Forecasting realized volatility of stock indices using the extra trees algorithm: an ablation study of hyperparameters
Received: 18.07.2026
Published: 29.06.2025
Abstract
This paper presents a systematic study of the influence of three key hyperparameters of the ExtraTreesRegressor algorithm — the number of base trees N, maximum depth max_depth, and minimum number of samples in a leaf min_samples_leaf — on the forecasting accuracy of realized volatility for stock indices and equities over a horizon of k = 5 trading days. The experiments were conducted on four financial instruments (AAPL, TSLA, ^GSPC, ^IXIC) using 11 years of daily trading data (2015–2026) and an expanding-window walk-forward protocol with K = 22 expanding folds. Based on 13 unique ExtraTrees configurations (a total of 1144 independent runs), the following findings were obtained: increasing N beyond 100 provides only a negligible reduction in RMSE while increasing training time by a factor of 10; restricting max_depth to 6–9 achieves the lowest RMSE, reflecting the bias–variance tradeoff under conditions of a highly noisy target variable; increasing min_samples_leaf from 5 to 50 monotonically reduces RMSE by 11–16% due to leaf regularization. The best configuration achieves RMSE = 0.00403 for the ^GSPC index, comparable to LightGBM (0.00392) and XGBoost (0.00403). The results provide practical recommendations for hyperparameter selection in daily-frequency volatility forecasting. Keywords: realized volatility; extremely randomized trees; ExtraTrees; volatility forecasting; ablation study; stock indices; walk-forward cross-validation; machine learning for finance.
Keywords
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