Evaluation of Several Error Measures Applied to the Sales Forecast System of Chemicals Supply Enterprises

BackgroundInfections caused by multidrug-resistant organisms (MDROs) continue to pose serious challenges for hospital infection control, often resulting in longer hospitalizations, increased patient morbidity, and higher healthcare costs. While time series forecasting has gained traction as a tool for anticipating MDROs trends, there remains a lack of real-world studies comparing the effectiveness of different modeling approaches using hospital-based data.ObjectiveThis study aimed to evaluate and compare the predictive performance of four time series models—SARIMA, ETS, Prophet, and NNETAR—using monthly MDROs infection data collected from a tertiary hospital in China between 2014 and 2023, with the goal of forecasting trends for 2024.MethodsMonthly MDROs infection rates from January 2014 to December 2023 were analyzed using R software. Stationarity was assessed through unit root tests, and appropriate differencing was applied as needed. Each model was fitted to the training dataset and used to forecast infection rates for the year 2024. Model accuracy was assessed by comparing forecasted values with actual 2024 data using root mean squared error (RMSE), mean absolute error (MAE), mean absolute percentage error (MAPE), symmetric mean absolute percentage error (sMAPE), and mean absolute scaled error (MASE).ResultsAmong the models, SARIMA produced the most consistent and reliable forecasts (RMSE = 0.0469, MAE = 0.0424, MAPE = 20.74%, sMAPE = 21.27%, MASE = 0.932), with residuals satisfying tests for independence and normality. Although the ETS model achieved lower numerical point errors (RMSE = 0.0367, MAE = 0.0305, MAPE = 14.46%, sMAPE = 14.81%, MASE = 0.670), its residual diagnostics raised concerns regarding robustness. The Prophet (RMSE = 0.0499, MAE = 0.0439, MAPE = 20.41%, sMAPE = 22.15%, MASE = 0.563) and NNETAR (RMSE = 0.0697, MAPE = 30.60%, sMAPE = 30.60%, MASE = 0.072) models captured certain aspects of the data dynamics but showed lower overall robustness compared with SARIMA.ConclusionBased on its overall robustness and diagnostic consistency, SARIMA is recommended for short- to medium-term forecasting of MDROs infection trends. The other models, while less reliable on their own, may still be valuable for validating trends and conducting sensitivity analyses to support hospital infection control planning.

<span>The study investigates the potential of integrating radon gas concentration telemonitoring systems with machine learning techniques to enhance earthquake magnitude prediction. Conducted in Pacitan, East Java, Indonesia, where the stations are near the active Grundulu fault, the research employs Random Forest (RF), Extreme Gradient Boosting (XGB), Neural Network (NN), AdaBoost (AB), and Support Vector Machine (SVM) methods. Utilizing real-time radon gas concentration measurements, the study aims to refine earthquake magnitude prediction, crucial for disaster preparedness. The evaluation involves multiple metrics like Mean Absolute Error (MAE), Mean Absolute Percentage Error (MAPE), Root Mean Square Error (RMSE), Mean Squared Error (MSE), Symmetric Mean Absolute Percentage Error (SMAPE), and cnSMAPE. XGB and SVM emerge as top performers, showcasing superior predictive accuracy with minimal errors across various metrics. XGB achieved MAE (0.33), MAPE (6.03%), RMSE (0.51), MSE (0.26), SMAPE (0.06), and cnMAPE (0.97), while SVM recorded MAE (0.34), MAPE (6.20%), RMSE (0.51), MSE (0.26), SMAPE (0.06), and cnMAPE (0.97). The analysis reveals XGB as the most effective method, boasting the lowest error values. The study underscores the importance of expanding data availability to enhance predictive models, ultimately contributing to more precise earthquake magnitude predictions and effective mitigation strategies.</span>

