Time series analysis-based seasonal autoregressive fractionally integrated moving average to estimate hepatitis B and C epidemics in China

BACKGROUND Hepatitis B(HB)and hepatitis C(HC)place the largest burden in China,and a goal of eliminating them as a major public health threat by 2030 has been set.Making more informed and accurate forecasts of their spread is essential for developing effective strategies,heightening the requirement for early warning to deal with such a major public health threat.AIM To monitor HB and HC epidemics by the design of a paradigmatic seasonal autoregressive fractionally integrated moving average(SARFIMA)for projections into 2030,and to compare the effectiveness with the seasonal autoregressive integrated moving average(SARIMA).METHODS Monthly HB and HC incidence cases in China were obtained from January 2004 to June 2023.Descriptive analysis and the Hodrick-Prescott method were employed to identify trends and seasonality.Two periods(from January 2004 to June 2022 and from January 2004 to December 2015,respectively)were used as the training sets to develop both models,while the remaining periods served as the test sets to evaluate the forecasting accuracy.RESULTS There were incidents of 23400874 HB cases and 3590867 HC cases from January 2004 to June 2023.Overall,HB remained steady[average annual percentage change(AAPC)=0.44,95%confidence interval(95%CI):-0.94-1.84]while HC was increasing(AAPC=8.91,95%CI:6.98-10.88),and both had a peak in March and a trough in February.In the 12-step-ahead HB forecast,the mean absolute deviation(15211.94),root mean square error(18762.94),mean absolute percentage error(0.17),mean error rate(0.15),and root mean square percentage error(0.25)under the best SARFIMA(3,0,0)(0,0.449,2)12 were smaller than those under the best SARIMA(3,0,0)(0,1,2)12(16867.71,20775.12,0.19,0.17,and 0.27,respectively).Similar results were also observed for the 90-step-ahead HB,12-step-ahead HC,and 90-step-ahead HC forecasts.The predicted HB incidents totaled 9865400(95%CI:7508093-12222709)cases and HC totaled 1659485(95%CI:856681-2462290)cases during 2023-2030.CONCLUSION Under current interventions,China faces enormous challenges to eliminate HB and HC epidemics by 2030,and effective strategies must be reinforced.The integration of SARFIMA into public health for the management of HB and HC epidemics can potentially result in more informed and efficient interventions,surpassing the capabilities of SARIMA.

Influencing Factors and Prediction of Risk of Returning to Ecological Poverty in Liupan Mountain Region,China

China has resolved its overall regional poverty in 2020 by attaining moderate societal prosperity.The country has entered a new development stage designed to achieve its second centenary goal.However,ecological fragility and risk susceptibility have increased the risk of returning to ecological poverty.In this paper,the Liupan Mountain Region of China was used as a case study,and the counties were used as the scale to reveal the spatiotempora differentiation and influcing factors of the risk of returning to poverty in study area.The indicator data for returning to ecological poverty from 2011-2020 were collected and summarized in three dimensions:ecological,economic and social.The autoregressive integrated moving average model(ARIMA)time series and exponential smoothing method(ES)were used to predict the multidimensional indicators of returning to ecological poverty for 61 counties(districts)in the Liupan Mountain Region for 2021-2030.The back propagation neural network(BPNN)and geographic information system(GIS)were used to generate the spatial distribution and time variation for the index of the risk of returning to ecological poverty(RREP index).The results show that 1)ecological factors were the main factors in the risk of returning to ecological poverty in Liupan Mountain Region.2)The RREP index for the 61 counties(districts)exhibited a downward trend from 2021-2030.The RREP index declined more in medium-and high-risk areas than in low-risk areas.From 2021 to 2025,the RREP index exhibited a slight downward trend.From 2026 to2030,the RREP index was expected to decline faster,especially from 2029-2030.3)Based on the RREP index,it can be roughly divided into three types,namely,the high-risk areas,the medium-risk areas,and the low-risk areas.The natural resource conditions in lowrisk areas of returning to ecological poverty,were better than those in medium-and high-risk areas.

