Energies, Vol. 18, Pages 6044: Hybrid Demand Forecasting in Fuel Supply Chains: ARIMA with Non-Homogeneous Markov Chains and Feature-Conditioned Evaluation
Energies doi: 10.3390/en18226044
Authors:
Daniel Kubek
Paweł Więcek
In the context of growing data availability and increasing complexity of demand patterns in retail fuel distribution, selecting effective forecasting models for large collections of time series is becoming a key operational challenge. This study investigates the effectiveness of a hybrid forecasting approach combining ARIMA models with dynamically updated Markov Chains. Unlike many existing studies that focus on isolated or small-scale experiments, this research evaluates the hybrid model across a full set of approximately 150 time series collected from multiple petrol stations, without pre-clustering or manual selection. A comprehensive set of statistical and structural features is extracted from each time series to analyze their relation to forecast performance. The results show that the hybrid ARIMA–Markov approach significantly outperforms both individual statistical models and commonly applied machine learning methods in many cases, particularly for non-stationary or regime-shifting series. In 100% of cases, the hybrid model reduced the error compared to both baseline models—the median RMSE improvement over ARIMA was 13.03%, and 15.64% over the Markov model, with statistical significance confirmed by the Wilcoxon signed-rank test. The analysis also highlights specific time series features—such as entropy, regime shift frequency, and autocorrelation structure—as strong indicators of whether hybrid modeling yields performance gains. Feature-conditioning analyses (e.g., lag-1 autocorrelation, volatility, entropy) explain when hybridization helps, enabling a feature-aware workflow that selectively deploys model components and narrows parameter searches. The greatest benefits of applying the hybrid model were observed for time series characterized by high variability, moderate entropy of differences, and a well-defined temporal dependency structure—the correlation values between these features and the improvement in hybrid performance relative to ARIMA and Markov models reached 0.55–0.58, ensuring adequate statistical significance. Such approaches are particularly valuable in enterprise environments dealing with thousands of time series, where automated model configuration becomes essential. The findings position interpretable, adaptive hybrids as a practical default for short-horizon demand forecasting in fuel supply chains and, more broadly, in energy-use applications characterized by heterogeneous profiles and evolving regimes.