Moving Average Model Research Articles

Epidemiological characteristics and prediction model construction of hand, foot and mouth disease in Quzhou City, China, 2005–2023

BackgroundHFMD is a common infectious disease that is prevalent worldwide. In many provinces in China, there have been outbreaks and epidemics of whooping cough, posing a threat to public health.PurposeIt is crucial to grasp the epidemiological characteristics of HFMD in Quzhou and establish a prediction model for HFMD to lay the foundation for early warning of HFMD.MethodDescriptive epidemiological methods were used to analyze the epidemic characteristics of HFMD, the incidence map was drawn by ArcGIS software, the Seasonal Auto Regressive Integrated Moving Average (SARIMA) and Prophet model were established by R software. Then, root mean square error (RMSE) and mean absolute error (MAE) were used to evaluate the fitting and prediction performances of the model.ResultsFrom 2010 to 2023, Quzhou City reported a total of 66,601 cases of hand, foot, and mouth disease (HFMD), with the annual number of reported cases fluctuating between 2,265 and 7,964. The average annual incidence rate was 216.88/100,000, with the lowest in 2010 (97.08 /100,000) and the highest in 2016 (373.37/100,000) (Ptrend < 0.001). The cases exhibited a seasonal bimodal distribution, with the first peak occurring from April to July and the second peak from October to December. The incidence rate of HFMD in males (246.71/100,000) was higher than that in females (185.81 /100,000). The performance of the SARIMA (1,0,1)(2,1,0)12 model was better than that of the Prophet model in terms of prediction accuracy.ConclusionThe incidence of hand, foot and mouth disease in Quzhou is on the rise in 2010–2016 and 2022–2023. In this study, the SARIMA prediction model was compared with the FB Prophet model. Data for more years can then be observed to better predict trends in the incidence of HFMD, providing a basis for prevention strategies and resource allocation. Further research can optimize the model to enhance predictive ability to improve the understanding and management of Chinese rival foot and mouth disease.

Time series models for the description and forecasting of incident cases of dengue: a case study in Londrina- Paraná

Objective: The objective of this study is to describe the temporal behavior of dengue cases and to model the temporal evolution of reported incident cases for the Londrina city, Paraná-Brazil using time series modeling, specifically Seasonal Autoregressive Integrated Moving Average (SARIMA) models from January 2015 to February 2023, with the aim of predicting new cases. Methods: This is an ecological epidemiological study with a time series component. Data were obtained monthly by InfoDengue site in a structured way for the Londrina city- Paraná between January 2015 and February 2023. Time series analysis was used and the SARIMA (Seasonal Autoregressive Integrated Moving Average) model was chosen, since these models incorporate a seasonal component, to fit the natural situation of the disease with recursive periodic peaks and drops over the series, considering thus the intrinsic seasonality of dengue in spring and summer periods with an increase in cases. Results: After several inductive adjustments, the SARIMA model (2,1,2)(1,1,1)12 provided the best fit for dengue incidence data, with good performance, including capturing the oscillation peaks of the year 2020 (period of the coronavirus pandemic). Conclusion: The main contribution of the work is a better understanding of the disease, allowing predictions of the number of cases in periods subsequent to the series studied, which brings support for decision-making in public policies for prevention and educational actions for the population, and possibility of managing the SUS priority health system.

Freight Volume Prediction for Logistics Sorting Centers Using an Integrated GCN-BiLSTM- Transformer Model

In this paper, a comprehensive learning model is proposed for predicting cargo volume at sorting centers, which integrates GCN (Graph Convolutional Network), BiLSTM (Bidirectional Long Short-Term Memory Network), ARIMA (Autoregressive Integrated Moving Average model), and Transformer models. To achieve this, a directed weighted graph is constructed considering the transport network and average cargo volume of each sorting center. The GCN model is employed to extract spatial features from the transport connection information of the sorting centers and these features are then fed into the BiLSTM network. The BiLSTM network leverages bidirectional information flow to learn the temporal characteristics of the data. Subsequently, the GCN-BiLSTM model, which combines spatial and temporal features, is used to predict the daily cargo volume for the next 30 days. The results demonstrate that the GCN-BiLSTM model and the ARIMA-BiLSTM integrated model significantly enhance prediction performance compared to single-model approaches.