Automated Machine Learning Algorithm Using Recurrent Neural Network to Perform Long-Term Time Series Forecasting

Long-term time series forecasting stands as a crucial research domain within the realm of automated machine learning(AutoML).At present,forecasting,whether rooted in machine learning or statistical learning,typically relies on expert input and necessitates substantial manual involvement.This manual effort spans model development,feature engineering,hyper-parameter tuning,and the intricate construction of time series models.The complexity of these tasks renders complete automation unfeasible,as they inherently demand human intervention at multiple junctures.To surmount these challenges,this article proposes leveraging Long Short-Term Memory,which is the variant of Recurrent Neural Networks,harnessing memory cells and gating mechanisms to facilitate long-term time series prediction.However,forecasting accuracy by particular neural network and traditional models can degrade significantly,when addressing long-term time-series tasks.Therefore,our research demonstrates that this innovative approach outperforms the traditional Autoregressive Integrated Moving Average(ARIMA)method in forecasting long-term univariate time series.ARIMA is a high-quality and competitive model in time series prediction,and yet it requires significant preprocessing efforts.Using multiple accuracy metrics,we have evaluated both ARIMA and proposed method on the simulated time-series data and real data in both short and long term.Furthermore,our findings indicate its superiority over alternative network architectures,including Fully Connected Neural Networks,Convolutional Neural Networks,and Nonpooling Convolutional Neural Networks.Our AutoML approach enables non-professional to attain highly accurate and effective time series forecasting,and can be widely applied to various domains,particularly in business and finance.

Application of Seasonal Auto-regressive Integrated Moving Average Model in Forecasting the Incidence of Hand-foot-mouth Disease in Wuhan,China

Outbreaks of hand-foot-mouth disease（HFMD） have occurred many times and caused serious health burden in China since 2008. Application of modern information technology to prediction and early response can be helpful for efficient HFMD prevention and control. A seasonal auto-regressive integrated moving average（ARIMA） model for time series analysis was designed in this study. Eighty-four-month（from January 2009 to December 2015） retrospective data obtained from the Chinese Information System for Disease Prevention and Control were subjected to ARIMA modeling. The coefficient of determination（R^2）, normalized Bayesian Information Criterion（BIC） and Q-test P value were used to evaluate the goodness-of-fit of constructed models. Subsequently, the best-fitted ARIMA model was applied to predict the expected incidence of HFMD from January 2016 to December 2016. The best-fitted seasonal ARIMA model was identified as（1,0,1）（0,1,1）12, with the largest coefficient of determination（R^2=0.743） and lowest normalized BIC（BIC=3.645） value. The residuals of the model also showed non-significant autocorrelations（P_（Box-Ljung（Q））=0.299）. The predictions by the optimum ARIMA model adequately captured the pattern in the data and exhibited two peaks of activity over the forecast interval, including a major peak during April to June, and again a light peak for September to November. The ARIMA model proposed in this study can forecast HFMD incidence trend effectively, which could provide useful support for future HFMD prevention and control in the study area. Besides, further observations should be added continually into the modeling data set, and parameters of the models should be adjusted accordingly.

Forecasting risk using auto regressive integrated moving average approach: an evidence from S&P BSE Sensex

