Spectrum-based estimators of the bivariate Hurst exponent

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.

arXiv comment15 pages, 4 figures

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Cited by in corpus (3)

• Multivariate Hadamard self-similarity: testing fractal connectivity
• Fractal approach towards power-law coherency to measure cross-correlations between time series
• Power-law cross-correlations estimation under heavy tails