Fitted Autoregressive Integrated Moving Average Model Research Articles

Autoregressive Integrated Moving Average (ARIMA) Model with Genetic Algorithm to Forecast the Chilli and Turmeric Productions in India

Aims: India holds the distinction of being the foremost producer of spices globally and has been long-run history in spice export. The quantity of Indian spice exports increased by 37% with $ 4.1 billion worth in 2021. With that, dried chilli, cumin, and turmeric alone contributed 44% of export value ($ 1.8 billion). Forecasting the production of major spices are key for exports and plays an essential role in supporting and achieving the target of $10 billion in exports by 2027. Data Source: The time series data of chilli and turmeric production data in India from 1970-2020 periods was collected from Indiastat. Methodology: The present study sought to forecast the production of chilli and turmeric in India using the ARIMA model and their parameters are estimated by stochastic optimization techniques (genetic algorithm). The parameters are estimated by minimizing the Mean Absolute Percentage Error (MAPE). Finally, ARIMA and ARIMA_GA models were compared based on their predictive ability. Results: The Root Mean Square Error (RMSE) and Mean Absolute Percentage Error (MAPE) were 254.01,11.32 (chilli) and 185.73, 15.24 (turmeric) for testing set of ARIMA_GA model which is lower than the fitted ARIMA model. Conclusion: This work has shown that ARIMA_GA (2,1,1) has been the best model to forecast the chilli and turmeric production in India. ARIMA_GA model will cope with parsimony and convergence of likelihood function to global optimum problems. Therefore ARIMA with GA will able to model the complexity and uncertainty of the data.

Modelling and Forecasting Somalia GDP Using Autoregressive Integrated Moving Average (ARIMA) Models

The Gross Domestic Product (GDP) is the total worth of all goods and services produced within a country's borders in a given year. The background of the study includes the importance of GDP as an important economic indicator reflecting the overall economic performance and growth of a country. As Somalia faces unique economic challenges, this research aims to provide insight into its GDP dynamics, trends, and potential future developments. In order to create the suitable Autoregressive-Integrated Moving-Average (ARIMA) model for the GDP data for Somalia, the Box-Jenkins method was used in this study. Data on the annual GDP of Somalia from 1972 through 2022 was taken from the Macrotrends database. ARIMA (3, 1, 8) was identified as the most suitable statistical model for the GDP of Somalia. The forecast for Somalia's GDP over the next five years was generated using this fitted ARIMA model. The findings indicated that a positive increase in Somalia's GDP over the next five years is expected. These forecasts line up with the historical trends and statistical correlations found by the ARIMA model

Time series and power law analysis of crop yield in some east African countries.

We carry out a time series analysis on the yearly crop yield data in six east African countries (Burundi, Kenya, Somalia, Tanzania, Uganda and Rwanda) using the autoregressive integrated moving average (ARIMA) model. We describe the upper tail of the yearly crop yield data in those countries using the power law, lognormal, Fréchet and stretched exponential distributions. The forecast of the fitted ARIMA models suggests that the majority of the crops in different countries will experience neither an increase nor a decrease in yield from 2019 to 2028. A few exceptional cases correspond to significant increase in the yield of sorghum and coffee in Burundi and Rwanda, respectively, and significant decrease in the yield of beans in Burundi, Kenya and Rwanda. Based on Vuong's similarity test p-value, we find that the power law distribution captured the upper tails of yield distribution better than other distributions with just one exceptional case in Uganda, suggesting that these crops have the tendency for producing high yield. We find that only sugar cane in Somalia and sweet potato in Tanzania have the potential of producing extremely high yield. We describe the yield behaviour of these two crops as black swan, where the "rich getting richer" or the "preferential attachment" could be the underlying generating process. Other crops in Burundi, Kenya, Somalia, Tanzania, Uganda and Rwanda can only produce high but not extremely high yields. Various climate adaptation/smart strategies (use of short-duration pigeon pea varieties, use of cassava mosaic disease resistant cassava varieties, use of improved maize varieties, intensive manuring with a combination of green and poultry manure, early planting, etc) that could be adapted to increase yields in east Africa are suggested. The paper could be useful for future agricultural planning and rates calibration in crop risk insurance.

