ARMA and/or SETAR Estimation and Out-of-Sample Forecast of the Mean-Reversion Between Brent Crude Oil and Gasoline Prices on the Ghanaian Market

Abstract

The study investigates the existence of long-run equilibrium or mean-reversion using bivariate analysis of paired prices, as well as to test for linear and nonlinear threshold-type mean-reversion of bivariate relationships. The coefficient parameters of (non)linear VECM and threshold parameter value are estimated, and the forecast performance accuracies of the SETAR are compared to linear models of the mean-reversion process.
The two-regime SETAR model gives a much better prediction of cointegration relation than linear AR model. In the test for the two-regime SETAR model for the cointegration relation against a three-regime model, the two-regime model cannot be rejected at any reasonable significance level. The 2-SETAR exhibits significant constant and trending intervention features of the price build-up process. The asymmetric behavior remained the dominant feature of our mean reversion, which was also apparent. Although the MAPE is somewhat higher than the AR and ARMA processes, the threshold models outperformed the AR and ARMA processes. In summary, the mean reversion property is heavily reliant on the events that occurred in the preceding four bi-weekly pricing-periods in the swift unusual directions. In contrast, in the slow usual direction, it relies on the occurrence of the same in the only bi-weekly pricing-periods immediately preceding it.