifies the impact of cross-dependence on estimator performance.

Establishes joint asymptotic distributions under infill asymptotics.

Enhances understanding of multivariate fractal index estimation.

Abstract

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.