Time-domain Data Analysis of Maglev System EMI Based on ARIMA Model

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.

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.

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.

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.

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.

In order to model and forecast exchange rates in both developed and emerging countries, majority of time series analysts have employed various technical and fundamental approaches, the forecast outcome differs depending on the approach chosen or implemented. In this view, this study is about hybridization of Autoregressive Integrated Moving Average (ARIMA) with Generalized Autoregressive Conditional Heteroscedastic (GARCH) model in forecasting exchange rate using monthly data of the Nigerian Naira against the U.S. Dollar for the period of January 2002 to February 2020. The stationarity of the exchange rate series is examined using unit root test of Augmented Dickey Fuller (ADF) test and Kwaitkowski-Philips-Schmidt-Shin (KPSS) which showed that the series is non stationary. To make the exchange rate series stationary, the data was transformed by first differencing and appropriate ARIMA models were obtained using Box-Jenkins method. ARIMA (0,1,1) and ARIMA(0,1,2) models were selected using AIC criteria and the residuals of these models were found to be serially correlated and heteroscedastic; hence the need for the hybridization of ARIMA with GARCH model. Therefore ARIMA models were hybridized with GARCH(1,1) to form ARIMA(0,1,1)-GARCH(1,1) and ARIMA(0,1,2)-GARCH(1,1). The results of forecast performance indicates that the best model is ARIMA(0,1,1)–GARCH(1,1) which has the lowest Root Means Square Error (RMSE) and Mean Absolute Error( MAE).

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

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.

The forecasting of evapotranspiration (ET) in some water-stressed regions remains a major challenge due to the lack of reliable and sufficient historical datasets. For efficient water balance, ET remains the major component and its proper forecasting and quantifying is of the utmost importance. This study utilises the 18-year (2001 to 2018) MODIS ET obtained from a drought-affected irrigation scheme in the Eastern Cape Province of South Africa. This study conducts a teleconnection evaluation between the satellite-derived evapotranspiration (ET) time series and other related remotely sensed parameters such as the Normalised Difference Vegetation Index (NDVI), Normalised Difference Water Index (NDWI), Normalised Difference Drought Index (NDDI), and precipitation (P). This comparative analysis was performed by adopting the Mann–Kendall (MK) test, Sequential Mann–Kendall (SQ-MK) test, and Multiple Linear Regression methods. Additionally, the ET detailed time-series analysis with the Keiskamma River streamflow (SF) and monthly volumes of the Sandile Dam, which are water supply sources close to the study area, was performed using the Wavelet Analysis, Breaks for Additive Seasonal and Trend (BFAST), Theil–Sen statistic, and Correlation statistics. The MODIS-obtained ET was then forecasted using the Autoregressive Integrated Moving Average (ARIMA) and Artificial Neural Networks (ANNs) for a period of 5 years and four modelling performance evaluations such as the Root Mean Square Error (RMSE), Mean Absolute Percentage Error (MAPE), Mean Absolute Error (MAE), and the Pearson Correlation Coefficient (R) were used to evaluate the model performances. The results of this study proved that ET could be forecasted using these two time-series modeling tools; however, the ARIMA modelling technique achieved lesser values according to the four statistical modelling techniques employed with the RMSE for the ARIMA = 37.58, over the ANN = 44.18; the MAE for the ARIMA = 32.37, over the ANN = 35.88; the MAPE for the ARIMA = 17.26, over the ANN = 24.26; and for the R ARIMA = 0.94 with the ANN = 0.86. These results are interesting as they give hope to water managers at the irrigation scheme and equally serve as a tool to effectively manage the irrigation scheme.

