Spectrum-based estimators of the bivariate Hurst exponent

TL;DR

This paper introduces two novel spectrum-based estimators for the bivariate Hurst exponent, demonstrating improved bias properties and potential as complements to existing time domain methods through simulation analysis.

Contribution

The paper presents the cross-periodogram and local X-Whittle estimators as new spectrum-based tools for estimating the bivariate Hurst exponent, extending univariate methods.

Findings

The new estimators are less biased than existing methods.

They show good performance across various bandwidths and correlation levels.

They can complement time domain estimators effectively.

Abstract

We introduce two new estimators of the bivariate Hurst exponent in the power-law cross-correlations setting -- the cross-periodogram and local $X$-Whittle estimators -- as generalizations of their univariate counterparts. As the spectrum-based estimators are dependent on a part of the spectrum taken into consideration during estimation, a simulation study showing performance of the estimators under varying bandwidth parameter as well as correlation between processes and their specification is provided as well. The newly introduced estimators are less biased than the already existent averaged periodogram estimator which, however, has slightly lower variance. The spectrum-based estimators can serve as a good complement to the popular time domain estimators.