Box-Jenkins Autoregressive Integrated Moving Average Research Articles

Forecasting of area, production, and yield of jute in Bangladesh using Box-Jenkins ARIMA model

Jute holds significant importance as a cash crop in Bangladesh and was once renowned as the country's "golden fiber." Before embarking on a comprehensive strategy, it is crucial to gain insight into the future scenarios of jute in Bangladesh. This study's main objective is to employ the Box-Jenkins method to choose the most suitable Autoregressive Integrated Moving Average (ARIMA) models for forecasting area, production, and yield of jute in Bangladesh for the period from 2023 to 2030. This research relies on historical time series data spanning from 1970 to 2022. After thorough analysis, the most appropriate models were determined: ARIMA (2,0,3) for area, ARIMA (1,0,2) for production, and ARIMA (1,0,3) for yield. These selections were made based on model selection criteria, normalized BIC values, examination of ACF and PACF plots, and confirmation that residuals from these chosen ARIMA models exhibit no serial correlation, as indicated by Ljung-Box Q statistics. The ARIMA model predicts a continuous upward trajectory for jute cultivation, projecting that the jute cultivation area will expand to 7.54 lac hectares by 2023 and 8.30 lac hectares by 2030. This represents an estimated increase of approximately 13.85 % compared to the jute area in 2022. However, projections indicate a decline in both jute production and yield. By 2023, production is forecasted to be 80.48 lac bales with a yield of 11.47 bales per hectare, while by 2030, production is expected to decrease to 74.34 lac bales with a yield of 11.22 bales per hectare, down from 84.58 lac bales and 11.59 bales per hectare respectively in 2022.These findings are valuable for researchers and policymakers as they provide new insights into the future dynamics of jute cultivation in Bangladesh. This information can guide the development of initiatives and plans aimed at enhancing jute area, production, and yield in the country.

Probability analysis and rainfall forecasting using ARIMA model

A 34-year rainfall data from 1976 to 2009 of ten sub-basins of the Vaigai River in Tamil Nadu were collected and analysed statistically using various probability distribution functions. The best-fit probability distributions for the annual, monthly and seasonal rainfall for the study area were found using two goodness-of-fit tests. The Box-Jenkins Autoregressive Integrated Moving Average (ARIMA) methodology has been adopted for model identification, diagnostic checking and forecasting the study area's annual rainfall. The best ARIMA models were selected for each sub-basin and the average annual precipitation for 2010, 2015, 2020 and 2025 has been forecasted. The forecasted result compared well with observed dataup to 2020, which indicates the appropriateness of the model.

Comparative Performance of Arima and Garch Models in Modelling and Forecasting Volatility of Kuala Lumpur Composite Index

Time series is a set of observations in sequence over time. Time series modelling is used to create an applicable model that defines the necessary arrangement of the series by study the previous information of a time series. The past information of a time series is used to generate forecast value for the series. It is well acknowledged that a time series are regularly affected with outliers. Outliers may impact the forecasting where the tendency in parameter estimates created by extreme observation will reduce its effectiveness because the optimum predictor for an Autoregressive Integrated Moving Average (ARIMA) model is determined by its parameters. Thus, the occurrence of extreme observations might have a huge effect on predictions value. Therefore, Generalized Autoregressive Conditional Heteroskedastic (GARCH) model has been used to compare the result obtain from ARIMA model. This study used ARIMA and GARCH to compare the best model for forecasting Kuala Lumpur Composite Index (KLCI) when the outlier exists. The best models of ARIMA and GARCH were evaluated using Mean Square Error (MSE), Root Mean Square Error (RMSE) and Mean Absolute Percentage Error (MAPE). It can be concluded that GARCH model performed better compared to Box-Jenkins ARIMA in forecasting KLCI.

Forecasting Area, Production and Productivity of Vegetable Crops in Nepal using the Box-Jenkins ARIMA Model

Forecasting of vegetable area, production, and productivity of Nepal was made from the historical data of 1977/78 to 2019/20 by using the Box-Jenkins Autoregressive Integrated Moving Average (ARIMA) models. The best fitted ARIMA models were chosen based on the minimum value of the selection criterion, Akaike information criteria (AIC) and Bayesian information criteria (BIC). ARIMA (0, 2, 1) model was found suitable for all areas and production, whereas ARIMA (0, 2, 0) model was best fitted for forecasting vegetable productivity. The model was cross-validated by comparing the point prediction with the actual test series data from 2015/16 to 2019/20. The performances of models were determined from the mean absolute percent error (MAPE) value. The MAPE was found to be 2.70%, 2.40%, and 3.80%, respectively for the prediction of area, production, and productivity. The forecast was made for the immediate five years (2020/21 to 2024/25), and it showed an increasing value for area and production while the forecasts of productivity had lower values. The vegetable production policy in Nepal should be planned following accurate forecasts to increase production in the upcoming years. Awareness among the vegetable growers should be raised in the following years with appropriate extension programs.