Wind energy is a promising alternativefor renewable source of energy pursued world-wide to reduce carbon emissions for a green future. The prediction of wind speed is a challenging subject and plays an instrumental role in development of wind power systems (particularly grid connected renewable energy systems where predicting wind speed facilitates manipulation of the load on the grid). Modern machine learning techniques including neural networks have been widely utilized for this purpose. Literature indicates availability of several models for estimation of the wind speed one hour ahead and the hourly wind speed data profile one day ahead. This paper considers the prediction of wind energy as a univariate time series (UVT) prediction problem and employs major prediction algorithms including the K-Nearest Neighbors (kNN), Random Forest (RF), Support Vector Regression (SVR), Holt-Winter and ARIMA method. Forecasting a univariate time series depends only on past wind speed data values, rather than use of external data attributes like wind direction or weather forecast for prediction algorithm. In the present study (as a case-study), 13 years of hourly average wind speed data (of the period 1970-1982) of Yanbu, Saudi Arabia has been utilized to evaluate the performance of selected algorithms. Yanbu is an industrial city that plays a major role in the economy of Saudi Arabia. The findings showed that SVR, RF and ARIMA methods exhibit a better forecastingperformance in relation to four evaluation parameters of Mean Absolute Percentage Error(MAPE),Symmetric Mean Absolute Percentage Error (sMAPE),Mean Absolute Error (MAE) and Mean Absolute Scaled Error (MASE).

BackgroundThis study adopted complete meteorological indicators, including eight items, to explore their impact on hand, foot, and mouth disease (HFMD) in Fuzhou, and predict the incidence of HFMD through the long short-term memory (LSTM) neural network algorithm of artificial intelligence.MethodA distributed lag nonlinear model (DLNM) was used to analyse the influence of meteorological factors on HFMD in Fuzhou from 2010 to 2021. Then, the numbers of HFMD cases in 2019, 2020 and 2021 were predicted using the LSTM model through multifactor single-step and multistep rolling methods. The root mean square error (RMSE), mean absolute error (MAE), mean absolute percentage error (MAPE) and symmetric mean absolute percentage error (SMAPE) were used to evaluate the accuracy of the model predictions.ResultsOverall, the effect of daily precipitation on HFMD was not significant. Low (4 hPa) and high (≥ 21 hPa) daily air pressure difference (PRSD) and low (< 7 °C) and high (> 12 °C) daily air temperature difference (TEMD) were risk factors for HFMD. The RMSE, MAE, MAPE and SMAPE of using the weekly multifactor data to predict the cases of HFMD on the following day, from 2019 to 2021, were lower than those of using the daily multifactor data to predict the cases of HFMD on the following day. In particular, the RMSE, MAE, MAPE and SMAPE of using weekly multifactor data to predict the following week's daily average cases of HFMD were much lower, and similar results were also found in urban and rural areas, which indicating that this approach was more accurate.ConclusionThis study’s LSTM models combined with meteorological factors (excluding PRE) can be used to accurately predict HFMD in Fuzhou, especially the method of predicting the daily average cases of HFMD in the following week using weekly multifactor data.

The air filtration system is the only line of defense for outside air to enter the gas turbine. It is of great significance to study and predict the variation trend of air filtration system performance to ensure the safety, economy and reliability of gas turbine. In this work, the gas turbine air filtration system test is carried out, and the test data of fine filter differential pressure, ambient temperature and relative humidity are measured. Then the LSTM and transformation-gated LSTM (GT-LSTM) methods are utilized to predict the variation trend of air filtration system performance. Finally, the root mean square error (RMSE), mean absolute error (MAE), mean absolute percentage error (MAPE), and symmetric mean absolute percentage error (SMAPE) are employed to evaluate the prediction effect quantitatively. The research results show that the RMSE, MAE, MAPE and SMAPE are only 0.0110, 0.0076, 3.3778 and 3.4655 by TG-LSTM method. The prediction error based on TG-LSTM method is smaller than LSTM method. Thus the prediction effect of TG-LSTM method is better than that of the LSTM method, and the TG-LSTM method is suitable for the performance prediction of gas turbine air filtration system.