The primary objective of the paper is to forecast the beta values of companies listed on Sensex,Bombay Stock Exchange(BSE).The BSE Sensex constitutes 30 top most companies listed which are popularly known as blue-chip companies.To reach out the predefined objectives of the research,Auto Regressive Integrated Moving Average method is used to forecast the future risk and returns for 10 years of historical data from April 2007 to March 2017.Validation accomplished by comparison of forecasted and actual beta values for the hold back period of 2 years.Root-Mean-Square-Error and Mean-Absolute-Error both are used for accuracy measurement.The results revealed that out of 30 listed companies in the BSE Sensex,10 companies’exhibits high beta values,12 companies are with moderate and 8 companies are with low beta values.Further,it is to note that Housing Development Finance Corporation(HDFC)exhibits more inconsistency in terms of beta values though the average beta value is lowest among the companies under the study.A mixed trend is found in forecasted beta values of the BSE Sensex.In this analysis,all the p-values are less than the F-stat values except the case of Tata Steel and Wipro.Therefore,the null hypotheses were rejected leaving Tata Steel and Wipro.The values of actual and forecasted values are showing the almost same results with low error percentage.Therefore,it is concluded from the study that the estimation ARIMA could be acceptable,and forecasted beta values are accurate.So far,there are many studies on ARIMA model to forecast the returns of the stocks based on their historical data.But,hardly there are very few studies which attempt to forecast the returns on the basis of their beta values.Certainly,the attempt so made is a novel approach which has linked risk directly with return.On the basis of the present study,authors try to through light on investment decisions by linking it with beta values of respective stocks.Further,the outcomes of the present study undoubtedly useful to academicians,researchers,and policy makers in their respective area of studies.

Applications of time series analysis in epidemiology: Literature review and our experience during COVID-19 pandemic

Time series analysis is a valuable tool in epidemiology that complements the classical epidemiological models in two different ways:Prediction and forecast.Prediction is related to explaining past and current data based on various internal and external influences that may or may not have a causative role.Forecasting is an exploration of the possible future values based on the predictive ability of the model and hypothesized future values of the external and/or internal influences.The time series analysis approach has the advantage of being easier to use(in the cases of more straightforward and linear models such as Auto-Regressive Integrated Moving Average).Still,it is limited in forecasting time,unlike the classical models such as Susceptible-Exposed-Infectious-Removed.Its applicability in forecasting comes from its better accuracy for short-term prediction.In its basic form,it does not assume much theoretical knowledge of the mechanisms of spreading and mutating pathogens or the reaction of people and regulatory structures(governments,companies,etc.).Instead,it estimates from the data directly.Its predictive ability allows testing hypotheses for different factors that positively or negatively contribute to the pandemic spread;be it school closures,emerging variants,etc.It can be used in mortality or hospital risk estimation from new cases,seroprevalence studies,assessing properties of emerging variants,and estimating excess mortality and its relationship with a pandemic.

天气衍生品气温预测模型对比研究

气温衍生品是天气衍生品交易中最活跃的合约之一,确定合理预测气温动态变化的模型,是气温衍生品开发设计的基础。考虑到气温在时间变化上具有趋势性、季节性和周期性等特点,文中使用了以O-U均值回复过程为基础的Continuous Time Autoregressive Model(CAR)模型、Seasonal Autoregressive Integrated Moving Average(SARIMA)模型和小波神经网络算法,并选择漠河、北京、乌鲁木齐、芜湖、昆明和海口具有地域性代表的城市气温进行拟合,使用无偏绝对百分比误差、绝对百分比误差和平均绝对比例误差检验指标检验了模型的预测精度。研究结果表明,小波神经网络算法在预测6个城市的无偏绝对百分比误差、绝对百分比误差和平均绝对比例误差的值最小;同时,相比CAR模型、SARIMA模型,其预测效果最优。因此,小波神经网络算法能够很好地拟合气温数据的变化,可以为我国气温天气衍生品的定价提供一定的指导。

Spatial-temporal Analysis and Prediction of Precipitation Extremes: A Case Study in the Weihe River Basin, China

