Enhancing drought prediction precision with EEMD-ARIMA modeling based on standardized precipitation index.

The matter of success in forecasting precipitation is of great significance to flood control and drought relief, and water resources planning and management. For the nonlinear problem in forecasting precipitation time series, a hybrid prediction model based on variational mode decomposition (VMD) coupled with extreme learning machine (ELM) is proposed to reduce the difficulty in modeling monthly precipitation forecasting and improve the prediction accuracy. The monthly precipitation data in the past 60 years from Yan’an City and Huashan Mountain, Shaanxi Province, are used as cases to test this new hybrid model. First, the nonstationary monthly precipitation time series are decomposed into several relatively stable intrinsic mode functions (IMFs) by using VMD. Then, an ELM prediction model is established for each IMF. Next, the predicted values of these components are accumulated to obtain the final prediction results. Finally, three predictive indicators are adopted to measure the prediction accuracy of the proposed hybrid model, back propagation (BP) neural network, Elman neural network (Elman), ELM, and EMD-ELM models: mean absolute error (MAE), root mean squared error (RMSE), and mean absolute percentage error (MAPE). The experimental simulation results show that the proposed hybrid model has higher prediction accuracy and can be used to predict the monthly precipitation time series.

This study introduces discrete wavelet transform (DWT) coupled with the long-short-term memory (LSTM) model for drought prediction. We evaluate the W-LSTM model against the traditional ARIMA and conventional LSTM methods, based on the monthly precipitation data from January 1968 to January 2018 of Badeggi District in Niger State – Nigeria; which were evaluated into standardized precipitation index (SPI) of various timescales of 3, 6, 9, and 12 respectively. To understand any of the underlying features in the data, each of the SPI series was plotted graphically. Subsequently, the SPIs undergoes decomposition using Wavelet resulting in (three Details and an Approximation) components. The next step involved determining the input data based on the number of significant lags observed in PACF of each component, thereby restructuring the data to conform to LSTM’s network architecture, thereby making the modelling and forecasting of the input series by the LSTM network. Statistical evaluation metrics which include the root-mean-square error (RMSE), mean absolute error (MAE), mean absolute percentage error (MAPE), R2 and percentage of bias (PBIAS) are employed to assess the model accuracy. The W-LSTM model demonstrated superior performance over ARIMA and LSTM in forecasting, significantly reducing RMSE by up to 83.4% and improving R² by up to 147.5%. For SPI-12, W-LSTM achieved a 56.2% RMSE reduction over ARIMA and a 74.8% reduction over LSTM, with a 46.7% increase in MaPE, a 1.1% increase in R², and recorded the best PBIAS value of 2.078, compared to the other models. Similar trends were observed across SPI-6, SPI-9, and SPI-12, confirming W-LSTM’s effectiveness in minimizing errors and enhancing predictive accuracy when compared to standalone ARIMA and LSTM models.