BackgroundArtificial intelligence tools, including large language models such as ChatGPT, are increasingly integrated into clinical and primary care research. However, their ability to assist with specialized statistical tasks, such as sample size estimation, remains largely unexplored.MethodsWe evaluated the accuracy and reproducibility of ChatGPT-4.0 and ChatGPT-4o in estimating sample sizes across 24 standard statistical scenarios. Examples were selected from a statistical textbook and an educational website, covering basic methods such as estimating means, proportions, and correlations. Each example was tested twice per model. Models were accessed through the ChatGPT web interface, with a new independent chat session initiated for each round. Accuracy was assessed using mean and median absolute percentage error compared with validated reference values. Reproducibility was assessed using symmetric mean and median absolute percentage error between rounds. Comparisons were performed using Wilcoxon signed-rank tests.ResultsFor ChatGPT-4.0 and ChatGPT-4o, absolute percentage errors ranged from 0% to 15.2% (except one case: 26.3%) and 0% to 14.3%, respectively, with most examples showing errors below 5%. ChatGPT-4o showed better accuracy than ChatGPT-4.0 (mean absolute percentage error: 3.1% vs. 4.1% in round#1, P-value = .01; 2.8% vs. 5.1% in round#2, P-value =.02) and lower symmetric mean absolute percentage error (0.8% vs. 2.5%), though not significant (P-value = .18).ConclusionsChatGPT-4.0 and ChatGPT-4o provided reasonably accurate sample size estimates across standard scenarios, with good reproducibility. However, inconsistencies were observed, underscoring the need for cautious interpretation and expert validation. Further research should assess performance in more complex contexts and across a broader range of AI models.

Pork is one of the main methods for human intake of animal protein, and its price level will directly affect people’s daily lives. In order to realize the prediction of the prices in the live pig (mid-term) market, based on monthly data provided by China National Database, in this paper we propose a combination of artificial neural network models based on bidirectional recurrent neural network and bidirectional long short-term memory as the backbone network. The prediction errors achieved on our data set for Mean Square Error (MSE), Root Mean Squared Error (RMSE), Mean Absolute Error (MAE), Mean Absolute Percentage Error (MAPE) and Symmetric Mean Absolute Percentage Error (SMAPE) are 0.48, 0.69, 0.53, 3.37%, 3.37% respectively. Compared with other deep learning models, the error of this method is small, which shows that it has the ability to predict the time series of pork price.

The wind power industry has experienced a significant increase and popularity in recent times, and the latest statistics indicate that this sector is still thriving. However, one of the essential steps in developing wind energy projects is finding suitable sites for wind farms, which involves understanding the nature of wind speed, wind direction, terrain, and environmental impacts. To predict the wind energy production over the expected lifespan of a wind farm, vertical wind speed extrapolation to the hub height of the wind turbine is necessary. Therefore, this study presents a comprehensive evaluation of seven statistical approaches for vertical wind speed extrapolation, including Generalized Linear Models (GLM), Linear Regression (LR), Support Vector Machines (SVM), Generalized Additive Models (GAM), Gaussian Process Regression (GPR), Regression Tree (RT), and Ensemble Regression (ER). The accuracy of these methods is assessed using performance metrics such as Mean Squared Error (MSE), Root Mean Squared Error (RMSE), Normalized RMSE (NRMSE), Normalized MSE (NMSE), Mean Bias Error (MBE), Mean Absolute Error (MAE), Mean Percentage Error (MPE), Mean Absolute Percentage Error (MAPE), Symmetric Mean Absolute Percentage Error (SMAPE), and R-squared (R2). The study concludes that, on average, GLM performs the best out of all seven statistical methods.