Evaluation of the Performance of Autoregressive Integrated Moving Average (ARIMA) and Artificial Neural Networks (ANNs) Models: Application to Confirmed Cases of Covid-19 in Nigeria

In this study, the performance of Autoregressive Integrated Moving Average (ARIMA) and Artificial Neural Networks (ANNs) models was investigated and evaluated using daily confirmed cases of COVID-19 in Nigeria. The stationarity status of the data collected was established using Augmented Dickey Fuller unit root test. The residual normality test was also carried out with the residual plots indicating adequacy of the fitted ARIMA model. The results of neural networks were analyzed using back-propagation for multilayer feed-forward powered by sigmoid function. Utilizing backpropagation method based on three factors expressed in terms of the learning rate, the distance between the actual output and predicted output and the activation function, the network weights were generated The performance indices for ARIMA and ANNs models were evaluated using Mean Square Error (MSE), Root Mean Square Error (RMSE) and Mean Absolute Error (MAE and the results revealed that the ARIMA model performed better than the ANN model considering the minimum prediction error and forecasting ability. The ARIMA (2, 1, 1) model appeared to be the best fitted model over the ANN model for the daily confirmed covid-19 cases considered.

Trend Analysis of Milk Production in India

Background: Dairy sector is a thriving enterprise in Indian agriculture showing colossal growth responsible for placing the country at the top position worldwide in milk production. This sector has seen a rising growth; however, there seems to be demand supply gap over the next few years. Under this backdrop, the study has been taken with the twin objectives of studying the trend and growth rate of production and per capita availability of milk and to forecast the production of milk through ARIMA modelling. Methods: The study is based on secondary data of milk production from 1989 to 2019. The growth was examined by estimating compound annual growth rate and the Autoregressive integrated moving average (ARIMA) methodology was applied for modeling and forecasting of milk production of India. Augmented dickey-fuller (ADF) test was used to determine the stationarity of the model after which it was used to forecast the future production. Result: The CAGR of milk production was higher in comparison to per capita availability (4.34 and 2.71 per cent per annum respectively). The forecast from the fitted ARIMA model show that the milk production is expected to be 244.7 million tonnes in 2024.

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.

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.

ARIMA Model for Forecasting of Black Gram Productivity in Odisha

A study was conducted on forecasting the productivity of black gram in Odisha. Box-Jenkins Autoregressive integrated moving average (ARIMA) time-series methodology was considered for Black gram yield forecasting. Different ARIMA models are selected on the basis of Autocorrelation Function (ACF) and Partial autocorrelation Function (PACF) at various lags .The data from 1971-72 to 2006-07 are used for model building of different ARIMA models and from 2007-08 to 2015-16 is used for successful cross-validation of the selected model, which is based on the Mean absolute percentage error(MAPE). To check the stationarity, ARIMA Models are fitted to the original time series data as well as first difference data. Based on the significant coefficient of autoregressive and moving average components, the possible ARIMA Models are identified. Based on low value of Root Mean Square Error (RMSE) and Mean Absolute Percentage Error (MAPE), the best fitted ARIMA models are selected. ARIMA (0,1,1) without constant found to be best fitted model for Black gram productivity having absolute percentage error ranging from 19.99% to 43.29% in cross-validation of the model. The best fitted ARIMA model has been used to forecast the productivity of black gram for the year 2016-17 to 2018-19. The model showed the forecast in productivity for the year 2018-19 to be about 221.45 kg per hectare with lower and upper limit 90.36 and 392.89 kg per hectare respectively.

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.

