Comparative analysis of mathematical models and estimation of errors in computer modeling of the gas consumption process

Abstract

The paper considers approaches to mathematical modeling of the gas consumption process based on three models: a model based on a cyclic random process and the classical ARIMA and SARIMA models. The gas consumption process is characterized by the presence of a trend, seasonality, cyclicity, and random disturbances, which necessitates the use of adequate mathematical models for its description and simulation. The paper presents a mathematical model of the gas consumption process in the form of an additive mixture of trend, cyclic, and random components. A comparative analysis of the ARIMA and SARIMA models, which are based on differencing operators and take seasonal features into account, is also provided. The models are compared in terms of adequacy, ability to capture cyclicity and seasonality, interpretability of parameters, and suitability for computer simulation and forecasting. To assess the accuracy of computer simulation of gas consumption process realizations, absolute and relative errors are used. It is shown that the SARIMA model is an effective baseline model for series with stable seasonality, whereas the model based on a cyclic random process is more suitable for describing gas consumption with a pronounced cyclic structure and is better suited for computer simulation tasks.