Analysing COVID-19 Verified, Recuperate and Death Cases in Ethiopia Using ARIMA Models

Applying a successful prediction of the confirmed, recovered and deaths is thought to be the basic requirement to successfully control the spreading rate of diseases. Time series models have extensively been considered as the suitable methods to forecast the confirmed, recovered and deaths because of the virus. The aim of this research is to apply the Autoregressive Integrated Moving Average (ARIMA) modelling approach for projectingCOVID-19 confirmed, recovered and deaths cases in Ethiopia. Over strict follows of all phases of Box-Jenkins strategy, ARIMA (1,1,1), ARIMA (16,1,2), and ARIMA (0,1,1)models for confirmed case, recovered and death case, respectively were selected as the best models for predicting coronavirus cases of Ethiopia. Using these models, a forecast of five-month a heads future situation of COVID-19 confirmed case, recovered and death case (Jan 3, 2021 to May 3, 2021) has been made. The results showed that in the coming five months from Jan 3, 2020 to May 3, 2021, the number of COVID-19 confirmed, recovered and deaths cases in Ethiopia may reach up to 320,597; 168,912 and 4438, respectively. Generally, the size of the coronavirus distribution was increased from time to time in the past ten months, until 3rd Jan, 2021, and it is expected to continue quicker than before for the coming 5-months, until the end of May, 2021, in Ethiopia and more rapidly than before while the peak will remain unknown yet. Therefore, effective implementation of the preventive measures and a rigorous compliance by avoiding negligence with the rules such as prohibiting public gatherings, travel restrictions, personal protection measures, and social distancing may improve the spreading rates of the virus. Further, through updating more new data with a continuous reconsideration of predictive model provide useful and more precise prediction

Comparative Performance of ARIMA and GARCH Model in Forecasting Crude Oil Price Data

This study compares the performance of Autoregressive Integrated Moving Average (ARIMA) and Generalized Autoregressive Conditional Heteroskedasticity models in forecasting Crude Oil Price data as obtained from (CBN 2019) Statistical Bulletin. The forecasting of Crude Oil Price, plays an important role in decision making for the Nigeria government and all other sectors of her economy. Crude Oil Prices are volatile time series data, as they have huge price swings in a shortage or an oversupply period. In this study, we use two time series models which are Box-Jenkins Autoregressive Integrated Moving Average (ARIMA) and Generalized Autoregressive Conditional Heterocedasticity (GARCH) models in modelling and forecasting Crude Oil Prices. The statistical analysis was performed by the use of time plot to display the trend of the data, Autocorrelation Function (ACF), Partial Autocorrelation Functions (PACF), Dickey-Fuller test for stationarity, forecasting was done based on the best fit models for both ARIMA and GARCH models. Our result shows that ARIMA (3, 1, 2) is the best ARIMA model to forecast monthly Crude Oil Price and we also found GARCH (1, 1) model is the best GARCH model and using a specified set of parameters, GARCH (1, 1) model is the best fit for our concerned data set.

Prediction of Area and Production of Groundnut Using Box-Jenkins Arima and Neural Network Approach

Selection of parameters for Auto Regressive Integrated Moving Average (ARIMA) model in the prediction process is one of the most important tasks. In the present study, groundnut data was utlised to decide appropriate p, d, q parameters for ARIMA model for the prediction purpose. Firstly, the models were fit to data without splitting into training and validation/testing sets and evaluated for their efficiency in predicting the area and production of groundnut over the years. Meanwhile, models are compared among other fitted ARIMA models with different p, d, q parameters based on decision criteria’s viz., ME, RMSE, MAPE, AIC, BIC and R-Square. The ARIMA model with parameters p-2 d-1-2, q-1-2 are found adequate in predicting the area as well as production of groundnut. The model ARIMA (2, 2, 2) and ARIMA (2,1,1) predicted the area of groundnut crop with minimum error estimates and residual characteristics (ei). The models were fit into split data i.e., training and test data set, but these models’ prediction power (R-Square) declined during testing. In case of predicting the area, ARIMA (2,2,2) was consistent over the split data but it was not consistent while predicting the production over years. Feed-forward neural networks with single hidden layer were fit to complete, training and split data. The neural network models provided better estimates compared to Box-Jenkins ARIMA models. The data was analysed using R-Studio.

