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The proposal of nonlinear models is one of the most important methods in time series analysis, which has a wide potential for predicting various phenomena, including physical, engineering and economic, by studying the characteristics of random disturbances in order to arrive at accurate predictions.In this, the autoregressive model with exogenous variable was built using a threshold as the first method, using two proposed approaches that were used to determine the best cutting point of [the predictability forward (forecasting) and the predictability in the time series (prediction), through the threshold point indicator]. B-J seasonal models are used as a second method based on the principle of the two proposed approaches in determining the best seasonal model. Then they are compared with the obtained models from two methods that mentioned above of the two approaches within a group of the criteria as AIC, MDL, Loss Function, BIC, FPE, MSE, in addition the proposed weighted comparison criteria to determine the best model for representing the wind speed data as input variable, soil and dust as an output variable, in Baghdad Station from January 1956 to December 2012.

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The researchers have great attention to the study of white noise tests, which consists of the white noise test to determine the significance of the self-correlation between the error limit series )εt) and the independence test، the correlation between the error limit series and the previous input series u(t) under the null hypothesis and the alternative hypothesis..Using the black box model, the ARX model, which is an important model that combines the time series method based on historical data and the regression method with explanatory variables. The process of building the ARX model consists of several traditional stages, namely diagnosis, using a number of criteria, a final prediction error criterion (FPE) and estimation using ordinary least squares method (OLS).

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ARX model is considered as one of the important models in time series analysis, and there are several and serial steps for building this model, one from those steps is orders identification. In this paper a comparison has been conducted between four criteria: Akaike information criterion (AIC), Minimum description length (MDL), Hannan and Quinn information criterion (HQIC), and the median between MDL and HQIC and denoted (MMH). The comparison carried out in time domain by using simulation, standing to number of success for each criterion in true order selection of model and for four ARX models with different orders (1,1,1), (2,1,1), (1,2,1), (2,2,1) in different samples sizes. And to become obvious that the criteria MDL, HQIC, MMH efficient in order selection, but in general MDL criterion is the best one.

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The models of time series often suffer from the problem of the existence of outliers that accompany the data collection process for many reasons, their existence may have a significant impact on the estimation of the parameters of the studied model. Access to highly efficient estimators is one of the most important stages of statistical analysis, And it is therefore important to choose the appropriate methods to obtain good estimators. The aim of this research is to compare the ordinary estimators and the robust estimators of the estimation of the parameters of the Autoregressive with exogenous variable (ARX) model with the order of (1,1,1) using real data containing outliers, the order (1,1,1) has been used based on a number of criteria for determining the rank, which were explained in the thesis under construction. The study showed that the method employed The Least Trimmed Squares (LTS) method is the best method of estimation. The comparison was done using the Root Mean Square Error (RMSE), Mean Absolute Percentage Error (MAPE) and Expected Error Percentag (EEP), A test was also carried out to ascertain the accuracy of the model reached and then used to predict future values.

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