Multifractal detrended fluctuation analysis based on exponential moving average and its application to stock index turnover ratios

In this paper, we propose a multifractal detrended fluctuation analysis method (MF-EMA-DFA) utilizing exponential moving averages as local trends, aiming to integrate and enhance the advantages and performance of MFDFA and MFDMA. Numerical simulations based on a series of benchmark models demonstrate that the proposed method exhibits higher accuracy and robustness, significantly improving the estimation precision of multifractal characteristics. Furthermore, for the first time, we apply this method to conduct a multifractal analysis on twelve stock index turnover ratios and their growth rates. The results indicate that the activity of the Chinese A-share market exhibits strong persistence under both large and small fluctuations, whereas the more S&P 500 exhibits a correction effect during extreme large fluctuations. Meanwhile, only the turnover of the HSI, Nasdaq, and S&P 500 exhibit intrinsic multifractal properties, while the others display apparent multifractal characteristics. Among the turnover growth rate sequences, only the SSE Composite Index and SZSE Component Index demonstrate apparent multifractal patterns. Finally, we introduce an indicator for measuring the comprehensive multifractal complexity, providing a novel tool for signal complexity ranking, anomaly detection, and cluster analysis.