Impact of pay-for-performance on hospital readmissions in Lebanon: an ARIMA-based intervention analysis using routine data

BackgroundThe objective of this paper was to estimate the impact of country-wide hospital pay-for-performance on readmissions for a set of common conditions in Lebanon.MethodsThis retrospective cohort study included all hospitalizations under the coverage of the Ministry of Public Health in Lebanon between 2011 and 2019. We calculated 30-day all-cause readmissions following general, pneumonia, cholecystectomy and stroke cases. We used an interrupted time series design, including the use of AutoRegressive Integrated Moving Average models. This nationwide study including 1,333,691 hospitalizations was undertaken in Lebanon, using hospitalizations at about 140 private and public hospitals contracted by the Ministry. The participants included citizens across all ages under the Ministry’s coverage (52% of citizens). The intervention was the engagement of hospital leaders by the Ministry, informing them of the addition of a readmissions component to the ongoing pay-for-performance initiative. Engagement participants included hospital directors and managers, and the leadership of the Syndicate of Private Hospitals. The main outcome measure was age-adjusted monthly all-cause readmission rates for each of general, pneumonia, cholecystectomy and stroke cases. We also assessed for change in readmissions for three conditions not included in the intervention (myocardial infarction, cataract surgery and appendectomy).ResultsAcross 2011–2019, the overall readmission rates were 6.00% (SD 0.24%) for general readmissions, 5.06% (SD 0.22%) for pneumonia, 2.54% (SD 0.16%) for cholecystectomy, and 6.55% (SD 0.25%) for stroke. Using ARIMA models we found a relative percentage decrease in mean monthly readmissions in the post-intervention period for cholecystectomy (5.9%; CI 0.1%-11.8%) and stroke (13.6%; CI 3.1%-24.2%). There was no evidence of intervention impact on pneumonia and general readmissions, both overall and among small, medium and large hospitals. There was also no evidence of change in non-P4P readmissions of myocardial infarction, cataract surgery and appendectomy.ConclusionsIncluding readmissions within pay-for-performance has the potential to improve hospital performance and patient outcomes, even in countries with more limited resources. Effects may vary across conditions, indicating the need for careful design and understanding of the particular context, both with respect to implementation and to evaluation of impact.

Patterns and centralisation in Ethereum-based token transaction networks

We explore patterns, regularities, and correlations in the evolving landscape of Ethereum-based tokens, both ERC-20 (fungible) and ERC-721 (non-fungible) to understand the factors contributing to the rise in certain tokens over others. By applying network science methodologies, minimum spanning trees, econometric autoregressive–moving-average (ARMA) models, and the study of accumulation processes, we are able to highlight a rising centralisation process. Not only do “rich” tokens get richer, but past transactions also emerge as more reliable predictors of new transactions. Our findings are validated across different samples of tokens.

Prediction model of insurance profit and loss under extreme weather based on PCA and ARIMA Models

Because global catastrophe insurance gap widening, insurance profit forecast is important for ensuring the operation of insurance companies under extreme weather. In this paper, on the basis of analyzing the profit structure of insurance, the dimensionality reduction capability of PCA and the flexibility of ARIMA are combined to establish a prediction model of insurance profit and loss under the extreme weather. On the basis of using PCA (Principal Component Analysis) to extract the important features of extreme weather data and to conduct correlation analysis, the influences of each factor on the expression of different principal components are clarified, and the calculation formula of the principal component is obtained. ARIMA (Autoregressive Integrated Moving Average Model) is used to fit historical catastrophe insurance data and capture trends, to predict the likely future compensation ratio in this region. This method can not only reduce the dimension of complex weather data to simplify the analysis, but also flexibly predict the risk degree of future losses of insurance companies. The results show that with the increase of the frequency of extreme weather and the maximum rainfall, the operating risk of insurance companies will rise. Finally, in order to better develop regional catastrophe insurance, it’s a good choice to carry out long-term and short-term planning according to the prediction model.

