Statistical methods are efficient and useful tools to perceive and evaluate climate behavior. One of statistical applications in climatology is modeling of climatic elements behavior. An applied statistic models is ARIMA. In this statistical pattern values are modeled based on their historical behavior modeled. In this paper, the annual temperature of Tabriz city was modeled during 1951-2005. To forecast Mean while adjusting method of ARIMA have been introduced step by step. The ARIMA (0, 1, 2)can was identified as final pattern based on common modeling. The first order of difference degree shows a linear trend what is approved by a constant term in co model. According to the ARIMA (0, 1, 2)canthe amount of this trend is 0.033 Ċ par year. The second order of moving average in Indicates that temperature for each year is functioned by stochastic parameters of previous year. Finally, According to the adjusted model, the temperature of 20 year with 95% confidence interval have been calculated.

Extended AbstractIntroductionDrought monitoring entails the simulation of indices which are categorized into single and combined types. Historically, simulations have predominantly relied on single indices, including Standardized Precipitation Index (SPI), Standardized Runoff Index (SRI), resulting in limited research on drought simulation using combined indices (i.e. MSPI and SPTI), particularly in conjunction with combined models. Over the years, several single models have been developed for simulating individual drought indices. For instance, the Autoregressive Integrated Moving Average (ARIMA) model has been applied to simulate drought indices like Standardized Precipitation Index (SPI) and Standard Index of Annual Precipitation (SIAP). Additionally, models such as Artificial Neural Network (ANN) and Long Short Term Memory (LSTM) have been used for simulating indices like SPI, DI, SIAP, and SHDI. Recent studies suggest that combined models outperform single models. Wavelet ARIMA ANN (W-2A) and Wavelet ANFIS combined models to simulate the single drought index SPEI. Other researchers have developed combined models such as ARIMA-LSTM, Wavelet-ARIMA-LSTM, Wavelet-ARIMA-ANN and LSTM-CM to simulate single drought indices SPI, DI, SIAP. Despite the progress in developing drought simulation models, including single models and particularly combined models, their application has primarily focused on individual indices. Historically, simulations have predominantly relied on single indices, resulting in limited research on drought simulation using combined indices, particularly in conjunction with combined models. This study has combined the strengths of the Wavelet transformation, Autoregressive Integrated Moving Average (ARIMA), Artificial Neural Network (ANN) and Long Short Term Memory (LSTM) to test new methods of hybrid models for their ability to drought simulations based on the new combined index SRGI, employing the combined models W-AL and W-2A.Materials and MethodsDrought simulated in the Alashtar sub-basin between 48, 15 east longitude and 33, 54 north latitudes, covering an area of 811 square kilometers from 1991 to 2020, utilizing individual indices such as SPI, SRI, SGI, and the combined index SRGI. The study area encompasses the Karkheh River basin. Both single models (ARIMA, LSTM, ANN) and combined models (W-AL and W-2A) were employed for this purpose. Root Mean Square Error (RMSE), Mean Absolute Error (MAE) and Mean Error (ME) were used to evaluate the performance of the models. Also, relative frequency and error distribution charts were used to evaluate and compare the results of the models.Individual indices were calculated based on fitting the best cumulative probability function to monthly precipitation, monthly discharge, and monthly water table data, respectively for indices SPI, SRI, and SGI, and then inversely transforming to a N (0,1). The SRGI index is a combination of two drought indices, SGI and SRI (Feng et al., 2020). For this purpose, the copula function is used to obtain the best joint probability distribution function governing precipitation and water table data. The selection of the best copula function was done through the Kolmogorov-Smirnov K-S test at a significant level of 5%. In the current research, four copula functions of Frank, Clayton, Gamble and Joe were used.The process of building the combined models includes the analysis of the time series of the studied drought index, using DWT and decompose into two series named approximate and partial. Then, the approximate and detail series modeled by ARIMA and ANN respectively, in W-2A model and ARIMA and LSTM, respectively, in W-AL model. Results and DiscussionThe results demonstrate that the combined models W-AL and W-2A exhibit higher accuracy across all indices, both individual and combined, compared to single models ARIMA, LSTM, and ANN. The RMSE ranges for the combined models were 0.44 to 0.71, while for single models, they ranged from 0.47 to 1.54. Specifically, model W- AL displayed superior accuracy across all individual indices, with RMSEs of 0.44, 0.62, and 0.59, in contrast to model W-2A, which yielded RMSEs of 0.49, 0.71, and 0.63. However, W-AL's performance lagged behind W-2A for the combined SRGI index, with respective RMSEs of 0.64 and 0.61. Thus, the simpler model yielded more acceptable results in simulating the composite index.ConclusionAmong all the combined and individual models, the combined models perform better in simulating drought, based on all indices, compared to the individual models. Therefore, it can be said that combined models are more suitable for simulating and monitoring drought compared to individual models. However, the performance of the two combined models, W-2A and W-AL, in simulating the combined SRGI index is different. The performance of the simpler W-2A model is better than the more complex W-AL model, with RMSE values of 0.61 and 0.64, respectively. Therefore, in combined indices, despite the complexity of their computational process, there is not necessarily a need to use a more complex combined model. Overall, the use of combined models is recommended for monitoring various types of indices, especially drought based on combined indices such as SRGI. The major objectives of this study are: (1) to use hybrid models Wavelet-ARIMA-LSTM (W-AL) and Wavelet-ARIMA-ANN (W-2A) methods to predict monthly drought. (2) To analyze drought characteristics in Alashtar basin based on the new combined drought index, SRGI. It is expected that the research results will help to provide decision support which in turn will help in planning adaptative measures to reduce drought impacts and provide decision support for disaster prevention.

