A Comparative Forecasting Framework for Weekly VIX Prediction Based on Statistical and Machine Learning Models with Bayesian Optimization

Abstract

Accurate forecasting of the CBOE Volatility Index (VIX) is an important problem in financial risk modeling and time-series prediction due to its role as a widely used indicator of market uncertainty. This study proposes a comparative forecasting framework for weekly VIX prediction by integrating statistical and machine learning models with Bayesian optimization for hyperparameter tuning. A compact set of publicly available macro-financial indicators obtained from the Federal Reserve Economic Data (FRED), including the S&P 500 Index, the TED spread, and the Chicago Fed National Financial Conditions Index, is employed as explanatory variables. Weekly observations from August 2016 to January 2022 are used to evaluate thirteen forecasting approaches: naive persistence, AR, HAR, GARCH(1,1), and ARIMA benchmarks, together with ridge regression, elastic net, support vector regression, KNN regression, random forest, gradient boosting, XGBoost, and a multilayer perceptron. Bayesian optimization is applied to tune the hyperparameters of the machine learning models under a unified chronological validation protocol. Forecast performance is assessed at 1-, 4-, and 12-week horizons using RMSE and MAE as primary accuracy metrics, with MAPE and directional accuracy reported as complementary diagnostics, under both a chronological 80/20 holdout split and a recursive rolling-origin evaluation. Feature-ablation analysis and Diebold–Mariano tests are further conducted to quantify predictor importance and examine the statistical significance of forecast differences. The empirical results indicate that persistence-based statistical models outperform more complex machine learning models under the fixed holdout evaluation, with the HAR model achieving the strongest overall accuracy in that design. Under recursive rolling-origin evaluation with expanding-window re-estimation, regularized linear models (Elastic Net and Ridge) attain the lowest RMSE at the 1- and 4-week horizons, whereas the Bayesian optimization-tuned XGBoost model achieves the lowest RMSE at the 12-week horizon. In addition, financial stress indicators contribute more predictive information than equity-level variables at short-to-medium horizons. The proposed framework provides a systematic and reproducible benchmark for volatility forecasting and demonstrates that the relative performance of statistical and machine learning methods depends jointly on the forecasting horizon, market regime, and evaluation strategy.

The authors' abstract, as published at the source. Mathematics, 2026 · DOI ↗