Malaria is a major public health concern in tropics and subtropics. Accurate malaria prediction is critical for reporting ongoing incidences of infection and its control. Hence, the purpose of this investigation was to evaluate the performances of different models of predicting malaria incidence in Marodijeh region, Somaliland. The study used monthly historical data from January 2011 to December 2020. Five deterministic and stochastic models, i.e. Seasonal Autoregressive Moving Average (SARIMA), Holt-Winters' Exponential Smoothing, Harmonic Model, Seasonal and Trend Decomposition using Loess (STL) and Artificial Neural Networks (ANN), were fitted to the malaria incidence data. The study employed Root Mean Square Error (RMSE), Mean Absolute Error (MAE), Mean Absolute Percentage Error (MAPE) and Mean Absolute Scaled Error (MASE) to measure the accuracy of each model. The results indicated that the artificial neural network (ANN) model outperformed other models in terms of the lowest values of RMSE (39.4044), MAE (29.1615), MAPE (31.3611) and MASE (0.6618). The study also incorporated three meteorological variables (Humidity, Rainfall and Temperature) into the ANN model. The incorporation of these variables into the model enhanced the prediction of malaria incidence in terms of achieving better prediction accuracy measures (RMSE = 8.6565, MAE = 6.1029, MAPE = 7.4526 and MASE = 0.1385). The 2-year generated forecasts based on the ANN model implied a significant increasing trend. The study recommends the ANN model for forecasting malaria cases and for taking the steps to reduce malaria incidence during the times of year when high incidence is reported in the Marodijeh region.

Regression analysis makes up a large part of supervised machine learning, and consists of the prediction of a continuous independent target from a set of other predictor variables. The difference between binary classification and regression is in the target range: in binary classification, the target can have only two values (usually encoded as 0 and 1), while in regression the target can have multiple values. Even if regression analysis has been employed in a huge number of machine learning studies, no consensus has been reached on a single, unified, standard metric to assess the results of the regression itself. Many studies employ the mean square error (MSE) and its rooted variant (RMSE), or the mean absolute error (MAE) and its percentage variant (MAPE). Although useful, these rates share a common drawback: since their values can range between zero and +infinity, a single value of them does not say much about the performance of the regression with respect to the distribution of the ground truth elements. In this study, we focus on two rates that actually generate a high score only if the majority of the elements of a ground truth group has been correctly predicted: the coefficient of determination (also known as R-squared or R2) and the symmetric mean absolute percentage error (SMAPE). After showing their mathematical properties, we report a comparison between R2 and SMAPE in several use cases and in two real medical scenarios. Our results demonstrate that the coefficient of determination (R-squared) is more informative and truthful than SMAPE, and does not have the interpretability limitations of MSE, RMSE, MAE and MAPE. We therefore suggest the usage of R-squared as standard metric to evaluate regression analyses in any scientific domain.

Purpose In today’s digital world, real-time health monitoring is becoming a most important challenge in the field of medical research. Body signals such as electrocardiogram (ECG), electromyogram and electroencephalogram (EEG) are produced in human body. This continuous monitoring generates huge count of data and thus an efficient method is required to shrink the size of the obtained large data. Compressed sensing (CS) is one of the techniques used to compress the data size. This technique is most used in certain applications, where the size of data is huge or the data acquisition process is too expensive to gather data from vast count of samples at Nyquist rate. This paper aims to propose Lion Mutated Crow search Algorithm (LM-CSA), to improve the performance of the LMCSA model. Design/methodology/approach A new CS algorithm is exploited in this paper, where the compression process undergoes three stages: designing of stable measurement matrix, signal compression and signal reconstruction. Here, the compression process falls under certain working principle, and is as follows: signal transformation, computation of Θ and normalization. As the main contribution, the theta value evaluation is proceeded by a new “Enhanced bi-orthogonal wavelet filter.” The enhancement is given under the scaling coefficients, where they are optimally tuned for processing the compression. However, the way of tuning seems to be the great crisis, and hence this work seeks the strategy of meta-heuristic algorithms. Moreover, a new hybrid algorithm is introduced that solves the above mentioned optimization inconsistency. The proposed algorithm is named as “Lion Mutated Crow search Algorithm (LM-CSA),” which is the hybridization of crow search algorithm (CSA) and lion algorithm (LA) to enhance the performance of the LM-CSA model. Findings Finally, the proposed LM-CSA model is compared over the traditional models in terms of certain error measures such as mean error percentage (MEP), symmetric mean absolute percentage error (SMAPE), mean absolute scaled error, mean absolute error (MAE), root mean square error, L1-norm and L2-normand infinity-norm. For ECG analysis, under bior 3.1, LM-CSA is 56.6, 62.5 and 81.5% better than bi-orthogonal wavelet in terms of MEP, SMAPE and MAE, respectively. Under bior 3.7 for ECG analysis, LM-CSA is 0.15% better than genetic algorithm (GA), 0.10% superior to particle search optimization (PSO), 0.22% superior to firefly (FF), 0.22% superior to CSA and 0.14% superior to LA, respectively, in terms of L1-norm. Further, for EEG analysis, LM-CSA is 86.9 and 91.2% better than the traditional bi-orthogonal wavelet under bior 3.1. Under bior 3.3, LM-CSA is 91.7 and 73.12% better than the bi-orthogonal wavelet in terms of MAE and MEP, respectively. Under bior 3.5 for EEG, L1-norm of LM-CSA is 0.64% superior to GA, 0.43% superior to PSO, 0.62% superior to FF, 0.84% superior to CSA and 0.60% better than LA, respectively. Originality/value This paper presents a novel CS framework using LM-CSA algorithm for EEG and ECG signal compression. To the best of the authors’ knowledge, this is the first work to use LM-CSA with enhanced bi-orthogonal wavelet filter for enhancing the CS capability as well reducing the errors.