Temperature changes are of particular importance as one of the symbols of climate change.The use of statistical methods in describing changes is a useful tool. One of the applications of statistics in climatology is modeling the behavior of climatic elements. One of the most widely used statistical models is ARIMA family models. In this family, the values are modeled based on their past behavior from the statistical models, and are projected into the future. In this research, using the annual temperature data of Sanandaj station during the period of 60 years (1961-2020), the general behavior of temperature in this station was investigated. And also using MATLAB software to fit the appropriate model from the polynomial family and ARIMA modeling. The result of modeling the family of polynomials indicates a quadratic trend of the species in Sanandaj temperature. On the other hand, in the family of the ARIMA model, after checking the AIC value, the ARIMA model (2,2,1) which was relatively better than the other models It was determined as a suitable model for predicting the annual temperature of Sanandaj station.

The overall objective of the present paper is demonstrating the utility of price forecasting of farm prices and validating the same for major crops namely, Paddy, Ragi and Maize in Karnataka state for the year 2016 using the time series data from 2002 to 2016. The results were obtained from the application of univariate ARIMA techniques to produce price forecasts for cereal and precision of the forecasts were evaluated using the standard criteria of MSE, MAPE and Theils U coefficient criteria. The results of ARIMA price forecasts amply demonstrated the power of the ARIMA model as a tool for price forecasting as revealed by pragmatic models of forecasted prices for 2020. The values of MSE, MAPE and Theils U were relatively lower, indicating validity of the forecasted prices of the three crops.

‎Air pressure is an important measure for weather forecasting‎ , ‎and is also used in air transport‎ , ‎agriculture ‎, ‎NRM (Natural Resource Management)‎ , ‎astronomical observation‎, ‎geophysics‎, ‎geodesy ‎, ‎etc ‎. Air pressure is an important criterion for weather forecasting‎ , ‎and is also widely used in some branches of science ‎. ‎In this paper ‎, ‎we propose the " ARIMA model " for modeling air pressure at the Isfahan Airport meteorological station ‎.‎In the next step ‎, ‎the model assumptions will be examined ‎. ‎Finally ‎, ‎we will show how well the model describes the data . For convenience, all R code used in the paper is included at the end of the paper in the Appendix section.

The increasing volatility in pricing and growing potential for profit in digital currency have made predicting the price of cryptocurrency a very attractive research topic. Several studies have already been conducted using various machine-learning models to predict crypto currency prices. This study presented in this paper applied a classic Autoregressive Integrated Moving Average (ARIMA) model to predict the prices of the three major cryptocurrencies â AT Bitcoin, XRP and Ethereum â AT using daily, weekly and monthly time series. The results demonstrated that ARIMA outperforms most other methods in predicting cryptocurrency prices on a daily time series basis in terms of mean absolute error (MAE), mean squared error (MSE) and root mean squared error (RMSE).

Gas-oil is one of the most important energy carriers and the changes in its prices could have significant effects in economic decisions. The price of this carrier should not be more than 90 percent of F.O.B price of Persian Gulf, legislated in subsidizes regulation law in Iran. Time series models have been used to forecast various phenomena in many fields. In this paper we fit time series models to forecast the weekly gas-oil prices using ARIMA and ARFIMA models and make predictions of each category. Data used in this paperstarted with the first week of the year 2009 until the first week of 2012 for fitting the model and the second week of 2012 until 13th week of 2012 for predicting the values, are extracted from the OPEC website. Our results indicate that the ARFIMA (0.0.-19, 1) model appear to be the better model than ARIMA (1, 1, 0) and the error criterions RMSE, MSE and MAPE for the forecasted amounts is given after the predictions, respectively.