Analysis of Bayesian Symbolic Regression Applied to Crude Oil Price

Forecasting crude oil spot prices even in moderate time horizon, like, 1-month, is not an easy task. Herein, the Bayesian Symbolic Regression (BSR) is applied to forecast the WTI spot prices. This novel method applies Bayesian symbolic trees methods to the Symbolic Regression. This type of econometric model can be especially useful when variable (feature) selection is necessary, as well as, model uncertainty emerges. Indeed, the literature claims that there can be several important crude oil price predictors. The great advantage of Symbolic Regression is its potential to “discover” the suitable functional form of a forecasting model. In particular, world oil production, OECD petroleum consumption, U.S. stocks, MSCI World index, Chinese stock market index, VXO index, U.S. short-term interest rate, the Kilian global economic activity index and U.S. exchange rate were taken as explanatory variables. The period between 1989 and 2021 was analysed. Monthly data were taken. Several models were taken as benchmarks. In particular, Dynamic Model Averaging (DMA), LASSO, RIDGE, the least-angle regressions, time-varying parameters regression, ARIMA and the no-change (NAÏVE) methods. Forecast accuracy was measured by Root Mean Square Error (RMSE) and other commonly used measures. Besides, forecasts were examined with the Diebold-Mariano test and Model Confidence Set testing procedure. A strong evidence was found in favour of DMA and ARIMA as superior models (in a sense of forecast accuracy). However, BSR forecasts were found at least not less accurate than those from many competing (benchmark) models.