HAR-RV-CARMA: A Kalman Filter-Weighted Hybrid Model for Enhanced Volatility Forecasting

This paper introduces a new hybrid model, HAR-RV-CARMA, which combines the Heterogeneous Autoregressive model for Realized Volatility (HAR-RV) with the Continuous Autoregressive Moving Average (CARMA) model. The key innovation of this study lies in the use of a Kalman filter-based dynamic state weighting mechanism to optimally combine the predictive capabilities of both models while mitigating overfitting. The proposed model is applied to five major Covered Call Exchange-Traded Funds (ETFs): QYLD, XYLD, RYLD, JEPI, and JEPQ, utilizing daily realized volatility data from 2019 to 2024. Model performance is evaluated against standalone HAR-RV and CARMA models using metrics such as Mean Absolute Error (MAE), Root Mean Squared Error (RMSE), Quasi-Likelihood (QLIKE), Akaike Information Criterion (AIC), and Bayesian Information Criterion (BIC). Additionally, the study assesses directional accuracy and conducts a Diebold-Mariano test to compare forecast performance against the standalone models statistically. Empirical results suggest that the HAR-RV-CARMA hybrid model significantly outperforms both HAR-RV and CARMA in volatility forecasting across all evaluation criteria. It achieves lower forecast errors, superior goodness-of-fit, and higher directional accuracy, with Diebold-Mariano test outcomes rejecting the null hypothesis of equal predictive ability at significant levels. These findings highlight the effectiveness of dynamic model weighting in improving predictive accuracy and offer a strong framework for volatility modeling in financial markets.