Forecasting End of COVID – 19 in India Based on Time Series Analysis

In this paper, the Box-Jenkins Autoregressive Integrated Moving Average (ARIMA) models for active and exponential smoothing HOLT for removed rates has been estimated using daily time series data from 1st April to 14thSeptember 2020.The active and removed rates are computed from cumulative confirmed, active, recovered and deceased cases. It has been found that ARIMA (0, 1, 1) and Holt exponential smoothing Models are best fit for active and removed rates respectively. Normalized BIC is 0.577and 0.898 for active and removed rates respectively and is minimum among all the six models considered. Lack of fit of models is tested by Ljung-BoX Q statistic. The pvalue is 0.925 and 0.840 for active and removed rates respectively Since for both the rates p-value is greater than 0.05, hence conclude that our model does not show a lack of fit. On the basis of our analysis, active rate will be nullified latest by 5th January 2020, if everything goes best, as P M of India has assured on eve of Independence Day that vaccine for corona will be available very soon. Otherwise by 9 th February 2021 if the past trend continued and in worst situation it will tends to zero on 26th March 2021. We expect the removed rates will reach 100 percent by 20TH October 2020 if everything goes best and by 5th January 2021 if the past trend continued. On the assumptions that Pandemic will come to an end when removed rate in the population tends to 100 percent and active rate to zero percent. Thus on the basis our analysis we expect that COVID – 19 Pandemic may come to end latest either by 9 th February 2021 or 26th March 2021 subject to condition that the social distance and safely measures remains vigilance to stabilize and control the pandemic and in achieving India’s recovery from COVID-19.

Intervention Time Series Modeling of Infant Mortality: Impact of Free Maternal Health Care

Infant mortality is an important marker of the overall society health. The 3rd goal of the Sustainable Development Goals aims at reducing infant deaths that occur due to preventable causes by 2030. Due to increased infant mortality the Kenyan government introduced Free Maternal Health Care as an intervention towards reducing infant mortality through elimination of the cost burden of accessing medical care by the mother and the infant. The study examines the impact of Free Maternal Health Care on infant mortality using Intervention time series analysis particularly the intervention Box Jenkins ARIMA (Autoregressive Integrated Moving Average) model. There was significant support that Free Maternal Health Care had a significant impact on infant mortality which was estimated to be a decrease of 10.15% in infant deaths per month.

Detection of Tea Export Potentiality from Bangladesh in the World Market: An Autoregressive Integrated Moving Average (ARIMA) Approach

Export plays an important role in promoting economic growth and development. The study is conducted to make an efficient forecasting of tea export from Bangladesh for mitigating the risk of export in the world market. Forecasting has been done by fitting Box-Jenkins type autoregressive integrated moving average (ARIMA) model. The best ARIMA model is selected by comparing the criteria- coefficient of determination (R2), root mean square error (RMSE), mean absolute percentage error (MAPE), mean absolute error (MAE) and Bayesian information criteria (BIC). Among the Box-Jenkins ARIMA type models for tea export the ARIMA (1,1,3) model is the most appropriate one for forecasting and the forecast values in thousand kilogram for the year 2017-18, 2018-19, 2019-20, 2020-21 and 2021-22, are 1096.48, 812.83, 1122.02, 776.25 and 794.33 with upper limit 1819.70, 1348.96, 1862.09, 1288.25, 1318.26 and lower limit 660.69, 489.78, 676.08, 467.74, 478.63, respectively. So, the result of this model may be helpful for the policymaker to make an export development plan for the country.

Forecasting the GDP per Capita for Egypt and Saudi Arabia Using ARIMA Models

Annual time series data is used to forecast GDP per capita using the Box-Jenkins Autoregressive-Integrated Moving-Average (ARIMA) model for the Egyptian and Saudi Arabian economies. The fitted ARIMA model is tested for per capita GDP forecasting of Egypt and of Saudi Arabia for the next ten years. Conclusions convey that the most accurate statistical model as in previous literature that forecast GDP per capita for Egypt and for Saudi Arabia is ARIMA (1,1,2) and ARIMA (1,1,1) respectively. The diagnostic tests reveal that the two models presented individually are both stable and reliable.

