Modeling of monthly temperature and precipitation time series in Tabriz using ARFIMA long-term memory model

Predicting the quantity and quality of climate change is one of the complex issues that has occupied the minds of climatologists. Now, with the help of access to new technologies and having multiple series of necessary data from climate variables and with the help of knowledge of understanding the relationships between these variables, basic steps in understanding and predicting climate trends have emerged. As now, computer models all respond to climate prediction issues and factors affecting climate change to the best of their ability. Completely accurate predictions with zero error, regardless of the field and subject matter, are very difficult and almost impossible, especially since the prediction process is in a very complex environment and in a dense cloud of uncertainties and actors and drivers. Numerous and effective effects on the environment and the data and information used in forecasting also have vague and gray features . Among climatic elements, temperature and precipitation are of special importance due to their wide effect on other factors and especially the effects they have on human activities. because human systems are dependent on climatic elements. Like agriculture, industries and the like are designed and operate on the basis of climate stability.Time series models are experimental models and a powerful tool for simulating and predicting the behavior of climatic and hydrological systems such as temperature and precipitation. The classical approach in terms of time series modeling depends on the static and non-static time series according to the application of the Jenkins box approach. If such series show long-term memory properties, the prediction value based on the moving average self-regression (ARMA) and stacked moving average (ARIMA) models will not be valid. If there is long-term memory in time series, there will be a significant correlation between series observations at very long distances, apart and far from each other, which indicates that observations are not independent of each other, there is a correlation between them and past observations. They will help to predict the data. With these descriptions, the existence of long-term memory in atmospheric parameters weakly violates market efficiency, and then changes in the capital market will not be accidental and will be predictable. In the early 1980s, Granger and Jokes proposed an alternative approach to long-term memory modeling by creating their own model of partial stack moving average (ARFIMA), since the ARFIMA model between the short-term memory process and the long-term memory process in series. When differentiated, it creates a distinct advantage over classical S / R analysis, which has a very high tendency to accept the assumption of zero long-term memory despite the short-term memory process .The data required in this article include the average monthly temperature and precipitation in the last half century (1969-2018), which was prepared by the Meteorological Organization. In time series data analysis, time series models including ARFIMA model have been used for modeling and simulation of the mentioned parameters.Changes in temperature and precipitation time series are among the most important climatic parameters in studying hydrological, agricultural, environmental, health, industrial, and economic processes. Assessing and forecasting temperature and precipitation will be of great help to managers and planners of agriculture and water resources. One way to examine time-series data is to use statistical models. Due to the importance of the subject, in this article, the amount of temperature and monthly rainfall in the last half-century (1969-2018) of Tabriz Synoptic Meteorological Station is examined using the ARFIMA model, and to fit the model, R / S and GPH models have been used. To investigate the statics of the model, autocorrelation (ADF), partial autocorrelation (PACF) functions, and differentiation methods have been used. However, since the synoptic meteorological station data is evaluated for the first time, the evaluation is based on the ARFIMA model, the Bayesian Information Criteria (BIC), root-mean-square error (RMSE), and the Akaike information criterion (AIC). The results of R/S and GPH tests show that the model with long-term memory of Tabriz temperature and precipitation time series is approved at a 95% level. The only difference is that in the case of precipitation, this act seems fragile. In addition, the analysis of different structures showed that the temperature and precipitation data have the best fit or performance using the ARFIMA (3,0.2,1) and the ARFIMA (1,0.0004,4), respectively. It should be noted that the RMSE value of the fitting models between the observed values and the simulation of temperature and precipitation was equal to 2.2 and 38.4, respectively, indicating the appropriate accuracy of the model and its applicability for forecasting.