“…Our models are extensions of ARMA-GARCH models, which have the advantages of no need for exogenous variables to predict volatilities. ARMA-GARCH models are used extensively in forecasting volatilities in different areas, including finance, real estate and weather ( Liu et al, 2019 ; Apergis et al, 2020 ; Zou et al, 2020 ). Our models are fitted to futures returns of oil, soybean, copper and gold, which are the most actively traded representative futures in energy, agricultural, industrial and precious metal commodity classes, respectively, with a data period from Jan 1, 2019 to June 30, 2021.…”