This article presents a time series estimation and prediction methods with the use of classic and advanced forecasting tools. In addition, rarely applied in practice approach using spectral analysis to an identification of variation patterns and prediction will be presented. The effect of spectral analysis will be an estimation of prediction model parameters. The main assumption is the model consist of trigonometric functions combination with a certain frequency. The model includes only those frequencies which have greatest influence on process variation. The effectiveness of the method will be examined by a numerical example. The area of the proposed methodology is broad and goes beyond economics

This article examines the influence of specific time series attributes on the efficacy of fuel demand forecasting. By utilising autoregressive models and Markov chains, the research aims to determine the impact of these attributes on the effectiveness of specific models. The study also proposes modifications to these models to enhance their performance in the context of the fuel industry’s unique fuel distribution. The research involves a comprehensive analysis, including identifying the impact of volatility, seasonality, trends, and sudden shocks within time series data on the suitability and accuracy of forecasting methods. The paper utilises ARIMA, SARIMA, and Markov chain models to assess their ability to integrate diverse time series features, improve forecast precision, and facilitate strategic logistical planning. The findings suggest that recognising and leveraging these time series characteristics can significantly enhance the management of fuel supplies, leading to reduced operational costs and environmental impacts.

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.