A Varying Precision Beta Prime Autoregressive Moving Average Model With Application to Water Flow Data

ABSTRACTWe introduce a dynamic model tailored for positively valued time series. It accommodates both autoregressive and moving average dynamics and allows for explanatory variables. The underlying assumption is that each random variable follows, conditional on the set of previous information, the beta prime distribution. A novel feature of the proposed model is that both the conditional mean and conditional precision evolve over time. The model thus comprises two dynamic submodels, one for each parameter. The proposed model for the conditional precision parameter is parsimonious, incorporating first‐order time dependence. Changes over time in the shape of the density are determined by the time evolution of two parameters, and not just of the conditional mean. We present simple closed‐form expressions for the model's conditional log‐likelihood function, score vector, and Fisher's information matrix. Monte Carlo simulation results are presented. Finally, we use the proposed approach to model and forecast two seasonal water flow time series. Specifically, we model the inflow and outflow rates of the reservoirs of two hydroelectric power plants. Overall, the forecasts obtained using the proposed model are more accurate than those yielded by alternative models.

Use of ARIMA Model for Forecasting Consequences Due to Traffic Crashes in the Kingdom of Saudi Arabia

Times series models are important statistical methods for analysing data recorded at points of time which considers the order of observations. In this study, the Autoregressive Integrated Moving Average (ARIMA) model was used to analyse the consequences of traffic crashes in the Kingdom of Saudi Arabia (KSA) from 2002-2022. Over the study period, there was a decreasing trend in the forecasted number of all types of injuries per 1,000 traffic crashes. Moreover, to check the validity of the fitted model, the actual observations are plotted with predicted values from 2016 to 2022 and showed a nearly equal and exact pattern between the total number of predicted values and the actual data. It is concluded that the ARIMA model is a good fit to forecast the parameter of consequences per 1,000 crashes. The decrease in consequences may be due to preventive or mitigation measures by various organisations in KSA.

Corporate Financial Risk Trend Prediction Using ARIMA-Based Machine Learning: A Semantic Literature Review

This research discusses the role of artificial intelligence (AI) technology in improving company financial risk predictions through the application of the Autoregressive Integrated Moving Average (ARIMA) model supported by machine learning. Using systematic literature analysis, this research explores how ARIMA, with the help of AI, can be applied in financial risk management to identify short-term and long-term trends, detect financial anomalies, and improve the quality of decision making. ARIMA models based on machine learning enable faster and more accurate identification of abnormal financial patterns, which is very important in helping companies respond to risks that have the potential to disrupt financial stability. Key findings show that the combination of ARIMA and AI not only makes it easier to analyze large and complex financial data, but also expands the potential of data-driven financial risk management by providing deeper insights. By integrating machine learning, ARIMA becomes more effective in handling dynamic and fluctuating financial data, so companies can anticipate risks more proactively. This study underscores the enormous potential of AI and ARIMA in helping companies build adaptive, high-precision risk prediction systems, offering new opportunities to strengthen financial resilience in an ever-changing business environment.

An Arima Model-Based Approach to Improve Electricity Reliability

Objective: The objective of this study was to forecast the number of critical days, for the period from July 2020 to December 2022, based on time series analysis, to model changes in the number of critical power days in a prospective way. Related Studies: This section provides an overview of the use of forecasting models and methods for measuring electricity demand, applied as decision-making support and as a tool for identifying anomalous phenomena. Method: The methodology for this research involves analysis and forecasting using the Autoregressive Integrated Moving Average (ARIMA) model of order (p,d,q)(p,d,q), applied to the time series of critical days. Model development and performance evaluation followed these steps and strategies: Specification (Pre-processing), Identification and Estimation, Verification, and Forecasting. Data collection was performed by analyzing time series observations from a Brazilian electric utility company responsible for energy supply in Rio Grande do Sul. Results and Discussion: The results indicated that the seasonal ARIMA (2,1,1)(2,1,1) model performed best, with the lowest Akaike Information Criterion (AIC) and Bayesian Information Criterion (BIC) values, as well as the lowest mean square error among the tested models. With the selected ARIMA model, forecasts were made for the following 30 months, estimating the number of monthly critical days. Research Implications: The paper discusses the practical and theoretical implications of forecasting critical days for power quality. Practically, it presents an ARIMA model to estimate these days, aiding power companies in projecting interruptions and improving preventive management and resource allocation. Theoretically, it contributes to the time series forecasting literature in the power sector, confirming the effectiveness of ARIMA models with seasonal components for grid management and adverse event forecasting in complex systems. Originality/Value: The study contributes to the literature by applying the ARIMA model with seasonal components to predict critical days of interruption in the distribution of electricity, an approach that has not yet been explored for specific adverse events. The originality lies in the application of the model in a context of quality and reliability in the supply and detailed seasonal analysis. The methodology proposes a solution for forecasting and managing these events, bringing new perspectives for proactive management in the sector. The study stands out for its potential to improve professional practice, allowing informed decisions for resource allocation and maintenance, increasing reliability and reducing costs and financial compensation.

