Enhanced state-space estimation of long-memory commodity volatility using the Unscented Kalman Filter and variational Bayes method for non-linear modeling

This study addresses the limitations of the Kalman Filter (KF) by extending the application of the Unscented Kalman Filter (UKF) and the variational Bayes method (VBM) for estimating long-memory (LM) volatility models. Our methodology formulated the Fractionally Integrated Generalized Autoregressive Conditional Heteroskedasticity (FIGARCH) and Hyperbolic Generalized Autoregressive Conditional Heteroskedasticity (HYGARCH) processes within a state-space framework and employed the UKF alongside the VBM to achieve robust estimation. The findings demonstrated that the UKF excelled based on key performance metrics and forecasts, showing superior training data and validation data volatility predictions. The UKF-FIGARCH (1, 0.4029, 1) was a better model for gold, followed by the VBM_FIGARCH model (1, 0.3525, 1). For tobacco, the VBM-FIGARCH model (1, 0.3025, 1) was superior to the UKF-FIGARCH (1, 0.1320, 1) model. Both methods yielded estimates consistent with the parameters used for simulation, falling within the established 95% confidence interval defined by the critical values.