Double asymmetric multifractal detrended fluctuation analysis (DA-MFDFA): Extending asymmetric multifractal methods for exogenous time series

Abstract

This paper introduces Double Asymmetric Multifractal Detrended Fluctuation Analysis (DA-MFDFA), a novel extension of traditional multifractal methods designed to capture the joint influence of price trends and trading volume on financial return dynamics. By integrating an exogenous volume-based asymmetry, DA-MFDFA provides a richer framework to analyze complex market behavior, especially under extreme bullish and bearish conditions. Applying DA-MFDFA to a comprehensive sample of S&P 500 stocks over multiple rolling windows, we identify distinct multifractal patterns characterized by varying degrees of long memory and reversal effects across different market regimes. Our findings demonstrate that strong volume-reinforced trends are associated with heightened reversal behaviors and increased market complexity, while standard trends exhibit greater persistence. These results carry important implications for portfolio management and trading strategies, enabling more adaptive risk assessment and regime-sensitive decision-making. The flexibility of the DA-MFDFA framework further allows incorporation of additional external factors, broadening its applicability in financial modeling and other fields. This study advances multifractal analysis by highlighting the critical role of volume dynamics in shaping market efficiency and return behavior.