BackgroundAccurate incidence prediction of sexually transmitted diseases (STDs) is critical for early prevention and better government strategic planning. In this paper, four different forecasting models were presented to predict the incidence of AIDS, gonorrhea, and syphilis.MethodsThe annual percentage changes in the incidence of AIDS, gonorrhea, and syphilis were estimated by using joinpoint regression. The performance of four methods, namely, the autoregressive integrated moving average (ARIMA) model, Elman neural network (ERNN) model, ARIMA-ERNN hybrid model and long short-term memory (LSTM) model, were assessed and compared. For 1-year prediction, the collected data from 2011 to 2020 were used for modeling to predict the incidence in 2021. For 5-year prediction, the collected data from 2011 to 2016 were used for modeling to predict the incidence from 2017 to 2021. The performance was evaluated based on four indices: mean square error (MSE), mean absolute error (MAE), and mean absolute percentage error (MAPE).ResultsThe morbidities of AIDS and syphilis are on the rise, and the morbidity of gonorrhea has declined in recent years. The optimal ARIMA models were determined: ARIMA(2,1,2)(0,1,1)12, ARIMA(1,1,2)(0,1,2)12, and ARIMA(3,1,2)(1,1,2)12 for AIDS, gonorrhea, and syphilis 1-year prediction, respectively; ARIMA (2,1,2)(0,1,1)12, ARIMA(1,1,2)(0,1,2)12, and ARIMA(2,1,1)(0,1,0)12 for AIDS, gonorrhea and syphilis 5-year prediction, respectively. For 1-year prediction, the MAPEs of ARIMA, ERNN, ARIMA-ERNN, and LSTM for AIDS are 23.26, 20.24, 18.34, and 18.63, respectively; For gonorrhea, the MAPEs are 19.44, 18.03, 17.77, and 5.09, respectively; For syphilis, the MAPEs are 9.80, 9.55, 8.67, and 5.79, respectively. For 5-year prediction, the MAPEs of ARIMA, ERNN, ARIMA-ERNN, and LSTM for AIDS are 12.86, 23.54, 14.74, and 25.43, respectively; For gonorrhea, the MAPEs are 17.07, 17.95, 16.46, and 15.13, respectively; For syphilis, the MAPEs are 21.88, 24.00, 20.18 and 11.20, respectively. In general, the performance ranking of the four models from high to low is LSTM, ARIMA-ERNN, ERNN, and ARIMA.ConclusionThe time series predictive models show their powerful performance in forecasting STDs incidence and can be applied by relevant authorities in the prevention and control of STDs.

Nowadays , nonlinear time series and artificial neural networks (ANN) models are used for forecasting in the field of business, agriculture and soon. Recent studies have shown, ANN have been successfully used for forecasting of financial and agriculture data series The classical methods used for time series prediction like Box-Jenkins or ARIMA assumes that there is a linear relationship between inputs and outputs. ANN have more advantages that can approximate to model both linear and nonlinear structures in time series, they are not able to handling both structures equally well. The autoregressive integrated moving average (ARIMA) model and two ANN models namely, Radial basis function neural networks (RBFNN), and Elman recurrent neural networks (ERNN) methods were applied to Hyderabad airport traffic data. The data obtained for 15 years from 2002–2003 to 2016–2017 about domestic and international passenger of International Airport of Hyderabad, India. In this research paper, we compared the performances of ARIMA, RBFNN and ERNN were based on three measures: mean absolute error (MAE), mean absolute percentage error (MAPE), and root mean square error (RMSE). The results showed that RBFNN obtained the smallest MAE, MAPE and RMSE in both the modeling and forecasting processes. The performances of the three models ranked in ascending order were: ARIMA, ERNN and the RBFNN model. Keywords: T ime series, forecasting, artificial neural networks, ARIMA models, radial basis function neural networks, and Elman recurrent neural networks Cite this Article R. Ramakrishna, Berhe Aregay, Tewodros Gebregergs. The Comparison in Time Series Forecasting of Air Traffic Data by Autoregressive Integrated Moving Average Model, Radial Basis Function and Elman Recurrent Neural Networks. Research & Reviews: Journal of Statistics . 2018; 7(3): 75–90p.

Food and non-alcoholic beverages are highly important for individuals to continue staying alive and living healthy lives. The increase in the prices of food and non-alcoholic beverages experienced across the world over years has continued to make food and non-alcoholic beverages not to be accessible and affordable to individuals and families having a low income. The aim of this particular research study was to identify how Kenya’s CPI of food and non-alcoholic beverages could be modelled using Autoregressive Integrated Moving Average (ARIMA) models for forecasting future values for the next two years. The data used for the study was that of Kenya’s CPI of food and non-alcoholic beverages for the period starting from February 2009 to April 2024 obtained from the International Monetary Fund (IMF) database. The best specification for the ARIMA model was identified using Akaike Information Criterion (AIC), root mean square error (RMSE), mean absolute error (MAE), mean absolute percentage error (MAPE) and mean absolute scaled error (MASE) and assessing whether residuals of the model were independent and normally distributed with a variance that is constant an whether the model has most of its coefficients being significant statistically. ARIMA (3, 1, 0) (1, 0, 0) model was identified as the best ARIMA model for modeling Kenya’s CPI of food and non-beverages for forecasting future values among the ARIMA models considered. Using this particular model, Kenya’s CPI of food and non-alcoholic beverages was forecasted to increase only slightly with time to reach a value of about 165.70 by March 2026.