A Statistical Evaluation of the Occurence of Meningitis in Takum, Taraba State, Nigeria

Meningitis remains a critical public health issue in Nigeria, particularly within the dry season when environmental factors such as low humidity and dust elevate transmission risks. Using historical incidence data from 2012 to 2021, this study utilizes the Autoregressive Integrated Moving Average (ARIMA) model estimate and predict the occurrence of meningitis occurrences. Findings frm the study revealed that the ARIMA(1,1,0) model emerged as the optimal fit, capturing the seasonal patterns and temporal trends in meningitis cases. This study recommends the integration of ARIMA-based forecasting into Nigeria’s public health strategies to strengthen early warning systems, optimize resource deployment, and enable more proactive responses during high-risk periods.

Robust Estimation for Threshold Autoregressive Moving-Average Models

Threshold autoregressive moving-average (TARMA) models extend the popular TAR model and are among the few parametric time series specifications to include a moving average in a nonlinear setting. The state dependent reactions to shocks is particularly appealing in Economics and Finance. However, no theory is currently available when the data present heavy tails or anomalous observations. Here we provide the first theoretical framework for robust M-estimation for TARMA models and study its practical relevance. Under mild conditions, we show that the robust estimator for the threshold parameter is super-consistent, while the estimators for autoregressive and moving-average parameters are strongly consistent and asymptotically normal. The Monte Carlo study shows that the M-estimator is superior, in terms of both bias and variance, to the least squares estimator, which can be heavily affected by outliers. The findings suggest that robust M-estimation should be generally preferred to the least squares method. We apply our methodology to a set of commodity price time series; the robust TARMA fit presents smaller standard errors and superior forecasting accuracy. The results support the hypothesis of a two-regime non-linearity characterized by slow expansions and fast contractions.

NH4 Modelling with ARIMA and LSTM

AI-Mining is a prototype designed to detect various environmental gases, including CO2, NH3, NH4, and hydrogen, alongside temperature, pressure, and humidity. This study emphasizes the importance of modeling NH4 time series data due to its critical role in environmental and health monitoring. Accurate NH4 predictions facilitate early pollution detection and timely greenhouse gas control interventions. The study investigates the effectiveness of AI-Mining in detecting and predicting gas levels, focusing on data collection and analysis. Initial data analysis employed the Autoregressive Moving Average (ARIMA) model, specifically ARIMA (1,1,1), described by the equation yt = 0.0311 - 0.0750yt-1 + 0.3842εt-1. Despite its use, ARIMA's Root Mean Square Error (RMSE) performance was found lacking compared to more advanced methods. Given the classification of the obtained data as big data and time series, the Long Short-Term Memory (LSTM) method was also applied. The LSTM model initially used two layers with tanh and relu activation functions, and its performance was further explored by adding a third layer and varying the number of neurons (64, 128, and 256). The Adam optimizer was consistently used across all LSTM variations. Results indicated that increasing layers and neurons did not significantly impact LSTM's performance, with RMSE values around 0.023. However, LSTM consistently outperformed ARIMA in prediction accuracy, highlighting its robustness and reliability. Consequently, the study recommends using LSTM for predicting other recorded data in AI-Mining, underscoring its superiority in handling complex environmental datasets.

Necessary for seizure forecasting outcome metrics: Seizure frequency and benchmark model

BackgroundThis study aims to illustrate the connection between seizure frequency (SF) and performance metrics in seizure forecasting, and to compare the effectiveness of a moving average (MA) model versus the commonly used permutation benchmark. MethodsMetrics of calibration and discrimination were computed for each dataset, comparing MA and permutation performance across SF values. Three datasets were used: (1) self-reported seizure diaries from 3994 Seizure Tracker patients, (2) automatically detected and sometimes manually reported or edited generalized tonic-clonic seizures from 2350 Empatica Embrace 2 and Mate App users, and (3) simulated datasets with varying SFs. ResultsMost metrics were found to depend on SF. The MA model outperformed or matched the permutation model in all cases. These more advanced metrics show that comparison to permutation will falsely elevate poor forecasting models. ConclusionsThe findings highlight SF's role in seizure forecasting accuracy and the MA model's suitability as a benchmark. This study underscores the need for considering patient SF in forecasting studies and suggests the MA model may provide a better standard for evaluating future seizure forecasting models.

