In order to simulate time series, various methods are presented such as times series models (AR, ARMA and ARMAX), multi-linear regression (MLR), and nonparametric regression (K-NN). In this research, performance of these models for estimation of missing values and prediction of future values of evaporation series (from open water) were assessed. ARMAX model with standardized input time series of Tmin, Tmax, Tav, Wind, RH, and sunshine hours, outperformed the other models and the K-NN and MLR were in the next ranks, respectively. Also after the principal component analysis, ARMAX model showed noticeable deviation for estimating missing values and MLR and K-NN in calibration and MLR in validation stage performed the best. For short-term predictions, ARMAX model has the best performance, but MLR performed better in long-term predictions, Time series models were not robust for long term predictions.

The watershed acts as a hydrological unit regulating the quantity and quality of the water cycle, and human beings have incurred high costs due to ignorance of this complex cycle and lack of planning of projects in terms of the relationship between water management and community development.Knowledge of features such as maximum flood discharge is essential for the design of hydraulic structures, such as dams, spillways, bridges, and culverts, in order to reduce potential damages and predict when peak discharges will be reached in the downstream areas when discussing flood warning. Rainfall-runoff modeling is one of the key tools in hydrology to achieve flood characteristics, such as peak rate and peak time. In current research, the performance of IHACRES model using "Hydromad" R package has been implemented to simulate flow in the Shoor river basin in Ghaen on a monthly scale. The model simulation was done to investigate the effect of selecting "ARMAX" and "EXPUH" methods in the linear part of the target function. Also, the modeling process and the optimized values of the model parameters were investigated.

The Shoor river basin with an area of 2412.92 square kilometers located in Ghaen between 59 degrees and 12 minutes to 59 degrees and 14 minutes east longitude and 33 degrees and 42 minutes to 33 degrees and 45 minutes north latitude. The study catchment with an average altitude of 1420 m above sea level and an average long-term annual rainfall of 173 mm has a dry climate. This river is the largest river in Ghaenat city which flows into Khaf Salt field. In this research, the IHACRES model was implemented using the Hydromad R package. To perform the flow simulation, precipitation, flow rate and temperature data on a monthly scale during the years 1998 to 2017 were used. The IHACRES model has two parts: the first part, which converts precipitation into effective precipitation at each time stage and the second part, which converts effective precipitation into modeled flow. These sections are called nonlinear and linear modules, respectively. To implement each of the sections of nonlinear modules and linear modules according to the data and conditions in the study area, methods with different parameters can be used. In this research, in the non-linear module section, the "CWI" method and in the linear module section, "ARMAX" and "EXPUH" methods have been used for proper routing in the "reverse" calibration section. In the validation section of the "ls" method, the performance criteria of KGE, NS and R2 were used to evaluate the performance of the model in both calibration and validation process.

Comparison of obtained results in this study with previous studies showed that in terms of examining the performance of the model with the EXPUH linear method, the obtained results are consistent with the results of Sadeghi et al. (2015) and Lotfi Rad et al. (2015) and the model with the EXPUH linear method. The NS criteria has shown acceptable performance. According to the results of the model in the calibration section, in terms of evaluation criteria NS, KGE and , and in terms of simulation of peak flow values and the time to peak using EXPUH method in the linear part showed  better performance than ARMAX method. The value of these criteria in EXPUH method is equal to 0.86, 0.93, and 0.86 and in ARMAX method are equal to 0.7, 0.85 and 0.73, respectively. In the validation section, the evaluation criteria in EXPUH method were equal to 0.51, 0.63, and 0.54 and in ARMAX method were equal to 0.55, 0.73 and 0.65, respectively, indicating better performance of the model by ARMAX method. Comparison of the EXPUH method, and also the model with ARMAX method showed more accurate performance in terms of peak discharges, quantity and time of occurrence. The values of NS, KGE and evaluation criteria in this section were 0.51, 0.63, and 0.54 using EXPUH method and 0.55, 0.73 and 0.65 with ARMAX method, respectively.