Time series analysis of aerosol optical depth over New Delhi using Box–Jenkins ARIMA modeling approach

The Standardized Precipitation Index (SPI) is widely used as drought meteorological index, to identify the duration and/or severity of a drought. The SPI is usually computed by fitting the gamma probability distribution to the observed precipitation data. In this work, the possibility to calculate SPI by fitting to the precipitation data the normal and the log-normal probability distributions was studied. For this purpose, 19 time series of monthly precipitation of 76 years were used, and the assumption that the gamma probability distribution would provide better representation of the precipitation data than log-normal and normal distributions, at various time scales (1, 3, 6, 12 and 24 months) was tested. It is concluded that for SPI of 12 or 24 months, the log-normal or the normal probability distribution can be used for simplicity, instead of gamma, producing almost the same results.

Globally, since the outbreak of the Omicron variant in November 2021, the number of confirmed cases of COVID-19 has continued to increase, posing a tremendous challenge to the prevention and control of this infectious disease in many countries. The global daily confirmed cases of COVID-19 between November 1, 2021, and February 17, 2022, were used as a database for modeling, and the ARIMA, MLR, and Prophet models were developed and compared. The prediction performance was evaluated using mean absolute error (MAE), mean absolute percentage error (MAPE), and root mean square error (RMSE). The study showed that ARIMA (7, 1, 0) was the optimum model, and the MAE, MAPE, and RMSE values were lower than those of the MLR and Prophet models in terms of fitting performance and forecasting performance. The ARIMA model had superior prediction performance compared to the MLR and Prophet models. In real-world research, an appropriate prediction model should be selected based on the characteristics of the data and the sample size, which is essential for obtaining more accurate predictions of infectious disease incidence.

Drought is a complex and frequently occurring natural hazard in many parts of the world. Therefore, accurate drought forecasting is essential to mitigate its adverse impacts. This research has inferred the implication and the appropriateness of the extreme learning machine (ELM) algorithm for drought forecasting. For numerical evaluation, time series data of the Standardized Precipitating Temperature Index (SPTI) are used for nine meteorological stations located in various climatological zones of Pakistan. To assess the performance of ELM, this research includes parallel inferences of multilayer perceptron (MLP) and autoregressive integrated moving average (ARIMA) models. The performance of each model is assessed using root mean square error (RMSE), mean absolute error (MAE), mean absolute percent error (MAPE), Kling‐Gupta efficiency (KGE), Willmott index (WI), and Karl Pearson’s correlation coefficient. Generally, graphical results illustrated an excellent performance of the ELM algorithm over MLP and ARIMA models. For training data of SPTI‐1, ELM’s best performance has observed at Chitral station (RMSE = 0.374, KGE = 0.838, WI = 0.960, MAE = 0.272, MAPE = 259.59, R = 0.93). For SPTI‐1 at Astore station, the numerical results are (RMSE = 0.688, KGE = 0.988, WI = 0.997, MAE = 0.798, MAPE = 247.35). The overall results indicate that the ELM outperformed by producing the smallest RMSE, MAE, and MAPE values and maximum values for KGE, WI, and correlation coefficient values at almost all the selected meteorological stations for (1, 3, 6, 9, and 12) month time scales. In summary, this research endorses the use of ELM for accurate drought forecasting.