Extreme precipitation events bring considerable risks to the natural ecosystem and human life.Investigating the spatial-temporal characteristics of extreme precipitation and predicting it quantitatively are critical for the flood prevention and water resources planning and management.In this study,daily precipitation data(1957–2019)were collected from 24 meteorological stations in the Weihe River Basin(WRB),Northwest China and its surrounding areas.We first analyzed the spatial-temporal change of precipitation extremes in the WRB based on space-time cube(STC),and then predicted precipitation extremes using long short-term memory(LSTM)network,auto-regressive integrated moving average(ARIMA),and hybrid ensemble empirical mode decomposition(EEMD)-LSTM-ARIMA models.The precipitation extremes increased as the spatial variation from northwest to southeast of the WRB.There were two clusters for each extreme precipitation index,which were distributed in the northwestern and southeastern or northern and southern of the WRB.The precipitation extremes in the WRB present a strong clustering pattern.Spatially,the pattern of only high-high cluster and only low-low cluster were primarily located in lower reaches and upper reaches of the WRB,respectively.Hot spots(25.00%–50.00%)were more than cold spots(4.17%–25.00%)in the WRB.Cold spots were mainly concentrated in the northwestern part,while hot spots were mostly located in the eastern and southern parts.For different extreme precipitation indices,the performances of the different models were different.The accuracy ranking was EEMD-LSTM-ARIMA>LSTM>ARIMA in predicting simple daily intensity index(SDII)and consecutive wet days(CWD),while the accuracy ranking was LSTM>EEMD-LSTM-ARIMA>ARIMA in predicting very wet days(R95 P).The hybrid EEMD-LSTM-ARIMA model proposed was generally superior to single models in the prediction of precipitation extremes.

Modeling and predicting dengue fever cases in key regions of the Philippines using remote sensing data

Objective: To correlate climatic and environmental factors such as land surface temperature, rainfall, humidity and normalized difference vegetation index with the incidence of dengue to develop prediction models for the Philippines using remote-sensing data.Methods: Timeseries analysis was performed using dengue cases in four regions of the Philippines and monthly climatic variables extracted from Global Satellite Mapping of Precipitation for rainfall, and MODIS for the land surface temperature and normalized difference vegetation index from 2008-2015.Consistent dataset during the period of study was utilized in Autoregressive Integrated Moving Average models to predict dengue incidence in the four regions being studied.Results: The best-fitting models were selected to characterize the relationship between dengue incidence and climate variables.The predicted cases of dengue for January to December 2015 period fitted well with the actual dengue cases of the same timeframe.It also showed significantly good linear regression with a square of correlation of 0.869 5 for the four regions combined.Conclusion: Climatic and environmental variables are positively associated with dengue incidence and suit best as predictor factors using Autoregressive Integrated Moving Average models.This finding could be a meaningful tool in developing an early warning model based on weather forecasts to deliver effective public health prevention and mitigation programs.

Performance evaluation of series and parallel strategies for financial time series forecasting

Background:Improving financial time series forecasting is one of the most challenging and vital issues facing numerous financial analysts and decision makers.Given its direct impact on related decisions,various attempts have been made to achieve more accurate and reliable forecasting results,of which the combining of individual models remains a widely applied approach.In general,individual models are combined under two main strategies:series and parallel.While it has been proven that these strategies can improve overall forecasting accuracy,the literature on time series forecasting remains vague on the choice of an appropriate strategy to generate a more accurate hybrid model.Methods:Therefore,this study’s key aim is to evaluate the performance of series and parallel strategies to determine a more accurate one.Results:Accordingly,the predictive capabilities of five hybrid models are constructed on the basis of series and parallel strategies compared with each other and with their base models to forecast stock price.To do so,autoregressive integrated moving average(ARIMA)and multilayer perceptrons(MLPs)are used to construct two series hybrid models,ARIMA-MLP and MLP-ARIMA,and three parallel hybrid models,simple average,linear regression,and genetic algorithm models.Conclusion:The empirical forecasting results for two benchmark datasets,that is,the closing of the Shenzhen Integrated Index(SZII)and that of Standard and Poor’s 500(S&P 500),indicate that although all hybrid models perform better than at least one of their individual components,the series combination strategy produces more accurate hybrid models for financial time series forecasting.

