Integrating Volatility Models within State Space Frameworks for Commodity Return Analysis

The study applies a Kalman filter (KF) to Generalized Autoregressive Conditional Heteroskedasticity (GARCH) models to create a hybrid model, to estimate the parameters of the GARCH model in the presence of time-varying volatility. We specify the GARCH model, represented in state space, and use the KF to estimate the volatility. Results are validated by comparing them with estimates obtained through MLE. State space models by nature of their mathematical formulation can handle both observed and latent volatility. The study used simulation data coupled with an empirical analysis of four commodity returns, Crude oil, Gold, Cotton and Lithium. Results show that the hybrid models in general outperformed their MLE counterparts. For the four commodities analyzed, the Skewed Student t-Distribution State Space-GARCH (SSTD_SS_GARCH (1, 1)) was suitable for crude oil and gold while the Process Innovations Volatility Decomposition State Space GARCH (PIVD_SS_GARCH (1, 1)) was fitted for cotton and the student t-distribution MLE GARCH (STD_MLEGARCH (1, 1)) was optimal for lithium. The hybrid model improves forecasting performance by combining the strengths of both GARCH and Kalman filter methodologies.