Abstract: Accurate short-term natural gas consumption forecasting is critical for enterprises’ procurement, scheduling, and inventory decisions, as well as for optimizing resource allocation and reducing operational costs. Since natural gas consumption is affected by seasonality, temperature variations, consumption habits, and other uncertain factors, a single forecasting model often fails to fully capture its complex dynamic characteristics. Combined forecasting methods have been widely applied in short-term forecasting within energy sectors such as natural gas and electricity, owing to their ability to integrate information from multiple models and improve forecasting accuracy. However, existing optimal combined forecasting methods generally determine combination weights by minimizing in-sample errors, without explicitly evaluating the representativeness of out-of-sample forecasts with respect to historical data patterns. As a result, the obtained combination weights may rely excessively on in-sample fitting performance, making it difficult to fully reflect the consistency between forecasting results and historical consumption characteristics. To address this issue, this paper introduces the Representativeness criterion (REP) into the weight optimization process of combined forecasting. By incorporating asynchronous errors into the objective function, the proposed methods optimize combination weights by considering both in-sample fitting errors and the representativeness of out-of-sample forecasts. Specifically, two typical optimal combined forecasting strategies are improved, and two REP-based optimal combined forecasting methods are developed, thereby extending the REP criterion from a model selection criterion to a constraint mechanism for combination weight determination. Experimental results based on four real-world natural gas demand datasets from Hangzhou, London, Athens, and Melbourne show that the proposed methods achieve higher forecasting accuracy than the corresponding benchmark combined forecasting methods. The results verify the effectiveness of applying the REP criterion to combination weight optimization, provide a methodological extension for optimal combined forecasting research, and offer decision support for natural gas procurement, scheduling, and inventory management.

Key words: natural gas consumption forecasting, optimal combined forecasting method, out-of-sample, asynchronous error.