Fractal Dimension and Chaotic Dynamics of Multiscale Network Factors in Asset Pricing: A Wavelet Packet Decomposition Approach Based on Fractal Market Hypothesis

The nature of nonlinear dynamics of financial markets results in fractal geometry and chaotic behavior that can be viewed on a variety of scales in time. This paper conducts research on the fractal characteristics of the stock network and its contribution to the price of assets based on the Fractal Market Hypothesis (FMH). A multiscale network centrality measure is built based on high-frequency return dependencies to measure the self-similar, scale-invariant nature of inter-stock dependencies. The network factor and portfolio returns are then broken down with the wavelet packet decomposition (WPD) to obtain frequency-domain profiles, which characterize the variability of risk transmission in relation to investment horizons. The profiles are consistent with scaling properties of fractal, but the decomposition does not identify causal pathways on its own. Estimation of fractal dimension by use of the box-counting technique aided by the Hurst exponent analysis reveals that the A-share of China market exhibited long-range dependence and multifractal scaling. Network factor has the largest explanatory power in mid-frequency between the D5 and D6 bands of 32 to 128 days. This intermediary frequency concentration is consistent with the hypothesis of heterogeneous markets, in which the groups of investors with varying time horizons generate scale-related price dynamics. The addition of the network factor to a 6-factor specification lowers the GRS under the 5-factor specification by 31.45 to 17.82 on the same test-asset universe, indicating better cross-sectional coverage in the sample. The estimates of the Lyapunov exponents (0.039) as well as the correlation dimension (D2=4.7) confirm the presence of low-dimensional chaotic processes of the network factor series, but these values are specific to the Chinese A-share market over the 2005–2023 sample period. These results provide a frequency-disaggregated use of network-based factor modeling and suggest that it can be applicable in multiscale portfolio risk management where the investor horizon is not uniform.