Fractional Differencing and Random Forest Framework for Financial Time-Series Forecasting

Fractional differencing offers a persistence-oriented representation of financial time series, while fractional volatility models provide information on persistent conditional variance. This study evaluates whether such fractional-econometric information adds predictive value to Random Forest models for daily stock returns. Daily closing prices of ten Indonesian stocks during 2021–2025 are analyzed using R/S, GPH, and Local Whittle persistence estimators, fractional differencing, an FD-ARMA baseline, FIGARCH volatility modeling, and Random Forest. Forecasts are evaluated using a leakage-free expanding-information one-step-ahead design with scheduled 20-trading-day refits and 220 out-of-sample observations per stock. R/S estimates indicate persistent scaling, but GPH estimates are insignificant across the examined bandwidths and Local Whittle evidence is limited to selected cases. Conventional ARMA and FD-ARMA each achieve an average RMSE of approximately 0.02178, compared with 0.02222 for the full Random Forest, and no Random Forest specification has the lowest RMSE for any stock. Formal forecast-comparison and directional tests provide no robust evidence of Random Forest superiority after multiple-testing adjustment. Fractional and volatility-derived predictors therefore provide small and heterogeneous incremental contributions. The results emphasize leakage-free evaluation, estimator robustness, and strong conventional benchmarks when assessing fractional-feature machine-learning frameworks for daily financial returns.