Joint Asymptotics for Estimating the Fractal Indices of Bivariate Gaussian Processes

Authors

Yuzhen Zhou, University of Nebraska - LincolnFollow
Yimin Xiao, Michigan State UniversityFollow

Document Type

Article

Date of this Version

2018

Citation

Journal of Miltivariate Analysis 165 (2018) 56-72.

Comments

Copyright 2017 Elsevier Inc.

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.