Challenging the Efficient Market Hypothesis: Multifractal Insights into Price – Volume Cross-Correlations in the S&P 500

Abstract

This study investigates the multifractal behaviour of prices, trading volume, and their cross-correlations in the S&P 500 index over the 2004–2024 period. To this end, we employ an integrated framework that combines the Bai–Perron structural break test with Multifractal Detrended Fluctuation Analysis (MFDFA) and Multifractal Detrended Cross-Correlation Analysis (MFDCCA). MFDFA is employed to detect scale-dependent long-range dependence and multifractality within individual time series, while MFDCCA extends this framework to examine multifractal cross-correlations between price and trading volume across different time scales. The structural break analysis reveals five endogenous break points, leading to six distinct market segments and allowing market dynamics to be examined on a segment-specific basis. The empirical evidence shows that both price and volume series display multifractal behaviour throughout the sample, although the intensity of multifractality varies across segments. By contrast, price–volume cross-correlations tend to exhibit broader and more asymmetric multifractal spectra, pointing to stronger nonlinear dependence and greater structural complexity in joint dynamics. Importantly, these results should not be interpreted as evidence of a permanent breakdown in market efficiency. Rather, they suggest that deviations from weak-form efficiency are time-varying and closely linked to changing market conditions, in line with the Adaptive Market Hypothesis and the Fractal Market Hypothesis. Overall, the joint analysis of price, volume, and their multifractal cross-structure within a structural-break-aware setting offers new insights into segment-dependent information transmission and the evolving nature of market efficiency in a major benchmark index.