On the Fourier Residual Modification of Arima Models in Modeling Malaria Incidence Rates among Pregnant Women

This work provides a general overview and consideration of Box-Jenkins models for temporal data and its extension known as Fourier residual autoregressive moving average models. We examined the modeling and forecasting of malaria incidence rate during pregnancy at Bishop Shannahan Hospital, Nsukka using Autoregressive Integrated Moving Average (ARIMA) Models propounded by Box and Jenkins. We adoptted the Box-Jenkins methodology to build ARIMA model for malaria incidences during pregnancy for a period of 10 years spanning from January 2006 to December 2016. Among the candidate models considered, ARIMA (3,1,1) was identified to be the most robust based on some model performance measures. The model was further improved upon by incorporating Fourier residual modification on the fitted ARIMA model. The Fourier Residual Autoregressive Moving Average (FARIMA) model obtained yielded improved result. Besides, model evaluation criterion such as Root Mean Square Error (RMSE), Mean Absolute Error (MAE), Mean Bias Error (MBE), Mean Bias Error (MBE), Mean Absolute Scaled Error (MASE), were used to access the models. FARIMA Model out performed ARIMA Model. Several time series plots and tests like augmented dickey fuller test, correlogram, Ljung-Box test for serial correlation of the residuals, etc were carried out in this study to test for stationarity, identify the order of ARIMA model and serial correlation residual respectively.

A Statistical out-of-Sample Forecast to Estimate Lithium-Ion Parameters That Determine State of Charge

Predicting state of charge (SOC) is crucial for an intelligent battery management system. Most of the existing SOC estimator models in literature use traditional methods such as bookkeeping and direct measurement, or rely on adaptive techniques such as neural networks. However, these models require the acquisition of significant experimental data on cell voltage and current, among others, to predict SOC with acceptable generalization performance. This paper proposes to compare two available statistical time-series forecasting methods, autoregressive integrated moving average (ARIMA) and Holt-Winters Exponential Smoothing (HWES), to forecast cell current and voltage of an actual 3.7V, 3.5Ah Lithium-ion battery for an unknown charging/discharging rate (C-rate) of C/10 using the values of the corresponding parameters from preceding C-rates of C/2, C/4, C/6, and C/8 obtained by performing lifecycle tests. The forecast values of current and voltage could, in practice, be used to calculate SOC using Coulomb-counting method [1]. The results are finally documented as a table in the attached figure. Proposed Work: Predicting the state of charge (SOC) of Lithium-ion batteries is critical for applications such as electric vehicles to determine the available capacity and function accordingly. Under scenarios where access to infrastructure and means to acquire experimental data on battery parameters is limited, the availability of an estimator model that is pre-trained for a given battery that can directly be used to predict SOC for any required C-rate is favorable. The paper proposes to use ARIMA and HWES algorithms to forecast current and voltage using historical time-series values of the same parameters obtained for C-rates C/2 to C/8. The voltage and current data are stationary as they both reject the null hypothesis in the Augmented Dickey-Fuller test [2] with a p-value of 0.01. Correlograms of the autocorrelation and partial autocorrelation functions for current and voltage are shown in Figure A in the attachment. The optimal values for the autoregressive integrative, and moving average terms are selected to be (34,1,4) such that their combination minimized the Akaike Information Criterion (AIC) [2]. The ACF and PACF plots for the fitted ARIMA model is illustrated in Figure B. The results of cell current and voltage predictions for C/10 made using the ARIMA model are shown in Figs. C and D, respectively, in the attachment. Results and discussion: The experimental setup comprised a 3.7V, 3.5Ah Li-ion battery that was subjected to different C-rates: C/2, C/4, C/6, C/8, and C/10, for 60 cycles each at discharging and charging currents of 850mAh and 2.6Ah for each test, respectively. The cell current and voltage values for C-rates C/2 through C/8 were augmented to form the time-series datasets to be used by ARIMA and HWES for model fitting. The corresponding datasets for C/10 were used solely during the forecasting phase, thereby making the forecasting process out-of-sample. For ARIMA, the mean squared error (MSE) between the forecast and observed values for C/10 voltage and current are 0.019 and 0.079, respectively. For HWES, the MSE values for C/10 voltage and current turned out to be higher, with 0.3996 and 1.6775, respectively. Besides MSE, three other errors, root mean square error (RMSE), mean absolute error (MAE), and mean absolute percentage error (MAPE), are also calculated for both models in predicting C/10 current and voltage. This table is also included in the attachment as Fig. G. It can be seen that ARIMA had a superior performance than HWES for this specific problem. Conclusion and Future Work: To develop a reliable SOC estimator model for intelligent battery management systems that are capable of predicting SOC for future, unseen C-rates using the available cell current and voltage data from previous C-rates, this paper proposes to use ARIMA. Results show that between ARIMA and HWES, the two most widely used statistical time-series forecasting methods, ARIMA shows superior performance. As a future work, artificial neural network-based SOC and voltage estimation techniques will be identified.

