Ridge regression outperforms nonlinear models for petrol price prediction in regulated Zambia

A machine-learning study of Zambia’s regulated petrol pricing system found that regularised Ridge regression outperformed Random Forest, Support Vector Regression and Long Short-Term Memory networks in out-of-sample prediction. Using data from January 2011 through September 2025, the conditional model achieved a test mean absolute error of 0.1302, a root mean squared error of 0.3783 and an R² of 0.9814.

The quantitative study examined how accurately petrol prices could be estimated from variables embedded in Zambia’s cost-plus framework. The Energy Regulation Board’s price build-up includes international petroleum costs, the kwacha-dollar exchange rate, excise duty, value added tax, transport costs, margins and regulatory fees. The dataset combined daily exchange-rate and international oil price observations with lower-frequency petrol price, tax and inflation data, producing approximately 5,387 daily-indexed observations.

Four algorithms were trained and evaluated on the same engineered feature set: five economic variables, calendar variables, petrol-price lags of one, seven and 30 days, and rolling means and standard deviations over three-, seven- and 14-day windows. The researchers used a chronological 70% training, 15% validation and 15% hold-out test split, with preprocessing fitted only on training data and temporal cross-validation used during development.

Ridge regression was substantially more reliable on the hold-out data than the competing nonlinear models. Its test R² of 0.9814 compared with 0.6693 for Support Vector Regression, −26.1367 for Random Forest and −1.5383 for LSTM. The nonlinear models fitted the training data closely but generalised poorly when test-period conditions differed from much of the historical sample, particularly after petrol prices increased structurally from 2021.

One-step-ahead Diebold–Mariano comparisons found significant differences between each machine-learning specification and a naive benchmark that carried the previous observed petrol price forward. The authors cautioned that these results measure conditional prediction accuracy, because contemporaneous exchange rates, oil prices, taxes and inflation were included. They are therefore not evidence that the model could predict future prices before those inputs were known.

Residual diagnostics showed that the Ridge specification did not capture all temporal dependence. Its Durbin–Watson statistic was 1.5355, and Ljung–Box tests rejected the null hypothesis of no autocorrelation at lags 1 and 10. Most residuals were small and centred around zero, while the largest deviations occurred near discrete regulatory price adjustments. Sensitivity analyses nevertheless found Ridge retained test R² values of about 0.98 in lagged-only specifications and when excise duty and VAT were excluded.

Explainable artificial intelligence results distinguished between structural and prediction-level influence. Coefficient-based analysis ranked the international oil price as the strongest predictor, while SHAP analysis identified the ZMW/US$ exchange rate as the largest contributor to individual predictions, followed by international oil price. Partial dependence plots showed positive, approximately linear relationships for those two market variables. Inflation had a weaker influence, while excise duty and VAT contributed limited day-to-day prediction variation after other features were accounted for; the study did not interpret that result as evidence that tax changes were unimportant to regulated pump prices.

Performance deteriorated substantially when the data were aggregated to monthly frequency, with Ridge test R² falling to −0.1816 in the monthly conditional specification and −0.1463 in the lagged-only version. The authors also noted that repeated values between policy updates increase the nominal observation count without adding equivalent new information. These limits, together with the use of contemporaneous inputs and a single-country dataset, constrain generalisation beyond Zambia’s regulated pricing conditions.

Subject of Research: Comparative machine-learning prediction and explainability analysis of petrol prices in Zambia’s regulated cost-plus pricing system

Article Title: Predicting petrol prices in Zambia using machine learning and explainable artificial intelligence under a regulated cost-plus pricing framework

Article References: Maliti, M., & Zimba, A. (2026). Predicting petrol prices in Zambia using machine learning and explainable artificial intelligence under a regulated cost-plus pricing framework. Discover Artificial Intelligence, 6(1), Article 1273. https://doi.org/10.1007/s44163-026-02356-z

Image Credits: AI Generated

DOI: 10.1007/s44163-026-02356-z

Keywords: Zambia, petrol prices, Ridge regression, machine learning, explainable AI, fuel regulation, cost-plus pricing, exchange rates, international oil prices, Predicting, petrol, prices