Rick Galbo , Wayy Research, USA

Time series forecasting in complex systems, particularly financial markets, remains fundamentally challenged by the inadequacy of linear, stationary models. This paper presents FracTime, a comprehensive computational framework that operationalizes the Fractal Market Hypothesis (FMH) through novel methodologies grounded in fractal geometry and chaos theory. We introduce specialized forecasting algorithms based on Rescaled Range (R/S) analysis and Detrended Fluctuation Analysis (DFA) for Hurst exponent estimation, coupled with Monte Carlo simulation for probabilistic scenario generation. Our framework explicitly leverages long-range dependence and self-similarity characteristics quantified through the Hurst exponent (H) and fractal dimension (D). Rigorous empirical validation via walk-forward backtesting across 26 diverse financial assets and 7,648 forecasts demonstrates that FracTime achieves superior directional accuracy (58.9%) compared to ARIMA (39.1%) and ETS (53.2%), while providing significantly better probabilistic calibration (91.2% coverage at 95% confidence intervals versus 80.6-81.3% for benchmark models). Diebold-Mariano tests confirm that point forecast accuracy (RMSE, MAE) is statistically equivalent across methods, establishing FracTime as achieving comparable point accuracy while delivering substantial advantages in directional prediction and uncertainty quantification. This work establishes FracTime as a rigorous, interpretable alternative to traditional econometric models for non-linear time series analysis.

Fractal Market Hypothesis, Hurst Exponent, Time Series Forecasting, Long-Range Dependence, Probabilistic Calibration, Monte Carlo Simulation, Detrended Fluctuation Analysis