Forecasting gasoline market volatility using non-linear time series models?

This study forecasts the dynamics of gasoline price returns using daily data from January 2, 1992, to June 6, 2022, and crude oil price returns as a regressor. The non-linear dependence in the volatility of the gasoline return is confirmed and the Markov Switching (MS), the Autoregressive Conditional Heteroskedasticity (ARCH) and the Generalized Autoregressive Conditional Heteroskedasticity (GARCH) models are estimated. To account for the linear dependence found in the initial estimates, a GARCH(1,1) model with lagged gasoline returns is used, while a GARCH(1,1) is fitted on the Markov switching residual to capture both the volatility in the conditional mean and variance. The forecasting performance of the estimated models is evaluated, and the GARCH(1,1) on the Markov Switching residual is found to be the best model to forecast the average gasoline returns, while the GARCH(1,1) with linear dependence is preferable for forecasting the volatility of gasoline returns. Identifying the best time series model is crucial for the market participants, and especially for oil companies to evaluate the market situation.