Dissecting Multifractal detrended cross-correlation analysis

TL;DR

This paper critically examines the multifractal detrended cross-correlation analysis method, proposing new approaches to handle negative cross-covariance, and provides computational tools tested on synthetic and real financial data.

Contribution

It introduces novel options for analyzing negative cross-covariance in multifractal analysis and offers fast, accessible code implementations for these methods.

Findings

New methods improve robustness of multifractal spectrum estimation

Code implementations in C, R, and Python are provided

Methods validated on synthetic and real-world financial data

Abstract

In this work we address the question of the Multifractal detrended cross-correlation analysis method that has been subject to some controversies since its inception almost two decades ago. To this end we propose several new options to deal with negative cross-covariance among two time series, that may serve to construct a more robust view of the multifractal spectrum among the series. We compare these novel options with the proposals already existing in the literature, and we provide fast code in C, R and Python for both new and the already existing proposals. We test different algorithms on synthetic series with an exact analytical solution, as well as on daily price series of ethanol and sugar in Brazil from 2010 to 2023.