Time-series analysis of monthly rainfall data for the Mahanadi River Basin, India

Time series analysis has two goals, modeling random mechanisms and predicting future series using historical data. In the present work, a uni-variate time series autoregressive integrated moving average （ARIMA） model has been developed for （a） simulating and forecasting mean rainfall, obtained using Theissen weights; over the Mahanadi River Basin in India, and （b） simula^ag and forecasting mean rainfall at 38 rain-gauge stations in district towns across the basin. For the analysis, monthly rainfall data of each district town for the years 1901-2002 （102 years） were used. Theissen weights were obtained over the basin and mean monthly rainfall was estimated. The trend and seasonality observed in ACF and PACF plots of rainfall data were removed using power transformation （a=0.5） and first order seasonal differencing prior to the development of the ARIMA model. Interestingly, the AR1MA model （1,0,0）（0,1,1）12 developed here was found to be most suitable for simulating and forecasting mean rainfall over the Mahanadi River Basin and for all 38 district town rain-gauge stations, separately. The Akaike Information Criterion （AIC）, good- ness of fit （Chi-square）, R2 （coefficient of determination）, MSE （mean square error） and MAE （mea absolute error） were used to test the validity and applicability of the developed ARIMA model at different stages. This model is considered appropriate to forecast the monthly rainfall for the upcoming 12 years in each district town to assist decision makers and policy makers establish priorities for water demand, storage, distribution, and disaster management.

Modeling and forecasting time series of precious metals:a new approach to multifractal data

We introduce a novel approach to multifractal data in order to achieve transcended modeling and forecasting performances by extracting time series out of local Hurst exponent calculations at a specified scale.First,the long range and co-movement dependencies of the time series are scrutinized on time-frequency space using multiple wavelet coherence analysis.Then,the multifractal behaviors of the series are verified by multifractal de-trended fluctuation analysis and its local Hurst exponents are calculated.Additionally,root mean squares of residuals at the specified scale are procured from an intermediate step during local Hurst exponent calculations.These internally calculated series have been used to estimate the process with vector autoregressive fractionally integrated moving average(VARFIMA)model and forecasted accordingly.In our study,the daily prices of gold,silver and platinum are used for assessment.The results have shown that all metals do behave in phase movement on long term periods and possess multifractal features.Furthermore,the intermediate time series obtained during local Hurst exponent calculations still appertain the co-movement as well as multifractal characteristics of the raw data and may be successfully re-scaled,modeled and forecasted by using VARFIMA model.Conclusively,VARFIMA model have notably surpassed its univariate counterpart(ARFIMA)in all efficacious trials while re-emphasizing the importance of comovement procurement in modeling.Our study’s novelty lies in using a multifractal de-trended fluctuation analysis,along with multiple wavelet coherence analysis,for forecasting purposes to an extent not seen before.The results will be of particular significance to finance researchers and practitioners.

NONEXISTENCE OF POSITIVE SOLUTIONS FOR A SEMI-LINEAR EQUATION INVOLVING THE FRACTIONAL LAPLACIAN IN R^N

In this paper, we consider the semilinear equation involving the fractional Laplacian in the Euclidian space R^n：（-△）^α/2u（x） ： f（xn）u^p（x）, x ∈R^n（0.1）in the subcritical case with 1〈 p〈n＋a/n-a.Instead of carrying out direct investigations on pseudo-differential equation （0.1）, we first seek its equivalent form in an integral equation as below：u（x）=∫R^nG∞（x, y） f（yn） u^p（y）dy,where G∞（x, y） is the Green＇s function associated with the fractional Laplacian in R^n. Employing the method of moving planes in integral forms, we are able to derive the nonexistence of positive solutions for （0.2） in the subcritical case. Thanks to the equivalence, same con- clusion is true for （0.1）.

