Detrended Multiple Cross-Correlation Analysis of Four Nonstationary Time Series: Formulation and Application to Solar Radiation

In this paper, we performed a (multiple) DCCA cross-correlation statistical analysis with the DFA and DCCA methods using the coefficients ρDCCA and DMCx2. Solar radiation was considered the main variable of interest. Understanding multi-scale fluctuations in solar radiation is crucial for climate modeling and predicting weather patterns, and it plays a critical role in environmental processes and human activities. Cross-correlation in the context of solar radiation refers to the statistical relationship or connection between solar radiation and various environmental or atmospheric variables. Analyzing cross-correlations helps to understand how changes in solar radiation relate to other factors over time or across different locations. Thus, we studied an area encompassing almost the entire territory of Brazil, using data from twenty-six automatic weather stations. To achieve this objective, we applied the DCCA multiple cross-correlation coefficient, DMCx2, between solar radiation and (air temperature, relative humidity, and wind speed). To the best of our knowledge, this is the first explicit analytical formulation and application of the DMCx2 coefficient involving one dependent variable and three independent variables. This formulation also enables the construction of multi-scale spatial color maps, revealing persistent multi-scale cross-correlation structures and systematically higher DMCx2 values in northeastern Brazil, not evident from pairwise analyses, or by classical methods.