According to the results, the IHACRES model using ARMAX method in the linear section resulted in more accurate performance than EXPUH method in simulation of peak flow values and time to peak.

Rainfall-runoff is one of complex hydrological processes that is affected by a variety of physical and hydrological factors. In this study statistical method ARMAX model, neural network, neuro-fuzzy (ANFIS subtractive clustering and grid partition) and two hybrid models of this methods were used to simulate rainfall-runoff and prediction of streamflow. In each method optimum structure was determined then, streamflow forecasted using the best model. The results showed that hybrid methods have better application than single models and artificial intelligent has better application than linear ARMAX model due to nonlinearity of rainfall-runoff process. In this study all methods showed relatively suitable application but ANFIS method with subtractive clustering is suggested for modeling rainfall-runoff and streamflow prediction.

The purpose of this paper is to forecast demand for crude oil of Iran using Artificial Neural Networks and ARMAX models. The result indicates that Artificial Neural Networks provides an accurate and better picture compared with ARMAX. In order to show whether the variables used in this study are true determinants of Crude oil demand, we have also applied the same techniques with the same variables to forecast crude oil demand of five selected OPEC countries. The result confirms our earlier findings for Iran. Applying rank correlation coefficient for these findings, show high correlation coefficients between the result for Iran and other countries. Therefore we may say that the variables such as GDP, population, net exports and the number of vehicles are key variables for any forecasting relating to crude oil demands in similar countries.

In this research, we used the support vector machine (SVM), support vector machine combine with wavelet transform (W-SVM), ARMAX and ARIMA models to predict the monthly values of precipitation. The study considers monthly time series data for precipitation stations located in Hamedan province during a 25-year period (1998-2016). The 25-year simulation period was divided into 17 years for training, 4 years for calibration and 4 years for validation. Statistical comparison of the results was done by using correlation coefficient (r), root mean square error (RMSE), and standard error (SE). Results showed that ARIMA, Support Vector Machines, ARMAX and support vector machine combine with wavelet transform were ranked first to forth, respectively. Furthermore, the support vector machine has fewer adjustable parameters than other models. So, the model is able to predict precipitation with greater ease and less time. For this reason, it is preferable to other methods.

Rivers flow forecasting has special importance in surface water management، especially in agricultural planning and risk reduction of floods and droughts. In recent years، studies have shown the superiority of time-series forecasting models based on artificial intelligence، such as artificial neural networks (ANN) and genetic programming (GP). In this paper، continuous and discrete historical flow records are used for Saeed-Abad monthly river flow forecasting in East Azarbaijan province، Iran. Auto regressive moving average with exogenous inputs (ARMAX)، ANN، and GP models are used and compared to each other. Coefficient of determination (R2) and root mean square error (RMSE) are used to evaluate the performance of the aforementioned models. Results show that for the two methods، the GP model is more effective than ARMAX and ANN in terms of accuracy. For continuous time-series forecasting، GP is a more precise model (R2 = 0. 7 and RMSE = 0. 172) than either ANN (R2 = 0. 627 and RMSE = 0. 193) or ARMAX (R2 = 0. 595 and RMSE = 0. 243). For discrete time-series forecasting، the superiority of the GP model is evident in almost all months. Moreover، results indicate that discrete monthly time-series forecasting method is superior to the continuous monthly time-series forecasting method.

Capital markets’ return is influenced by multiple and various factors. These factors range from macro global factors to dependent variable historical behaviors. Each of many researchers has selected a segment or segments of this vast range of factors impacting capital market return in different countries and embarked on devising a model for projection of the respective capital market return. The present research has utilized self-explanatory and combined models for the purpose of modeling and projecting Tehran Exchange’s return using Autoregressive Moving Average (ARMA) and Autoregressive Moving Average with External Inputs (ARMAX) models. In this research, to utterly expound the model and to factor in maximum factors, following examination of return issues and the factors impacting return, the subject of projection and the common methodology thereof have been surveyed and different models of projecting capital market return have been examined in detail. Then, Classic Linear Regression Models, Autoregressive Moving Average (ARMA) and Autoregressive Moving Average with External Inputs (ARMAX) models were used to predict the return of Tehran Exchange. After estimating the above models, deploying 99-period data and confirming the power of expressing them via applying diagnostic tests, the return of Tehran Exchange for the next 4 periods was projected. These predictions by applying estimation models were compared with the real data and the optimum model was selected using Akaike Information Criterion (AIC), Schwartz-Bayesian Information Criterion, Hannan-Quinn and also MSE, MAE, MAPE criteria. The final result indicates superiority of ARMA over ARMAX

