Real-Time Algorithm for Detrended Cross-Correlation Analysis of Long-Range Coupled Processes

Abstract

Assessing power-law cross-correlations between a pair – or among a set – of processes is of great significance in diverse fields of analyses ranging from neuroscience to financial markets. In most cases such analyses are computationally expensive and thus carried out offline once the entire signal is obtained. However, many applications – such as mental state monitoring or financial forecasting – call for fast algorithms capable of estimating scale-free coupling in real time. Detrended cross-correlation analysis (DCCA), a generalization of the detrended fluctuation analysis (DFA) to the bivariate domain, has been introduced as a method designed to quantify power-law cross-correlations between a pair of non-stationary signals. Later, in analogy with the Pearson cross-correlation coefficient, DCCA was adapted to the detrended cross-correlation coefficient (DCCC), however as of now no online algorithms were provided for either of these analysis techniques. Here we introduce a new formula for obtaining the scaling functions in real time for DCCA. Moreover, the formula can be generalized via matrix notation to obtain the scaling relationship between not only a pair of signals, but also all possible pairs among a set of signals at the same time. This includes parallel estimation of the DFA scaling function of each individual process as well, thus allowing also for real-time acquisition of DCCC. The proposed algorithm matches its offline variants in precision, while being substantially more efficient in terms of execution time. We demonstrate that the method can be utilized for mental state monitoring on multi-channel electroencephalographic recordings obtained in eyes-closed and eyes-open resting conditions.

Multiscale Detrended Cross-Correlation Coefficient: Estimating Coupling in Nonstationary Neurophysiological Signals

“…The calculation of MDC 3 using different scaling exponents would add another layer of complexity to the interpretation of the outputs. Recently, a real-time algorithm for the estimation of DCCC was presented (50,51), which can be extended for MDC 3 as well. This means that MDC 3 can be used in brain-computer interfaces or clinical monitoring of patients, where constant tracking of network dynamics is needed.…”

Combining detrended cross-correlation analysis with Riemannian geometry-based classification for improved brain-computer interface performance

“…First, we evaluated the detection pipeline offline (and pseudo-online) on previously collected data in order to assess its potential effects on performance in an MI task. Then, we tested if rtDCCA (Kaposzta et al, 2022 ) can indeed be utilized online in a BCI application. Finally, we further validated our proposed method on an independent, publicly available dataset (Schalk et al, 2004 ).…”

“…In its original formulation DCCA is computationally expensive, which contradicts its applicability in online BCI applications where real-time performance is essential. Recently, however, Kaposzta et al ( 2022 ) proposed an online formula for DCCA (rtDCCA) allowing for real-time computation of the DCCA matrix from multivariate data and thus resolving this limitation.…”

An Examination of Negative Correlations Using Pearson Correlation Analysis to Optimize the Diversification of Cryptocurrency Portfolios

“…This approach provides valuable insights into how specific cryptocurrency pairs may move in opposite directions, which can be essential information for investors seeking portfolio diversification and risk reduction. The Pearson Correlation method applied in this research is a reliable and relevant analytical tool for understanding the relationships between crypto assets in this dynamic market [27].…”