<![CDATA[The dominance of the US dollar (USD) as the global reserve currency has begun to face structural challenges since the 2007-2008 financial crisis, which triggered the strengthening of the BRICS alliance. Although this alliance now controls 35% of the world's GDP and is actively pursuing de-dollarization, analysis of the volatility of their collective currencies is often limited to univariate parametric models that fail to capture inter-country dependencies and complex periodic fluctuation patterns. This study aims to fill this gap by applying a nonparametric multiresponse Fourier series regression to simultaneously model the interdependence of the five major BRICS currencies against the USD. Using weekly secondary data from June 2009 to February 2025 (817 observations) from investing.com, this study positions time as the predictor and the exchange rates of the five BRICS currencies as the response. The analysis results show that the best estimation model is obtained through a sine function without a trend component with an optimal oscillation parameter k=1, based on a minimum Generalized Cross Validation (GCV) value of 0.000702363. The prediction results from the training data produce a MAPE value of 4.7521%, which classifies the analysis as highly accurate. These findings strategically support the validation of the de-dollarization movement, providing a predictive instrument for developing countries to reduce their dependence on the USD, as well as strengthening the bargaining position of Eastern economies in a more multipolar international financial order.]]>
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