Forecasting of Rice Cultivation in India–A Comparative Analysis with ARIMA and LSTM-NN Models

In India, due to the blessing by the outbreak of the National Food Security Mission, the production of cereals such as wheat, rice etc, has increased in an alarming rate. In this Study, forecasting is done with the help Auto Regressive Integrated Moving Average (ARIMA) and Long Short-Term Memory Neural Network (LSTM-NN) models on the basis of the historical data of rice cultivation from the year 1950-51 to 2017-18. The well fitted ARIMA models for the parameters such as Area under Cultivation (0,1,1), Production (0,1,1) and Yielding (2,2,1) are obtained from the significant spikes of their respective Auto Correlation Function (ACF) and Partial Auto Correlation Function (PACF) plots. But, the models fitted with a supervised deep learning neural network known as LSTM-NN are found much better time series forecasting model than the ARIMA models. The performances of these models validated with the Root Mean Square Error (RMSE) and Mean Absolute Percentage Error (MAPE) values. From the study, the LSTM-NN’s are more flexible and able to develop accurate models for predicting the behavior of agricultural parameters than the ARIMA models.

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.

Modelling the prevalence of hepatitis C virus amongst blood donors in Libya: An investigation of providing a preventive strategy.

To determine hepatitis C virus (HCV) seroprevalence among the Libyan population using blood donors and applying the autoregressive integrated moving average (ARIMA) model to predict future trends and formulate plans to minimize the burden of HCV infection. HCV positive cases were collected from 1008214 healthy blood donors over a 6-year period from 2008 to 2013. Data were used to construct the ARIMA model to forecast HCV seroprevalence among blood donors. The validity of the model was assessed using the mean absolute percentage error between the observed and fitted seroprevalence. The fitted ARIMA model was used to forecast the incidence of HCV beyond the observed period for the year 2014 and further to 2055. The overall prevalence of HCV among blood donors was 1.8%, varying over the study period from 1.7% to 2.5%, though no significant variation was found within each calendar year. The ARIMA model showed a non-significant auto-correlation of the residuals, and the prevalence was steady within the last 3 years as expressed by the goodness-of-fit test. The forecast incidence showed an increase in HCV seropositivity in 2014, ranging from 500 to 700 per 10000 population, with an overall prevalence of 2.3%-2.7%. This may be extended to 2055 with minimal periodical variation within each 6-year period. The applied model was found to be valuable in evaluating the seroprevalence of HCV among blood donors, and highlighted the growing burden of such infection on the Libyan health care system. The model may help in formulating national policies to prevent increases in HCV infection and plan future strategies that target the consequences of the infection.

Modeling and Forecasting Kenyan GDP Using Autoregressive Integrated Moving Average (ARIMA) Models

The Gross Domestic Product (GDP) is the market value of all goods and services produced within the borders of a nation in a year. In this paper, Kenya’s annual GDP data obtained from the Kenya National Bureau of statistics for the years 1960 to 2012 was studied. Gretl and SPSS 21 statistical softwares were used to build a class of ARIMA (autoregressive integrated moving average) models following the Box-Jenkins method to model the GDP. ARIMA (2, 2, 2) time series model was established as the best for modeling the Kenyan GDP according to the recognition rules and stationary test of time series under the AIC criterion. The results of an in-sample forecast showed that the relative and predicted values were within the range of 5%, and the forecasting effect of this model was relatively adequate and efficient in modeling the annual returns of the Kenyan GDP. Finally, we used the fitted ARIMA model to forecast the GDP of Kenya for the next five years.

