The purpose of this study was to investigate two ARMA and ARCH linear and nonlinear models in modeling the maximum and minimum temperature of Birjand synoptic station in the statistical period of 1961-2005 and finally presenting the ARMA-ARCH and ARMA-ACA-ARCH hybrid models for model These values should be set. This study evaluates the accuracy of modeling the minimum and maximum temperature of the Birjand synoptic station with a new approach in modeling the residual values of linear time series models. In this study, two ARMA and ARCH base models and three ARMA-ARCH, ARMA-ACA and ARMA-ACR-ARCH hybrid models were used. Also, ant colony algorithm has been used to optimize the parameters of the ACA model. After completing and correcting the used data, the models were applied to the minimum and maximum temperature data of the Birjand synoptic station. The results of the investigation of the accuracy and efficiency of the models used showed that ARMA, ARMA-ACA, ARMA-ARA-ARCH and ARMA-ARCH models were the most accurate and efficient respectively. The results showed that by combining the ARMA model with ACA model, the error rate of modeling the minimum and maximum temperature values of the Birjand station was improved about 12 and 20 percemt, respectively. In the combining the ARMA and ARCH model, the modeling error rate in the modeling of the minimum and the maximum temperature of the Birjand synoptic station decreased about 74% and 94%, respectively.