CLASSIFICATION OF POSITIVE SOLUTIONS TO ASYSTEM OF HARDY-SOBOLEV TYPE EQUATIONS

In this paper, we are concerned with the following Hardy-Sobolev type system{(-?)^(α/2) u(x) =v^q(x)/|y|^(t_2) (-?)α/2 v(x) =u^p(x)/|y|^(t_1),x =(y, z) ∈(R ~k\{0}) × R^(n-k),(0.1)where 0 < α < n, 0 < t_1, t_2 < min{α, k}, and 1 < p ≤ τ_1 :=(n+α-2t_1)/( n-α), 1 < q ≤ τ_2 :=(n+α-2 t_2)/( n-α).We first establish the equivalence of classical and weak solutions between PDE system(0.1)and the following integral equations(IE) system{u(x) =∫_( R^n) G_α(x, ξ)v^q(ξ)/|η|t^2 dξ v(x) =∫_(R^n) G_α(x, ξ)(u^p(ξ))/|η|^(t_1) dξ,(0.2)where Gα(x, ξ) =(c n,α)/(|x-ξ|^(n-α))is the Green's function of(-?)^(α/2) in R^n. Then, by the method of moving planes in the integral forms, in the critical case p = τ_1 and q = τ_2, we prove that each pair of nonnegative solutions(u, v) of(0.1) is radially symmetric and monotone decreasing about the origin in R^k and some point z0 in R^(n-k). In the subcritical case (n-t_1)/(p+1)+(n-t_2)/(q+1)> n-α,1 < p ≤ τ_1 and 1 < q ≤ τ_2, we derive the nonexistence of nontrivial nonnegative solutions for(0.1).

云南省总人口预测模型的比较研究

本文以1973~2018年云南省总人口为例,分别建立Holt两参数指数平滑模型、ARIMA模型和三次多项式模型,利用最小AIC准则从ARIMA模型中选出了ARIMA(4,3,1)模型,与Holt两参数指数平滑模型和三次多项式模型做比较。通过模型预测值的平均误差率和残差的波动幅度的比较后,发现ARIMA(4,3,1)模型的拟合精度较高,适合用来预测短期的总人口数。基于此分析对云南省总人口进行了8期数的预测,发现云南省总人口数量呈现不断增加的趋势,但总人口数增长速率下降,总人口数量趋向饱和状态。

Anomaly Detection and Pattern Differentiation in Monitoring Data from Power Transformers

Aiming at the problem of abnormal data generated by a power transformer on-line monitoring system due to the influences of transformer operation state change,external environmental interference,communication interruption,and other factors,a method of anomaly recognition and differentiation for monitoring data was proposed.Firstly,the empirical wavelet transform(EWT)and the autoregressive integrated moving average(ARIMA)model were used for time series modelling of monitoring data to obtain the residual sequence reflecting the anomaly monitoring data value,and then the isolation forest algorithm was used to identify the abnormal information,and the monitoring sequence was segmented according to the recognition results.Secondly,the segmented sequence was symbolised by the improved multi-dimensional SAX vector representation method,and the assessment of the anomaly pattern was made by calculating the similarity score of the adjacent symbol vectors,and the monitoring sequence correlation was further used to verify the assessment.Finally,the case study result shows that the proposed method can reliably recognise abnormal data and accurately distinguish between invalid and valid anomaly patterns.

Predicting Electric Energy Consumption for a Jerky Enterprise

Wholesale and retail markets for electricity and power require consumers to forecast electricity consumption at different time intervals. The study aims to increase economic efficiency of the enterprise through the introduction of algorithm for forecasting electric energy consumption unchanged in technological process. Qualitative forecast allows you to essentially reduce costs of electrical energy, because power cannot be stockpiled. Therefore, when buying excess electrical power, costs can increase either by selling it on the balancing energy market or by maintaining reserve capacity. If the purchased power is insufficient, the costs increase is due to the purchase of additional capacity. This paper illustrates three methods of forecasting electric energy consumption: autoregressive integrated moving average method, artificial neural networks and classification and regression trees. Actual data from consuming of electrical energy was used to make day, week and month ahead prediction. The prediction effect of prediction model was proved in Statistica simulation environment. Analysis of estimation of the economic efficiency of prediction methods demonstrated that the use of the artificial neural networks method for short-term forecast allowed reducing the cost of electricity more efficiently. However, for mid- range predictions, the classification and regression tree was the most efficient method for a Jerky Enterprise. The results indicate that calculation error reduction allows decreases expenses for the purchase of electric energy.