Precipitation is one of the most variable climatic parameters, as it is determined by many physical processes. The spatiotemporal characteristics of precipitation have been significantly affected by climate change during the past decades. Analysis of precipitation trends is challenging, especially in regions such as Greece, which is characterized by complex topography and includes several ungauged areas. With this study, we aim to shed new light on the climatic characteristics and inter-annual trends of precipitation over Greece. For this purpose, we used ERA5 monthly precipitation data from 1950 to 2020 to estimate annual Theil–Sen trends and Mann–Kendall significance over Greece and surrounding areas. Additionally, in order to analyze and model the nonlinear relationships of monthly precipitation time series, we used generalized additive models (GAMs). The results indicated significant declining inter-annual trends of areal precipitation over the study area. Declining trends were more pronounced in winter over western and eastern Greece, but trends in spring, summer and autumn were mostly not significant. GAMs showcased that the trends were generally characterized by nonlinearity and precipitation over the study area presented high inter-decadal variability. Combining the results, we concluded that precipitation did not linearly change during the past 7 decades, but it first increased from the 1950s to the late 1960s, consequently decreased until the early 1990s and, afterwards, presented an increase until 2020 with a smaller rate than the 1950–1960s.

Oilseeds have been the backbone of India’s agricultural economy since long. Oilseed crops play the second most important role in Indian agricultural economy, next to food grains, in terms of area and production. Oilseeds production in India has increased with time, however, the increasing demand for edible oils necessitated the imports in large quantities, leading to a substantial drain of foreign exchange. The need for addressing this deficit motivated a systematic study of the oilseeds economy to formulate appropriate strategies to bridge the demand-supply gap. In this study, an effort is made to forecast oilseeds production by using Autoregressive Integrated Moving Average (ARIMA) model, which is the most widely used model for forecasting time series. One of the main drawbacks of this model is the presumption of linearity. The Group Method of Data Handling (GMDH) model has also been applied for forecasting the oilseeds production because it contains nonlinear patterns. Both ARIMA and GMDH are mathematical models well-known for time series forecasting. The results obtained by the GMDH are compared with the results of ARIMA model. The comparison of modeling results shows that the GMDH model perform better than the ARIMA model in terms of mean absolute error (MAE), mean absolute percentage error (MAPE), and root mean square error (RMSE). The experimental results of both models indicate that the GMDH model is a powerful tool to handle the time series data and it provides a promising technique in time series forecasting methods.

Monkeypox virus is gaining attention due to its severity and spread among people. This study sheds light on the modeling and forecasting of new monkeypox cases. Knowledge about the future situation of the virus using a more accurate time series and stochastic models is required for future actions and plans to cope with the challenge. We conduct a side-by-side comparison of the machine learning approach with the traditional time series model. The multilayer perceptron model (MLP), a machine learning technique, and the Box-Jenkins methodology, also known as the ARIMA model, are used for classical modeling. Both methods are applied to the Monkeypox cumulative data set and compared using different model selection criteria such as root mean square error, mean square error, mean absolute error, and mean absolute percentage error. With a root mean square error of 150.78, the monkeypox series follows the ARIMA (7,1,7) model among the other potential models. Comparatively, we use the multilayer perceptron (MLP) model, which employs the sigmoid activation function and has a different number of hidden neurons in a single hidden layer. The root mean square error of the MLP model, which uses a single input and ten hidden neurons, is 54.40, significantly lower than that of the ARIMA model. The actual confirmed cases versus estimated or fitted plots also demonstrate that the multilayer perceptron model has a better fit for the monkeypox data than the ARIMA model. When it comes to predicting monkeypox, the machine learning method outperforms the traditional time series. A better match can be achieved in future studies by applying the extreme learning machine model (ELM), support vector machine (SVM), and some other methods with various activation functions. It is thus concluded that the selected data provide a real picture of the virus. If the situations remain the same, governments and other stockholders should ensure the follow-up of Standard Operating Procedures (SOPs) among the masses, as the trends will continue rising in the upcoming 10 days. However, governments should take some serious interventions to cope with the virus. In the ARIMA models selected for forecasting, we did not incorporate the effect of covariates such as the effect of net migration of monkeypox virus patients, government interventions, etc.