Predicting price volatility has been the interest of many scholars in different markets such as stock and commodity market. Electricity like other commodities has been traded in the market in recent years. Hence, a large number of countries around the world have recently started restructuring processes in their energy sectors. However, the pace and aim of the improvements varies across countries. With the introduction of competitive wholesale electricity markets, and power derivative contracts, both exchange-traded and over the counter (OTC), providing a number of different contract provisions to meet the needs of the electricity market participants. Among all countries, Iran is not an exception for the rule. Trading electricity along other commodities in the exchange market is a new progress for this market. These changes arises this necessity to study the nature of price volatilities so that the restructuring development and adopted actions would be done in a correct and meaningful way.
This study attempts to study the price volatilities in the Iranian electricity market by an ARMAX and GARCH type model and introduce the best simulation for the period of March 2012 to March 2014. Therefore, ARMAX model in a combination with GARCH, GJR-GARCH, and EGARCH type will be compared along with Gaussian, Generalize Error, and Student-t distribution.

Stochastic drainage of rainfed lands (due to its dependence on rainfall) led to the application of random variables and time series modeling in predicting the performance of drainage systems. The aim of this study was to investigate the potential of time-series models in predicting drainage water and soil salinity in rainfed farms of subsurface drainage in Ran Behshahr, Iran. First, Drainmod-S model was calibrated using measured data. Then, drainage water and soil salinity were simulated via the calibrated Drainmod-S model. The simulated outputs were used for evaluation of the results of the time-series models including AR, ARX, ARMA and ARMAX. The results showed that the ARMAX model with exogenous variables including daily value, precipitation during the previous days and average desired variables in the last two days was efficient in predicting soil and drainage water salinity, so that the absolute mean modeling error for soil surface salinity (0-50cm), soil subsurface salinity (50-100cm) and drainage water salinity was 4%, 0.4% and 5%, respectively. Comparison between the selected times-series models and the calibrated Drainmod –S model results indicated that the application of time-series models in predicting the performance of the subsurface drainage system was satisfactory. The coefficients of determination were 0.75, 0.63 and 0.57 for for salinity of soil surface and subsurface layers and drainage water, respectively. The root mean squared errors for these variables were 2412.6, 331.8 and 1724.6 mg/ L, respectively. According to the evaluation indicies, time series models were efficient in predicting soil and drainage water salinity.

Over the past few years, the growth and development of the capital market of countries and the introduction of new tools, mechanisms, and phenomena in it, have enhanced the importance of the capital market in the economy. In this research, the researcher aims to predict Stock Price Resilience in the Iranian Stock Exchange using the multilayer perceptron model of artificial neural networks. The present study has an applied approach that pays special attention to providing a purposeful method in designing stock price resilience forecasts. The statistical population is the companies listed on the Tehran Stock Exchange in the period 2009-2019. The dynamic artificial neural network structure design is done in the MATLAB software environment. Comparison of AR and ARMAX statistical methods and NAR and NARX networks has been used to predict the average Stock Price Resilience for the next year. The results show that in estimating Stock Price Resilience, the highest amount of R2 is present in NARX, NAR, ARMAX, AR models, respectively. This means that the best models for estimating Stock Price Resilience are listed in order. Based on the criteria of mean square error, total square error, coefficient of explanation, prediction error of the NARX model for the stock price parameter is very low, so this model has a much higher accuracy in predicting the stock price resilience than other models so Which is a lower amount of prediction error.