Forecasting Brent Crude Oil Prices Using Nonparametric Kernel Regression with the Nadaraya-Watson Estimator

Abstract

Brent Crude oil prices exhibit high volatility that significantly affects national economic stability, particularly for Indonesia, which holds the status of a net oil importer. This study examines the feasibility of the ARIMA model before applying a nonparametric approach as an alternative. The data used are monthly closing prices of Brent Crude for the period from January 2011 to June 2026, comprising 186 observations obtained from Investing.com. The Augmented Dickey-Fuller test shows the level data are non-stationary with a 0.1672 p-value, achieving stationarity only after first differencing with a 0.0000 p-value. Among eight estimated ARIMA models, ARIMA(3,1,0) yielded the lowest Akaike Information Criterion at 1249.92. While all models exhibit independent residuals according to Ljung-Box tests with p-values exceeding 0.05, they consistently violate the residual normality assumption based on Shapiro-Wilk tests with p-values below 0.0001, rendering ARIMA unsuitable for this data. As an alternative, a multivariate Nonparametric Kernel Regression with the Nadaraya-Watson estimator is employed, with the input variable X_i=(Y_(t-1),Y_(t-2)) representing the prices of one and two months prior, and the target variable Y_i=Y_t representing the current price, and a product kernel weighting (product kernel). Seven kernel functions, namely biweight, cosine, epanechnikov, gaussian, optcosine, rectangular, and triangular, were compared, with the bandwidth for each selected through Leave-One-Out Cross Validation (LOOCV). The results show that the Gaussian Kernel provides the best performance, yielding a minimum cross-validation value of 59.03, an optimal bandwidth of 4.34, and a Mean Squared Error of 42.06. Recursive forecasting for the next six months from July to December 2026 produces price projections of 69.50, 73.82, 76.32, 77.49, 77.05, and 76.64 USD/barrel. It is concluded that Nadaraya-Watson Kernel Regression with the Gaussian Kernel function is a more appropriate alternative than ARIMA for forecasting volatile commodity prices such as Brent Crude.