Abstract: To address the problem of temperature errors in secondary instruments operating in high- and low-temperature environments, this paper proposed a temperature correction method based on the ARIMA–GM(1,1) model. First, a standard source was connected to a temperature secondary instrument placed in a high- and low-temperature circulation box. The errors between the measurements of the standard source and the secondary instrument could be calculated and obtained a set of error sequences. Second, the error sequences were used to establish an ARIMA model and obtained a set of predicted values. And the residual between the errors and the predicted values could be calculated. To improve the accuracy of the ARIMA model, a GM(1,1) residual correction model was established based on the residual sequences. Lastly, the ARIMA and the GM(1,1) models were combined to formulate an ARIMA–GM model that could perform error self-correction for the temperature secondary instrument. In application experiments, the model achieved smaller average relative errors than a traditional ARIMA and hybrid models. Finally, we developed the ARIMA–GM(1,1) model into a software and applied it to cases of actual detection. 

Key words: Error correction model, ARIMA model, GM(1,1) model, ARIMA–GM(1,1) model