The primary objective of this study is to evaluate the accuracy of different forecasting models for monthly wind farm electricity production. This study compares the effectiveness of three forecasting models: Autoregressive Integrated Moving Average (ARIMA), Seasonal ARIMA (SARIMA), and Support Vector Regression (SVR). This study utilizes data from two wind farms located in Poland—‘Gizałki’ and ‘Łęki Dukielskie’—to exclude the possibility of biased results due to specific characteristics of a single farm and to allow for a more comprehensive comparison of the effectiveness of both time series analysis methods. Model parameterization was optimized through a grid search based on the Mean Absolute Percentage Error (MAPE). The performance of the best models was evaluated using Mean Bias Error (MBE), MAPE, Mean Absolute Error (MAE), and R2Score. For the Gizałki farm, the ARIMA model outperformed SARIMA and SVR, while for the Łęki Dukielskie farm, SARIMA proved to be the most accurate, highlighting the importance of optimizing seasonal parameters. The SVR method demonstrated the lowest effectiveness for both datasets. The results indicate that the ARIMA and SARIMA models are effective for forecasting wind farm energy production. However, their performance is influenced by the specificity of the data and seasonal patterns. The study provides an in-depth analysis of the results and offers suggestions for future research, such as extending the data to include multidimensional time series. Our findings have practical implications for enhancing the accuracy of wind farm energy forecasts, which can significantly improve operational efficiency and planning.

Dengue hemorrhagic fever (DHF) is one of the most widespread and deadly diseases in several parts of Indonesia. An accurate forecast-based model is required to reduce the incidence rate of this disease. Time-series methods such as autoregressive integrated moving average (ARIMA) models are used in epidemiology as statistical tools to study and forecast DHF and other infectious diseases. The present study attempted to forecast the monthly confirmed DHF cases via a time-series approach. The ARIMA, seasonal ARIMA (SARIMA), and long short-term memory (LSTM) models were compared to select the most accurate forecasting method for the deadly disease. The data were obtained from the Surabaya Health Office covering January 2014 to December 2016. The data were partitioned into the training and testing sets. The best forecasting model was selected based on the lowest values of accuracy metrics such as the root mean square error (RMSE), mean absolute error (MAE), and mean absolute percentage error (MAPE). The findings demonstrated that the SARIMA (2,1,1) (1,0,0) model was able to forecast the DHF outbreaks in Surabaya City compared to the ARIMA (2,1,1) and LSTM models. We further forecasted the DHF cases for 12 month horizons starting from January 2017 to December 2017 using the SARIMA (2,1,1) (1,0,0), ARIMA (2,1,1), and LSTM models. The results revealed that the SARIMA (2,1,1) (1,0,0) model outperformed the ARIMA (2,1,1) and LSTM models based on the goodness-of-fit measure. The results showed significant seasonal outbreaks of DHF, particularly from March to September. The highest cases observed in May suggested a significant seasonal correlation between DHF and air temperature. This research is the first attempt to analyze the time-series model for DHF cases in Surabaya City and forecast future outbreaks. The findings could help policymakers and public health specialists develop efficient public health strategies to detect and control the disease, especially in the early phases of outbreaks.

. Drought exerts a significant impact on both the environment and agricultural sectors, particularly in farming. Addressing the impact of drough is essential for all stackholders who depends on natural water sources. Adaptive Neuro-Fuzzy Inference System (ANFIS), one of the hybrid artificial neural networks, is primarily used in this study to model the drought. The study utilizes the monthly precipitation data spanning for last 39 years for the Coimbatore district. Initial steps involve the estimating of Standardized Precipitation Index (SPI) values at a 3-month scale using monthly precipitation values, considering the impact of North-East Monsoon over the district. Several ANFIS forecasting models are developed using the mean precipitation value of North-East Monsoon season and the computed values of SPI. The evaluation of these models incorporates several error metrics like Root Mean Square Error (RMSE), Mean Absolute Error (MAE), and the coefficient of determination (R2), allowing for a comprehensive comparison between the projected ANFIS model and observed values. The model which exhibits the lowest RMSE and MAE, coupled with a high R2, are considered as robust fit to the data.