Nonlinear Dynamics of RMB Exchange Rate Volatility: A Multifractal Perspective Within the G-Expectation Framework

Traditional linear models struggle to capture the complex behavior of financial markets. This study revisits RMB exchange rate volatility through a nonlinear perspective based on G-expectation and multifractal theory. Using multifractal detrended fluctuation analysis (MF-DFA), we examine the scaling properties and efficiency of RMB volatility. We further apply multifractal detrended cross-correlation analysis (MF-DCCA) to explore nonlinear linkages among different RMB exchange rate volatilities. Mixing and phase randomization are employed to identify the sources of multifractality. The results reveal that adverse shocks weaken market efficiency and amplify multifractality. Significant cross-correlations are detected across RMB volatilities, with the Hurst exponent and multifractal spectrum indicating persistent long-range dependence and fat-tailed distributions. Moreover, USDCNY volatility exhibits stronger multifractality than other RMB pairs, underscoring its dominant role in volatility transmission. The time-varying Hurst exponent effectively captures nonlinear and memory effects, offering predictive value for exchange rate trends. These findings deepen our understanding of RMB exchange rate dynamics and provide implications for monetary regulation and risk management under uncertainty.