Forecasting of saline intrusion in Ham Luong river, Ben Tre province (Southern Vietnam) using Box-Jenkins ARIMA models

Introduction: Ham Luong River is a branch of Mekong River located in Ben Tre Province, which has played a crucial role in supporting livelihoods of local residents and the province's economic development. However, the saline intrusion has been expanding in Ham Luong River, which seriously affects the productive agriculture, aquaculture, and further causes tremendous difficulties for local people's lives. Thus, it is crucial to have research for forecast the saline intrusion in Ham Luong River. Our aim was to develop mathematical models in order to forecast the saline intrusion in Ham Luong River, Ben Tre Province.
 Methods: The Auto regressive integrated moving average (ARIMA) model was built to forecast the weekly saline intrusion in Ham Luong River, which has been obtained from Ben Tre Province's Hydro-Meteorological Forecasting Center over eight years (from 2012 to 2019).
 Results: The saline concentration increased from January to March and then decreased from April to June. The highest salinity occurred in February and March while the lowest salinity was observed in early June. Moreover, the ARIMA technique provided an adequate predictive model for a forecast of the saline intrusion in An Thuan, Son Doc, and An Hiep station. However, the ARIMA model in My Hoa and Vam Mon might be improved upon by other forecasting methods.
 Conclusion: Our study suggested that the nonseasonal/seasonal ARIMA is an easy-to-use modeling tool for a quick forecast of the saline intrusion.

Forecasting GDP Movements in Nepal Using Autoregressive Integrated Moving Average (ARIMA) Modelling Process

This study attempts to test the ARIMA model and forecast annual time series of GDP in Nepal from mid-July, 1960 to mid-July, 2018. The annual time series on GDP used in this study consists of total 59 observations. Out of them, three years’ data from mid-July 2016 to mid-July 2018 have been used for in-sample forecasting and evaluation. The study uses univariate Box-Jenkins ARIMA modelling process to identify the best fitted model that describes the sample data set. The study examines a number of ARIMA family models and recommends ARIMA (0,1,2) as the most appropriate model that best describes the annual GDP series of the sampled period. The ARIMA (0, 1, 2) model incorporates zero lag order for autoregression, integrated with 2 lag order for moving average model using first difference operator. The ARIMA model forecasts documented in this study are not significantly different from actual because the actual annual GDP series observed in forecast period fall within 95 per cent confidence interval of estimates. Hence, ARIMA (0,1,2) model can best capture the GDP movement in Nepal for the sample period.

Predicting Rice Production using Autoregressive Integrated Moving Average Model

A study was conducted on time-series data on rice production in India. Box-Jenkins Autoregressive Integrated Moving Average (ARIMA) time-series process was considered for predicting country's rice production using the time series data from 1950–51 to 2017–18. Data from 1950–51 to 2014–15 were used for model development and three years data from 2015–16 and 2017–18 were kept for validation The augmented Dicky Fuller test was applied to test stationarity in data set. Root mean square error. Based on ACF and PACF, the model was defined and tested for its suitability. Akaike information criterion and Bayesian information criterion were used to judge the suitability of the model to be fitted. The performance of the fitted model was examined using mean absolute error, mean percent forecast error, root mean square error and Theil's inequality coefficients. IMA (0, 1, 1) model performed well for forecasting purposes. The percent prediction error for the last three years i.e. from 2015–16 and 2017–18, was below 3%. The predicted values along with their standard errors up to the year 2099, were also obtained using the model.

Time Series Analysis on Monthly Stock Market Returns of the Nigerian Stock Exchange: An Arima Modeling Approach

This research work studied the autoregressive integrated moving average (ARIMA) model that best fitted monthly stock market returns of the Nigerian Stock Exchange between January, 2008 to September, 2018. The study collected secondary data from Central Bank of Nigeria (CBN) Statistical Bulletin 2018 on monthly stock market index of NSE to compute the monthly stock market returns. The Box-Jenkins ARIMA modeling was adopted for this work. The series was tested for stationarity using Augmented Dickey Fuller test. Several ARIMA (p, d, q) models were applied to the monthly stock market returns to ascertain the best fit model for the series. The ARIMA (2, 0, 3) model was selected as the best fit for the data since it has minimum values of Akaike Information Criteria and Mean Squared Errors. The forecasted period showed a market with an unstable monthly stock market returns. Therefore, investors were advised to weigh the risks before venturing into the market to invest.

Optimization of ARIMA Forecasting Model using Firefly Algorithm

Time series prediction aims to control or recognize the behavior of the system based on the data in a certain period of time. One of the most widely used method in time series prediction is ARIMA (Autoregressive Integrated Moving Average). However, ARIMA has a weakness in determining the optimal model. firefly algorithm is used to optimize ARIMA model (p, d, q). by finding the smallest AIC (Akaike Information Criterion) value in determining the best ARIMA model. The data used in the study are daily stock data JCI period January 2013 until August 2016 and data of foreign tourist visits to Indonesia period January 1988 to November 2017.Based on testing, for JCI data, obtained predicted results with Box-Jenkins ARIMA model produces RMSE 49.72, whereas the prediction with the ARIMA Optimization model yielded RMSE 49.48. For the data of Foreign Tourist Visits, the predicted results with the Box-Jenkins ARIMA model resulted in RMSE 46088.9, whereas the predicted results with ARIMA optimization resulted in RMSE 44678.4. From these results it can be concluded that the optimization of ARIMA model with Firefly Algorithm produces better forecasting model than ARIMA model without Optimization.