Two-phase micro-and macro-time scales in particle-laden turbulent channel flows

The micro- and macro-time scales in two-phase turbulent channel flows are investigated using the direct nu- merical simulation and the Lagrangian particle trajectory methods for the fluid- and the particle-phases, respectively. Lagrangian and Eulerian time scales of both phases are cal- culated using velocity correlation functions. Due to flow anisotropy, micro-time scales are not the same with the theo- retical estimations in large Reynolds number （isotropic） tur- bulence. Lagrangian macro-time scales of particle-phase and of fluid-phase seen by particles are both dependent on particle Stokes number. The fluid-phase Lagrangian inte- gral time scales increase with distance from the wall, longer than those time scales seen by particles. The Eulerian inte- gral macro-time scales increase in near-wall regions but de- crease in out-layer regions. The moving Eulerian time scales are also investigated and compared with Lagrangian integral time scales, and in good agreement with previous measure- ments and numerical predictions. For the fluid particles the micro Eulerian time scales are longer than the Lagrangian ones in the near wall regions, while away from the walls the micro Lagrangian time scales are longer. The Lagrangian integral time scales are longer than the Eulerian ones. The results are useful for further understanding two-phase flow physics and especially for constructing accurate prediction models of inertial particle dispersion.

Forecasting the Monthly Reported Cases of Human Immunodeficiency Virus (HIV) at Minna Niger State, Nigeria

There has been a moderate increase in newly diagnosed HIV-infected Minna populace, which calls for serious attention. This study used time series data based on monthly HIV cases from January 2007 to December 2018 taken from the statistical data document on HIV prevalence recorded in General Hospital Minna, Niger State. The methodology employed to analyze the data is based on mathematical models of ARMA, ARIMA and SARIMA which were computed and diagnosed. From the results of parameter estimation of the models, ARMA(2, 1) model was the best model among the other ARMA models using information criteria (AIC). Diagnostic test was run on the ARMA(2, 1) model where the results show that the model was adequate and normally distributed using Box-Lung test and Q-Q plot respectively. Furthermore, ARIMA of first and second differences was estimated and ARIMA(1, 0, 1) was the best model from the result of the AIC and diagnostic test carried out which revealed that the model was adequate and normally distributed using Box-Lung and Q-Q plot respectively. Furthermore, the results obtained in the ARMA and ARIMA models were used to arrive at a combined model given as ARIMA(1, 0, 1) × SARIMA(1, 0, 1)12 which was subsequently estimated and found to be adequate from the result of the Box-Lung and Q-Q plot respectively. Post forecasting estimation and performance evolution were evaluated using the RMSE and MAE. The results showed that, ARIMA(1, 0, 1) × SARIMA(1, 0, 1)12 is the best forecasting model followed by ARIMA(1, 0, 2) on monthly HIV prevalence in Minna, Niger state.

A Hybrid Methodology for Short Term Temperature Forecasting

Developing a reliable weather forecasting model is a complicated task, as it requires heavy IT resources as well as heavy investments beyond the financial capabilities of most countries. In Lebanon, the prediction model used by the civil aviation weather service at Rafic Hariri International Airport in Beirut (BRHIA) is the ARPEGE model, (0.5) developed by the weather service in France. Unfortunately, forecasts provided by ARPEGE have been erroneous and biased by several factors such as the chaotic character of the physical modeling equations of some atmospheric phenomena (advection, convection, etc.) and the nature of the Lebanese topography. In this paper, we proposed the time series method ARIMA (Auto Regressive Integrated Moving Average) to forecast the minimum daily temperature and compared its result with ARPEGE. As a result, ARIMA method shows better mean accuracy (91%) over the numerical model ARPEGE (68%), for the prediction of five days in January 2017. Moreover, back to five months ago, in order to validate the accuracy of the proposed model, a simulation has been applied on the first five days of August 2016. Results have shown that the time series ARIMA method has offered better mean accuracy (98%) over the numerical model ARPEGE (89%) for the prediction of five days of August 2016. This paper discusses a multiprocessing approach applied to ARIMA in order to enhance the efficiency of ARIMA in terms of complexity and resources.