<title>Abstract</title> <bold>Background</bold> Dengue remains an enduring public health concern across tropical and subtropical regions of China, with a disproportionate burden observed in economically disadvantaged areas. Dengue outbreaks can overwhelm healthcare systems and impede economic development. The development of timely and accurate predictive models for dengue incidence is critical for strengthening early warning systems and informing the strategic allocation of public health resources. <bold>Methods</bold> Monthly reported dengue cases in China from 2004–2024 were publicly available from the Chinese Center for Disease Control and Prevention. For model development and validation, the data were divided into training and testing subsets. Three models were subsequently constructed, namely, the autoregressive integrated moving average (ARIMA) model, a combined model of ARIMA and the back propagation neural network (ARIMA-BPNN), and a combined model of ARIMA and the Elman recurrent neural network (ARIMA-ERNN). The predictive accuracy of each model was evaluated via the mean absolute error (MAE), root mean square error (RMSE), corrected mean absolute percentage error (cMAPE) and coefficient of determination (R²) on both the training and testing sets. <bold>Results</bold> From 2004–2024, the average incidence of dengue in mainland China was 0.486 cases per 1,000,000 people annually, with yearly rates ranging from 0.031–34.161 cases per 1,000,000 people. While all three models demonstrated adequate performance in fitting the observed data, the ARIMA-BPNN model and the ARIMA-ERNN model consistently outperformed the conventional ARIMA model. Specifically, the ARIMA-BPNN model yielded the lowest MAE, RMSE, and cMAPE values, along with the highest R² across both the training and testing datasets. These findings suggest that the ARIMA-BPNN model possesses an enhanced ability to capture the nonlinear and dynamic patterns inherent in dengue transmission. In contrast, the ARIMA model exhibited reduced accuracy in forecasting peak incidences and abrupt temporal fluctuations, highlighting its limitations in modelling complex epidemiological trends. <bold>Conclusion</bold> Hybrid modelling approaches that combine ARIMA with neural network architectures, particularly the ARIMA-BPNN model, have demonstrated superior predictive accuracy in forecasting dengue incidence. These findings may contribute to outbreak preparedness and the timeliness and effectiveness of dengue control in China.

Forecasting the dynamics of cumulative COVID-19 cases (confirmed, recovered and deaths) for top-16 countries using statistical machine learning models: Auto-Regressive Integrated Moving Average (ARIMA) and Seasonal Auto-Regressive Integrated Moving Average (SARIMA)

Solar energy is one of the most promising renewable energy sources in Indonesia, particularly in Bali, which has relatively high solar irradiance throughout the year. However, daily variability in solar radiation caused by weather conditions and atmospheric factors leads to fluctuations in solar energy production, making accurate forecasting essential for effective energy planning. This study aims to evaluate the performance of the Autoregressive Integrated Moving Average (ARIMA), Long Short-Term Memory (LSTM), and hybrid ARIMA–LSTM models in forecasting daily solar energy at the Jembrana Climatological Station, Bali. The dataset consists of 10-minute solar radiation observations obtained from an Automatic Weather Station (AWS) for the period January 2023 to September 2025, which were aggregated into daily solar energy values expressed in kWh/m². Data preprocessing included missing value handling, outlier correction, normalization, and an 80:20 split between training and testing datasets. Model performance was evaluated using Root Mean Square Error (RMSE), Mean Absolute Error (MAE), and Mean Absolute Percentage Error (MAPE). The results show that the hybrid ARIMA–LSTM model achieved the best performance, with an RMSE of 0.960 kWh/m², MAE of 0.771 kWh/m², and MAPE of 22.245%, outperforming both the ARIMA and LSTM models. These findings indicate that the hybrid approach is more effective in capturing both linear and nonlinear characteristics of daily solar energy time series.

The present study was carried out to estimate the trends of area, production and productivity of wheat in North Gujarat. Yearly time series data on area, production and productivity of wheat of North Gujarat for the period of 1991-92 to 2021-22 were collected from the published reports by Directorate of Agriculture, Gujarat state, Gandhinagar. Polynomial and Autoregressive Integrated Moving Average (ARIMA) models were applied to analyze the area, production and productivity of wheat in North Gujarat. First, second and third-degree polynomial models were fitted to the original data and moving averages, with the best model selected based on adjusted R², Root Mean Square Error (RMSE), Mean Absolute Error (MAE), normality by the Shapiro-Wilk (1965) test and randomness of residuals by the Run test. ARIMA models were evaluated for stationarity and different orders (p, d, q) were assessed using autocorrelation function (ACF), partial autocorrelation function (PACF) and the models were selected on the basis of significant autoregressive and moving average term, lower value of Akaike’s Information Criteria (AIC) and Schwartz-Bayesian Criteria (SBC) and normality of residuals by Shapiro-Wilk (1965) test and Box-Ljung (1978) test. The cubic polynomial model on a four year moving average was most suitable for wheat production trends, while ARIMA (0, 2, 1) and ARIMA (0, 2, 2) were optimal for wheat area and production patterns.

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.

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.