Realized Covariance Forecasting for Environmental Data through Multivariate GARCH Models

This study investigates the application of multivariate GARCH (MGARCH) models for forecasting realized covariance using high-frequency environmental data. Preliminary statistical analyses, including descriptive statistics, time plots, correlation analysis, heatmaps, stationarity tests, and volatility diagnostics, revealed significant persistence and volatility clustering (heteroskedastic behaviour) in six environmental variables: Wind Speed (80 m), Wind Speed (30 m), Wind Direction, Temperature, Relative Humidity, and Pressure. Two MGARCH models with simple specifications BEKK (1,1) and DCC (1,1) were estimated to capture the dynamic covariance structure. Model selection based on AIC, BIC, HQ, and Log-Likelihood (LL) consistently indicated the superior performance of the BEKK (1,1) model over the DCC (1,1). Diagnostic checks on standardized residuals confirmed the adequacy of the BEKK specification in modelling conditional heteroskedasticity. Furthermore, out-of-sample forecast evaluations using MAE, MSE, and RMSE demonstrated that the BEKK (1,1) model consistently outperformed the DCC (1,1). Overall, the results highlight the effectiveness and robustness of the BEKK (1,1) approach for modelling and forecasting realized covariance in high-frequency environmental time series.