Price volatility in steel reinforcement bars (rebar) plays a pivotal role in managing construction project costs, with precise forecasting being essential for maintaining corporate profitability and ensuring market stability. This research conducts a comprehensive evaluation of five prominent forecasting models—Autoregressive Integrated Moving Average (ARIMA), eXtreme Gradient Boosting (XGBoost), Prophet, Long Short-Term Memory (LSTM), and Transformer—specifically applied to steel rebar price prediction. The study emphasizes the influence of feature selection, defined as the number of historical price data points utilized for prediction, on the accuracy of these models. Furthermore, it develops a hybrid forecasting framework grounded in a residual complementarity mechanism aimed at improving long-term predictive performance. The results reveal that the ARIMA model delivers consistent and reliable short-term forecasts, particularly within a two-month horizon, whereas the Prophet model effectively captures long-term price trends but suffers from notable short-term bias. A two-stage hybrid model (referred to as Combination Model II), which integrates ARIMA and Prophet through residual inversion, demonstrates superior forecasting accuracy over a six-month period. This hybrid approach surpasses the standalone ARIMA model by more than 70% across key evaluation metrics—including Root Mean Square Error (RMSE), Mean Absolute Error (MAE), Mean Absolute Percentage Error (MAPE), Symmetric Mean Absolute Percentage Error (SMAPE), and Mean Absolute Scaled Error (MASE)—and exceeds the performance of the standalone Prophet model by over 90%. This integration effectively combines the high short-term precision of ARIMA with the long-term trend stability of Prophet. Within the domain of machine learning and deep learning models, XGBoost achieves optimal predictive accuracy when utilizing between one and four features. The predictive performance of LSTM does not exhibit a straightforward linear relationship with the number of features; however, certain feature combinations enable it to outperform other models. Transformer models maintain stable accuracy when employing feature sets ranging from one to five and twelve to seventeen, but display considerable variability in performance when the feature count lies between five and twelve. This investigation delineates the optimal parameter ranges and contextual applicability for each model. The proposed hybrid forecasting methodology, alongside a model transfer strategy encompassing data preprocessing adjustments, parameter optimization, and weight adaptation, offers practical applicability to other commodity markets such as cement and concrete. Consequently, this research provides a scientifically grounded framework to support procurement decision-making processes within construction enterprises.

