DCCA Algorithm for Detrended Cross-Correlation Analysis with MATLAB Implementation

In this article, we present a comprehensive guide to implementing the DCCA algorithm using MATLAB for detrended cross-correlation analysis. This algorithm enables researchers to analyze the covariance between two datasets and derive DCCA exponents. To establish a solid foundation, let's first examine the underlying principles of this methodology.

The Detrended Cross-Correlation Analysis (DCCA) algorithm is a powerful method for investigating relationships between two time series. It effectively identifies correlations between time series while eliminating trend influences that might distort the results. The implementation involves several key steps: detrending both time series using polynomial fitting or moving average techniques, computing the cross-correlation function through integrated residual series, and calculating fluctuation functions across different time scales. The algorithm typically employs window-based segmentation where local trends are removed from overlapping segments of both series before computing covariance.

This article provides detailed MATLAB implementation guidelines covering data preprocessing, cross-correlation computation using built-in functions like xcov or custom covariance calculations, and statistical validation through T-tests. We'll demonstrate how to use MATLAB's statistical toolbox for hypothesis testing, including calculating p-values and confidence intervals. The implementation will feature code segments showing how to handle variable window sizes, normalize covariance functions, and compute scaling exponents through linear regression in log-log plots. By studying this material, you will gain both theoretical understanding of DCCA principles and practical skills for MATLAB implementation suitable for scientific research applications.