Power-law cross-correlations estimation under heavy tails

TL;DR

This paper compares six estimators of power-law cross-correlations under heavy-tailed distributions, revealing that frequency domain estimators are robust to heavy tails, while time domain estimators are biased but have lower variance for short series.

Contribution

It provides a comprehensive analysis of estimator performance under heavy tails, highlighting their biases and variances, and offers guidance for empirical applications.

Findings

Frequency domain estimators are unaffected by heavy tails.

Time domain estimators are upward biased with heavy tails.

Estimator suitability depends on distributional properties and series length.

Abstract

We examine the performance of six estimators of the power-law cross-correlations -- the detrended cross-correlation analysis, the detrending moving-average cross-correlation analysis, the height cross-correlation analysis, the averaged periodogram estimator, the cross-periodogram estimator and the local cross-Whittle estimator -- under heavy-tailed distributions. The selection of estimators allows to separate these into the time and frequency domain estimators. By varying the characteristic exponent of the $\alpha$-stable distributions which controls the tails behavior, we report several interesting findings. First, the frequency domain estimators are practically unaffected by heavy tails bias-wise. Second, the time domain estimators are upward biased for heavy tails but they have lower estimator variance than the other group for short series. Third, specific estimators are more appropriate depending on distributional properties and length of the analyzed series. In addition, we provide a discussion of implications of these results for empirical applications as well as theoretical explanations.