Fractal Analysis of Long-Range Dependence in IoT-Blockchain Time Series:A Methodological Framework Using Hurst Exponent, R/S, and DFA
Oothongsap, P. Mingkhwan A.
Journal of Networking Technology, Vol. 17, No. 2, 2026.
DOI: https://doi.org/10.6025/jnt/2026/17/2/83-94
Link: https://www.dline.info/jnt/fulltext/v17n2/jntv17n2_3.pdf
Abstract:
This study presents a methodological framework for analyzing long-range dependence (LRD) in IoT blockchain
time series through fractal analysis. Utilizing a synthetically generated Fractional Gaussian Noise (FGN)
dataset that emulates high speed network traffic, the research employs the Hurst exponent as a primary
metric to quantify temporal persistence and scaling behavior. Two classical yet robust techniques Rescaled
Range (R/S) analysis and Detrended Fluctuation Analysis (DFA) are systematically applied to estimate the
Hurst exponent across multiple temporal scales. The results demonstrate strong power law scaling, with
linear log log relationships confirming scale invariant dynamics. Quantitative estimates yield Hurst exponents
of approximately 0.91 (R/S) and 0.88 (DFA), both significantly exceeding the 0.5 threshold for random
walks, thereby indicating strong persistent behavior and long term memory. Corresponding fractal dimension
values (1.09 and 1.12) reveal moderate smoothness combined with structured irregularity, highlighting the
intrinsic complexity of the underlying processes. The high consistency between R/S and DFA outcomes
validates the framework's reliability, while DFA's detrending mechanism ensures robustness to nonstationarity.
These findings carry significant implications for IoT blockchain ecosystems, particularly in
predictive modeling, multi-scale anomaly detection, and adaptive resource allocation. By capturing selfsimilar
traffic patterns, the framework enhances system resilience against congestion and stealthy cyber
threats. Future research will extend this univariate approach to multivariate network data and explore realtime
fractal monitoring for edge-computing environments.