Predicting the incidence of hand, foot and mouth disease in Sichuan province, China using the ARIMA model.

Hand, foot and mouth disease (HFMD) is an infectious disease caused by enteroviruses, which usually occurs in children aged <5 years. In China, the HFMD situation is worsening, with increasing number of cases nationwide. Therefore, monitoring and predicting HFMD incidence are urgently needed to make control measures more effective. In this study, we applied an autoregressive integrated moving average (ARIMA) model to forecast HFMD incidence in Sichuan province, China. HFMD infection data from January 2010 to June 2014 were used to fit the ARIMA model. The coefficient of determination (R 2), normalized Bayesian Information Criterion (BIC) and mean absolute percentage of error (MAPE) were used to evaluate the goodness-of-fit of the constructed models. The fitted ARIMA model was applied to forecast the incidence of HMFD from April to June 2014. The goodness-of-fit test generated the optimum general multiplicative seasonal ARIMA (1,0,1) × (0,1,0)12 model (R 2 = 0·692, MAPE = 15·982, BIC = 5·265), which also showed non-significant autocorrelations in the residuals of the model (P = 0·893). The forecast incidence values of the ARIMA (1,0,1) × (0,1,0)12 model from July to December 2014 were 4103-9987, which were proximate forecasts. The ARIMA model could be applied to forecast HMFD incidence trend and provide support for HMFD prevention and control. Further observations should be carried out continually into the time sequence, and the parameters of the models could be adjusted because HMFD incidence will not be absolutely stationary in the future.

Maize Area and Production Forecasting in Eastern Region of Madhya Pradesh: An Application of Box-Jenkins ARIMA Model

Maize is an important crop in India. In this study an attempt has been made to forecast the area and production of maize crop in Madhya Pradesh, India. The Madhya Pradesh is one of the traditional and potential maize producing state in the country. Its production and productivity in the recent time call for major concern. Auto Regressive Integrated Moving Average (ARIMA) model have been fitted and projection was made on the basis of the best fitted ARIMA model for acreage and production. Time Series data covering the period of 19901991 to 2011-2012 was used for the Study. The maize area and production forecasts for 2012-13 to 202526 for all the selected districts in the region were made in this study. This projection is important as it helps in framing good policies with respect to relative production, price structure as well as consumption of maize in the region and in the state as a whole. The projection results reflected that maize will play vital role to solve food security problem in the region and in the state in general. Thus, policy makers, stake holders and beneficiaries (farmers) should take necessary steps to check the decline trend in area under maize production without further delay.

Forecasting Rice Productivity and Production of Odisha, India, Using Autoregressive Integrated Moving Average Models

Forecasting of rice area, production, and productivity of Odisha was made from the historical data of 1950-51 to 2008-09 by using univariate autoregressive integrated moving average (ARIMA) models and was compared with the forecasted all Indian data. The autoregressive (p) and moving average (q) parameters were identified based on the significant spikes in the plots of partial autocorrelation function (PACF) and autocorrelation function (ACF) of the different time series. ARIMA (2, 1, 0) model was found suitable for all Indian rice productivity and production, whereas ARIMA (1, 1, 1) was best fitted for forecasting of rice productivity and production in Odisha. Prediction was made for the immediate next three years, that is, 2007-08, 2008-09, and 2009-10, using the best fitted ARIMA models based on minimum value of the selection criterion, that is, Akaike information criteria (AIC) and Schwarz-Bayesian information criteria (SBC). The performances of models were validated by comparing with percentage deviation from the actual values and mean absolute percent error (MAPE), which was found to be 0.61 and 2.99% for the area under rice in Odisha and India, respectively. Similarly for prediction of rice production and productivity in Odisha and India, the MAPE was found to be less than 6%.