BackgroundInfluenza epidemics pose a threat to human health. It has been reported that meteorological factors (MFs) are associated with influenza. This study aimed to explore the similarities and differences between the influences of more comprehensive MFs on influenza in cities with different economic, geographical and climatic characteristics in Fujian Province. Then, the information was used to predict the daily number of cases of influenza in various cities based on MFs to provide bases for early warning systems and outbreak prevention.MethodDistributed lag nonlinear models (DLNMs) were used to analyse the influence of MFs on influenza in different regions of Fujian Province from 2010 to 2021. Long short-term memory (LSTM) was used to train and model daily cases of influenza in 2010–2018, 2010–2019, and 2010–2020 based on meteorological daily values. Daily cases of influenza in 2019, 2020 and 2021 were predicted. The root mean squared error (RMSE), mean absolute error (MAE), mean absolute percentage error (MAPE) and symmetric mean absolute percentage error (SMAPE) were used to quantify the accuracy of model predictions.ResultsThe cumulative effect of low and high values of air pressure (PRS), air temperature (TEM), air temperature difference (TEMD) and sunshine duration (SSD) on the risk of influenza was obvious. Low (< 979 hPa), medium (983 to 987 hPa) and high (> 112 hPa) PRS were associated with a higher risk of influenza in women, children aged 0 to 12 years, and rural populations. Low (< 9 °C) and high (> 23 °C) TEM were risk factors for influenza in four cities. Wind speed (WIN) had a more significant effect on the risk of influenza in the ≥ 60-year-old group. Low (< 40%) and high (> 80%) relative humidity (RHU) in Fuzhou and Xiamen had a significant effect on influenza. When PRS was between 1005–1015 hPa, RHU > 60%, PRE was low, TEM was between 10–20 °C, and WIN was low, the interaction between different MFs and influenza was most obvious. The RMSE, MAE, MAPE, and SMAPE evaluation indices of the predictions in 2019, 2020 and 2021 were low, and the prediction accuracy was high.ConclusionAll eight MFs studied had an impact on influenza in four cities, but there were similarities and differences. The LSTM model, combined with these eight MFs, was highly accurate in predicting the daily cases of influenza. These MFs and prediction models could be incorporated into the influenza early warning and prediction system of each city and used as a reference to formulate prevention strategies for relevant departments.

Error measures for fuzzy linear regression: Monte Carlo simulation approach

Precipitation is considered a crucial component in the hydrological cycle and changes in its spatial pattern directly influence the water resources. We compare different interpolation techniques in predicting the spatial distribution pattern of precipitation in Chongqing. Six interpolation methods, i.e., Inverse Distance Weighting (IDW), Radial Basis Function (RBF), Diffusion Interpolation with Barrier (DIB), Kernel Interpolation with Barrier (KIB), Ordinary Kriging (OK) and Empirical Bayesian Kriging (EBK), were applied to estimate different rainfall patterns. Annual mean, rainy season and dry-season precipitation was calculated from the daily precipitation time series of 34 meteorological stations with a time span of 1991 to 2019, based on Leave-One-Out Cross-Validation (LOOCV), Mean Square Error (MSE), Mean Absolute Error (MAE), Mean Absolute Percentage Error (MAPE), Symmetric Mean Absolute Percentage Error (SMAPE) and Nash–Sutcliffe Efficiency coefficient (NSE) as validation indexes of the applied models for calculating the error degree and accuracy. Correlation test and Spearman coefficient was performed on the estimated and observed values. A method combining Entropy Weight and Technique for Order Preference by Similarity to Ideal Solution (Entropy-Weighted TOPSIS) was introduced to rank the performance of six interpolation methods. The results indicate that interpolation technique performs better in estimating during periods of low precipitation (i.e., dry season, relative to rainy season and mean annual). The performance priorities of the six methods under the combined multiple precipitation distribution patterns are KIB &gt; EBK &gt; OK &gt; RBF &gt; DIB &gt; IDW. Among them, KIB method has the highest accuracy which maps more accurate precipitation surfaces, with the disadvantage that estimation error is prone to outliers. EBK method is the second highest, and IDW method has the lowest accuracy with a high degree of error. This paper provides information for the application of interpolation methods in estimating rainfall spatial pattern and for water resource management of concerned regions.