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An algorithm based on predicting the residuals of the nonlinear autoregressive neural network model with external input (NARX), which can improve the prediction accuracy, was proposed. Data of the concentration of one of the main greenhouse gases methane (CH4) on the Arctic Island of Belyy, Russia, were used for prediction. A time interval, which was characterized by high daily fluctuations in the CH4 concentration was selected. The forecast accuracy was determined by the mean absolute error (MAE), root mean squared error (RMSE) and root mean squared relative error (RMSRE) errors. The use of the algorithm allowed to increase the forecast accuracy from 11% for RMSE to 20% for RMSRE. [ABSTRACT FROM AUTHOR]