A Univariate Time Series Autoregressive Integrated Moving Average Model for the Exchange Rate Between Nigerian Naira and US Dollar

This research fit a univariate time series ARIMA model to the Monthly data of exchange rate between Nigerian Naira and US Dollar from January 1980 to December 2015. The Box-Jenkins Autoregressive Integrated Moving Average (ARIMA) model was estimated and the best fitted ARIMA model is used to obtain the post-sample forecasts for three years (January 2016 to December 2018). The data was analyzed with the aid of R statistical package and the best model was selected using Auto. ARIMA. The fitted model is ARIMA (0,1,1) with Akaike Information Criteria (AIC) of 2313.19, Normalized Bayesian Information Criteria (BIC) of 2325.39. This model was further validated by Ljung-Box test with no significant Autocorrelation between the residuals at different lag times and subsequently by white noise of residuals from the diagnostic check performed which clearly portray randomness of the standard error of the residuals, no significant spike in the residual plots of ACF and PACF. The forecasts value indicates clearly that Naira will continue to depreciate against the US Dollar between the periodsunderstudy.

Forecasting ozone concentration levels using Box-Jenkins ARIMA modelling and artificial neural networks: A comparative study

An accurate forecasting of tropospheric ozone (O3) concentration is beneficial for strategic planning of air quality. In this study, various forecasting techniques are used to forecast the daily maximum O3 concentration levels at a monitoring station in the Klang Valley, Malaysia. The Box-Jenkins autoregressive integrated moving-average (ARIMA) approach and three types of neural network models, namely, back-propagation neural network, Elman recurrent neural network and radial basis function neural network are considered. The daily maximum data, spanning from 1 January 2011 to 7 August 2011, was obtained from the Department of Environment, Malaysia. The performance of the four methods in forecasting future values of ozone concentrations is evaluated based on three criteria, which are root mean square error (RMSE), mean absolute error (MAE) and mean absolute percentage error (MAPE). The findings show that the Box-Jenkins approach outperformed the artificial neural network methods.

Forecasting Aus Rice Area and Production in Bangladesh using Box-Jenkins Approach

Forecasting of rice area and production is an essential procedure in supporting policy decision regarding food security and environmental issues. The main aim of this paper is to forecast Aus rice area and production in Bangladesh. Box-Jenkins Autoregressive Integrated Moving Average (ARIMA) time-series methodology is considered for modeling and forecasting country's Aus rice area and production data commencing from 1971-72 to 2013-14. It was observed that ARIMA (1, 1, 5) and ARIMA (1, 1, 4) model were performed better than the other ARIMA models for forecasting Aus area and production respectively. The Aus rice areas were forecasted 1041.12 and 499.31 thousand hectares and for production it was 2059.642 and 1781.545 thousand metric tons in 2014-15 and 2023-24 respectively. The forecasted Aus rice area and production both were showed a decreasing trend. Government should create an enabling environment to develop HYV rice varieties for Aus rice crop to ensure ongoing food security by increasing cultivated area and production.Bangladesh Rice j. 2016, 20(1): 1-10

ARIMA Based Wind Speed Modeling for Wind Farm Reliability Analysis and Cost Estimation

Necessity has compelled man to improve upon the art of tapping wind energy for power generation; an apt reliever of strain exerted on the non-renewable fossil fuel. The power generation in a Wind Farm (WF) depends on site and wind velocity which varies with time and season which in turn determine wind power modeling. It implies, the development of an accurate wind speed model to predict wind power fluctuations at a particular site is significant. In this paper, Box-Jenkins ARIMA (Auto Regressive Integrated Moving Average) time series model for wind speed is developed for a 99MW wind farm in the southern region of India. Because of the uncertainty in wind power developed, the economic viability and reliability of power generation is significant. Life Cycle Costing (LCC) method is used to determine the economic viability of WF generated power. Reliability models of WF are developed with the help of load curve of the utility grid and Capacity Outage Probability Table (COPT). ARIMA wind speed model is used for developing COPT. The values of annual reliability indices and variations of risk index of the WF with system peak load are calculated. Such reliability models of large WF can be used in generation system planning.