Institute of Geophysics, University of TehranJournal of the Earth and Space Physics2538-371XArticles in Press20220110Statistical modeling of the mean annual temperature at Mehrabad station, TehranStatistical modeling of the mean annual temperature at Mehrabad station, Tehran8544710.22059/jesphys.2022.332720.1007372FAArmanJahediClimatology, Geography, Faculty of Humanities, University of Zanjan, Zanjan, Iran.Journal Article20211021Regarding climate changes and global warming, it seems that the behavior of climate elements in the future should be predicted and known. Therefore, in this study, using modeling in a set of ARIMA statistical models, models on the time series of the mean annual temperature at Mehrabad station in Tehran during 1951-2015 were fitted to investigate a significant model for trial and error in order to identify the most appropriate model. Since the time series of the observations had a normal distribution, modeling was performed on the time series without applying Box Cox transformation. First, for static and non-static investigations, the time series of annual mean temperature observations was plotted simply in diagrams. In addition, the first and second order regression line equations were used to further ensure the type of time series behavior of the mean annual temperature. The results showed that the time series behavior of temperature at this station is linear. Since the time series behavior was linear, the order d = 1 was determined. Second, the first-order differentiation was performed on the time series. In the third step, the order p and q were determined using autocorrelation and partial autocorrelation of the differentiated values (w_t). After investigating the significance of the order of the components of each of the models, the following models were selected as significant models, respectively:<br />
1) ARIMA(0,1,1)_{theta_0}<br />
2) ARIMA(2,1,0)_{theta_0}<br />
Since the first significant model was observed with suspicion, as a result each of the components (p, d, q) of the above two models were tested up to the 3th order. Finally, these two models were selected as significant models. Also, Akaike information criterion (AIC) was considered to determine the most appropriate model among the above two models. ARIMA model (0,1,1)_{theta_0} had the minimum value of AIC compared to the other model. As a result, using this model, the temperature time series at this station was predicted from the end of the period to ¼ of the first time series. Given the concept of uncertainty, which underlies descriptive and inferential statistics, as a result, it seems that uncertainties should be expressed with high statistical certainty. In this regard, we used statistical tests of autocorrelation, Pearson correlation coefficient, standard normal homogeneity, cumulative deviations, milestones, sign on the time series of ARIMA model residues (0,1,1)_{theta_0}, and drawing methods for residual normality, residual independence, constant residual variance and portmanteau test to consider further criteria to increase the statistical reliability of the applied model. The results of all statistical tests showed the random residual time series of the model. These tests showed that the best model for modeling the time series of the mean annual temperature at Mehrabad station, Tehran is ARIMA model (0,1,1)_{theta_0}. Since the upper and lower limits of the predicted series as well as the predicted observations show the same behavior of the temperature time series at Mehrabad station, it can be said that the estimation of the predicted numerical values is still appropriate for this model to predict the temperature variable at this station. Finally, the results showed that the mean temperature of the predicted series is likely 17.742 ͦ C, and the mean annual temperature will increase by 0.038 ͦ C compared to the previous year.Regarding climate changes and global warming, it seems that the behavior of climate elements in the future should be predicted and known. Therefore, in this study, using modeling in a set of ARIMA statistical models, models on the time series of the mean annual temperature at Mehrabad station in Tehran during 1951-2015 were fitted to investigate a significant model for trial and error in order to identify the most appropriate model. Since the time series of the observations had a normal distribution, modeling was performed on the time series without applying Box Cox transformation. First, for static and non-static investigations, the time series of annual mean temperature observations was plotted simply in diagrams. In addition, the first and second order regression line equations were used to further ensure the type of time series behavior of the mean annual temperature. The results showed that the time series behavior of temperature at this station is linear. Since the time series behavior was linear, the order d = 1 was determined. Second, the first-order differentiation was performed on the time series. In the third step, the order p and q were determined using autocorrelation and partial autocorrelation of the differentiated values (w_t). After investigating the significance of the order of the components of each of the models, the following models were selected as significant models, respectively:<br />
1) ARIMA(0,1,1)_{theta_0}<br />
2) ARIMA(2,1,0)_{theta_0}<br />
Since the first significant model was observed with suspicion, as a result each of the components (p, d, q) of the above two models were tested up to the 3th order. Finally, these two models were selected as significant models. Also, Akaike information criterion (AIC) was considered to determine the most appropriate model among the above two models. ARIMA model (0,1,1)_{theta_0} had the minimum value of AIC compared to the other model. As a result, using this model, the temperature time series at this station was predicted from the end of the period to ¼ of the first time series. Given the concept of uncertainty, which underlies descriptive and inferential statistics, as a result, it seems that uncertainties should be expressed with high statistical certainty. In this regard, we used statistical tests of autocorrelation, Pearson correlation coefficient, standard normal homogeneity, cumulative deviations, milestones, sign on the time series of ARIMA model residues (0,1,1)_{theta_0}, and drawing methods for residual normality, residual independence, constant residual variance and portmanteau test to consider further criteria to increase the statistical reliability of the applied model. The results of all statistical tests showed the random residual time series of the model. These tests showed that the best model for modeling the time series of the mean annual temperature at Mehrabad station, Tehran is ARIMA model (0,1,1)_{theta_0}. Since the upper and lower limits of the predicted series as well as the predicted observations show the same behavior of the temperature time series at Mehrabad station, it can be said that the estimation of the predicted numerical values is still appropriate for this model to predict the temperature variable at this station. Finally, the results showed that the mean temperature of the predicted series is likely 17.742 ͦ C, and the mean annual temperature will increase by 0.038 ͦ C compared to the previous year.