Forecasting the Number of Human Immunodeficiency Virus Infections in the Korean Population Using the Autoregressive Integrated Moving Average Model

ObjectivesFrom the introduction of HIV into the Republic of Korea in 1985 through 2012, 9,410 HIV-infected Koreans have been identified. Since 2000, there has been a sharp increase in newly diagnosed HIV-infected Koreans. It is necessary to estimate the changes in HIV infection to plan budgets and to modify HIV/AIDS prevention policy. We constructed autoregressive integrated moving average (ARIMA) models to forecast the number of HIV infections from 2013 to 2017. MethodsHIV infection data from 1985 to 2012 were used to fit ARIMA models. Akaike Information Criterion and Schwartz Bayesian Criterion statistics were used to evaluate the constructed models. Estimation was via the maximum likelihood method. To assess the validity of the proposed models, the mean absolute percentage error (MAPE) between the number of observed and fitted HIV infections from 1985 to 2012 was calculated. Finally, the fitted ARIMA models were used to forecast the number of HIV infections from 2013 to 2017. ResultsThe fitted number of HIV infections was calculated by optimum ARIMA (2,2,1) model from 1985–2012. The fitted number was similar to the observed number of HIV infections, with a MAPE of 13.7%. The forecasted number of new HIV infections in 2013 was 962 (95% confidence interval (CI): 889–1,036) and in 2017 was 1,111 (95% CI: 805–1,418). The forecasted cumulative number of HIV infections in 2013 was 10,372 (95% CI: 10,308–10,437) and in 2017 was14,724 (95% CI: 13,893–15,555) by ARIMA (1,2,3). ConclusionBased on the forecast of the number of newly diagnosed HIV infections and the current cumulative number of HIV infections, the cumulative number of HIV-infected Koreans in 2017 would reach about 15,000.

Forecasting incidence of hemorrhagic fever with renal syndrome in China using ARIMA model

BackgroundChina is a country that is most seriously affected by hemorrhagic fever with renal syndrome (HFRS) with 90% of HFRS cases reported globally. At present, HFRS is getting worse with increasing cases and natural foci in China. Therefore, there is an urgent need for monitoring and predicting HFRS incidence to make the control of HFRS more effective. In this study, we applied a stochastic autoregressive integrated moving average (ARIMA) model with the objective of monitoring and short-term forecasting HFRS incidence in China.MethodsChinese HFRS data from 1975 to 2008 were used to fit ARIMA model. Akaike Information Criterion (AIC) and Ljung-Box test were used to evaluate the constructed models. Subsequently, the fitted ARIMA model was applied to obtain the fitted HFRS incidence from 1978 to 2008 and contrast with corresponding observed values. To assess the validity of the proposed model, the mean absolute percentage error (MAPE) between the observed and fitted HFRS incidence (1978-2008) was calculated. Finally, the fitted ARIMA model was used to forecast the incidence of HFRS of the years 2009 to 2011. All analyses were performed using SAS9.1 with a significant level of p < 0.05.ResultsThe goodness-of-fit test of the optimum ARIMA (0,3,1) model showed non-significant autocorrelations in the residuals of the model (Ljung-Box Q statistic = 5.95,P = 0.3113). The fitted values made by ARIMA (0,3,1) model for years 1978-2008 closely followed the observed values for the same years, with a mean absolute percentage error (MAPE) of 12.20%. The forecast values from 2009 to 2011 were 0.69, 0.86, and 1.21per 100,000 population, respectively.ConclusionARIMA models applied to historical HFRS incidence data are an important tool for HFRS surveillance in China. This study shows that accurate forecasting of the HFRS incidence is possible using an ARIMA model. If predicted values from this study are accurate, China can expect a rise in HFRS incidence.