ARIMA modeling for annual precipitation in Mashhad

Following the global warming phenomenon, the general circulation pattern and the temporal-spatial pattern of precipitation have also changed. The use of statistical methods in describing changes is a useful and effective tool. Since precipitation as a climatic element; has non-linear behavior, does not follow the normal distribution. As a result, the usage of modeling to understand the general behavior of precipitation is very efficient. There are various methods for modeling precipitation changes, including linear modeling (least absolute of deviations, least squares error method, etc.) and nonlinear modeling (polynomial modeling, artificial neural network). For the present study, the precipitation data of Mashhad airport station during the statistical period of 57 years (1960-2016) have been used to identify the long-term precipitation behavior of this station. In order to study the general behavior of Mashhad precipitation, it was tried to fit the appropriate pattern of the polynomial family and ARIMA modeling using MINITAB software. The result of modeling a polynomial family indicates a quadratic equation, parabolic pattern in Mashhad precipitation. On the other hand, in the ARIMA model family, the ARIMA (4,1,1) model, which was relatively better than the other models, was determined as a suitable model. Also, by performing the box-cox conversion, the converted precipitations were evaluated again, the candidate models and their predictions were made, and finally, the model selected for Mashhad precipitation was the ARIMA (0,1,1) model. It should be noted that based on the results of modeling and model prediction outputs, it can be inferred that linear ARIMA is not a suitable model for fitting Mashhad precipitation. On the other hand, due to the unsuitability of this model for Mashhad precipitation, the selected models do not match the trend in the observations, in other words, the order of differencing of the models is equal to one, which indicates a linear trend and not a parabola in the observations.