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In this paper, the average monthly temperature of the Karachi region, Pakistan, has been modelled. The time period of the procured dataset is from January 1989 to December 2018. The Autoregressive Integrated Moving Average (ARIMA) modelling technique in conjunction with the Box–Jenkins approach has been applied to forecast the average monthly temperature of the study area. A total of 83.33% of the trained dataset is used for construction of the model, and the remaining 16.67% of the dataset is used for the validation of the model. The best-fitted model is identified as ARIMA (2, 1, 4), generated on the basis of minimum values of the Akaike Information Criterion (AIC) and Bayesian Information Criterion (BIC) procedures. The accuracy parameters considered are Root Mean Square Error (RMSE) and Mean Absolute Error (MAE). Both parameters show that the model is 98.152% and 98.413% accurate, respectively. In addition, the Autoregressive Conditional Heteroscedasticity-Lagrange Multiplier (ARCH-LM) test has been conducted to check the presence of heteroscedasticity in the residuals of the identified model. This test shows no heteroscedasticity present in the residual series. By means of Autocorrelation Function (ACF) and Partial Autocorrelation Function (PACF) plots, the most appropriate orders of the ARIMA model are determined and evaluated. The model has been employed to investigate the time series variables' precise impact on the scale of the regional warming scenario. Accordingly, the created model can help in determining future strategies related to weather conditions in the Karachi region. From the forecast result, it is found that the average temperature seems to show an increasing trend. Such an increasing trend can potentially upset the weather conditions and economic activities of the coastal area of Pakistan. [ABSTRACT FROM AUTHOR]

Pakistan's agricultural economy is reliant on the Indus River's irrigation system, which is fed by the water coming from the great Himalayas-Karakoram Glacier Mountains. Because of hilly terrain areas, the climatic variations have an intense effect on the river flow, especially during the winter and monsoon months. Consequently, significant variations, which are observed annually, result in flooding situations in the monsoon months and reduced flows in the winter season. Thousands of people have lost their lives and massive property destruction has taken place due to disastrous floods that occurred during 2010 and 2016. Past studies have focused on proper water resources and the management of extreme events such as floods and droughts; however, modelling and forecasting based on the various climatic factors and stochastic variations are rare. This paper attempts to forecast Indus River flows using multiple linear regression (MLR), the stochastic time series, the seasonal autoregressive integrated moving average (SARIMA), and its reduced heteroscedasticity model, i.e., SARIMA-GARCH (generalized autoregressive conditional heteroscedasticity) methods at the Kalabagh station. The results show that MLR is best over the short-term; SARIMA is better over the long-term, and SARIMA-GARCH may be superior for a very long-term forecast. [ABSTRACT FROM AUTHOR]

Automatic Teller Machine (ATM) are still largely used to dispense cash to the customers. ATM cash replenishment is a process of refilling ATM machine with a specific amount of cash. Due to vacillating users demands and seasonal patterns, it is a very challenging problem for the financial institutions to keep the optimal amount of cash for each ATM. In this paper, we present a time series model based on Auto Regressive Integrated Moving Average (ARIMA) technique called Time Series ARIMA Model for ATM (TASM4ATM). This study used ATM back-end refilling historical data from 6 different financial organizations in Pakistan. There are 2040 distinct ATMs and 18 month of replenishment data from these ATMs are used to train the proposed model. The model is compared with the state-of- the-art models like Recurrent Neural Network (RNN) and Amazon's DeepAR model. Two approaches are used for forecasting (i) Single ATM and (ii) clusters of ATMs (In which ATMs are clustered with similar cash-demands). The Mean Absolute Percentage Error (MAPE) and Symmetric Mean Absolute Percentage Error (SMAPE) are used to evaluate the models. The suggested model produces far better forecasting as compared to the models in comparison and produced an average of 7.86/7.99 values for MAPE/SMAPE errors on individual ATMs and average of 6.57/6.64 values for MAPE/SMAPE errors on clusters of ATMs. [ABSTRACT FROM AUTHOR]

This paper forecasts guava area and production in Pakistan using time series data over the period 1997-98 to 2014-15. The study used the Box Jenkins approach and forecast was made up to the period 2029-30. The order of ARIMA model was identified using autocorrelation function (ACF) and partial autocorrelation function (PACF). Suitable model for area and production of guava are ARIMA (0,0,0) and ARIMA (1,1,0) respectively. The projected area of guava for the forecasted period is 61.37 thousand hectares each year. Area of guava shows a static trend throughout the forecasted period. The forecasted production of guava is 502.14 thousand tonnes in the year 2029-30. Guava production can be increased using improved guava cultivars, improved system of irrigation and adequate cultural practices. Strategy should be adopted to bring more barren land under guava cultivation. This would help to increase guava production in future. [ABSTRACT FROM AUTHOR]

From the day one, mankind has always been interested into the future. As the civilization advanced with growing sophistication in all phases of life, the need to look into the future also grew with it. Today every government, public private organizations, as well as an individual would like to predict and plan for the future. In order to attain a better growth in the economy of a country, modeling and forecasting is the most important tool now a day, this can be done by one of the statistical technique called a Time series analysis. In this paper we tried to build a time series model called ARIMA (Auto Regressive Integrated Moving Average) model with particular reference of Box and Jenkins approach on annually total Imports and Exports of Pakistan from the year 1947 to the year 2013 with useful statistical software R. Validity of the fitted model is tested using standard statistical techniques. The fitted model is then used to forecast some future values of Imports and export of Pakistan. It is found that an ARIMA (2, 2, 2) and ARIMA (1, 2, 2) model looks suitable to forecast the annual Imports and Exports of Pakistan respectively. We also found an increasing trend both in case of Imports and Exports during this study. [ABSTRACT FROM AUTHOR]