Conditional parametric bootstrap in GLARMA models

Due to situations where asymptotic results are not valid or when we do not know the true distributions of the data set, the bootstrap technique stands out as an effective alternative to make inferences about model parameters. In this context, we introduce the conditional parametric bootstrap, applied to time series data, specifically using the Generalized Linear Autoregressive Moving Average (GLARMA) model. Our interest is to use the procedure to correct possible biases and construct confidence intervals and hypothesis testing for the parameters of the GLARMA model. We conducted simulation studies to evaluate the performance of the procedure in finite samples. The results show that the proposed technique is promising and can be applied in practical situations. An example is the analysis of the monthly number of chronic obstructive pulmonary disease (COPD) cases, which illustrates the potential of the proposed approach in a real situation.

Enhancing periodic mobility planning: ARIMA-driven prognostications for subway passenger volume dynamics

Abstract. This study aims to accurately predict urban subway passenger flow using the Auto-Regressive Integrated Moving Average (ARIMA) and Seasonal Auto Regressive Integrated Moving Average (SARIMA) model, with the intention of providing a scientific basis for subway operation management. By meticulously sorting and analyzing the existing traffic data of a large city's subway system, this research constructs a model that comprehensively considering the seasonal, trend, and stochastic characteristics of time series data. During the model construction process, data preprocessing is carried out, including stationarity tests, differencing, model order determination, and parameter estimation, ultimately identifying an ARIMA and SARIMA model with good fitting results, effectively identifying and forecasting characteristics such as numerical fluctuations. Additionally, this study conducts a special analysis of the prediction effects at diverse time scales, verifying the applicability and superiority of the ARIMA and SARIMA model in subway passenger flow prediction. This research not only provides a powerful tool for passenger flow prediction for subway operation management departments, aiding in the reasonable allocation of capacity and optimization of operation strategies, but also holds significant reference and application value for the passenger flow prediction and management of other urban public transportation systems.

Characteristics of Machine Learning-based Univariate Time Series Imputation Method

Handling missing values in univariate time series analysis poses a challenge, potentially leading to inaccurate conclusions, especially with frequently occurring consecutive missing values. Machine Learning-based Univariate Time Series Imputation (MLBUI) methods, utilizing Random Forest Regression (RFR) and Support Vector Regression (SVR), aim to address this challenge. Considering factors such as time series patterns, missing data patterns, and volume, this study explores the performance of MLBUI in simulated Autoregressive Integrated Moving Average (ARIMA) datasets. Various missing data scenarios (6%, 10%, and 14%) and model scenarios (Autoregressive (AR) models: AR(1) and AR(2); Moving Average (MA) models: MA(1) and MA(2); Autoregressive Moving Average (ARMA) models: ARMA(1,1) and ARMA(2,2); and Autoregressive Integrated Moving Average (ARIMA) models: ARIMA(1,1,1) and ARIMA(1,2,1)) with different standard deviations (0.5, 1, and 2) were examined. Five comparative methods were also used in this research, including Kalman StructTS, Kalman Auto-ARIMA, Spline Interpolation, Stine Interpolation, and Moving Average. The research findings indicate that MLBUI performs exceptionally well in imputing successive missing values. The results of this study indicate that the performance of MLBUI in imputing consecutive missing values, based on MAPE, yielded values of less than 10% across all scenarios used.

Modeling Survey Time Series Data with Flow-Observed CARMA Processes

Published survey data often are delivered as estimates computed over an epoch of time. Customers may desire to obtain survey estimates corresponding to epochs, or time points, that differ from the published estimates. This “change of support” problem can be addressed through the use of continuous-time models of the underlying population process, while taking into account the sampling error that survey data is subject to. The application of a Continuous AutoRegressive Moving Average (CARMA) model is investigated as a tool to provide change of support applications, thereby allowing interpolation for published survey estimates. A simulation study provides comparisons of competing estimation methods, and a synthetically constructed data set is developed in order to elucidate real data applications. The proposed method can be successful for change of support problems, despite modeling challenges with the CARMA framework.

Modelling Motor Insurance Claims Using Arma Model And Appropriate Statistical Distribution Of Insurance Companies, Machakos County, Kenya

The prediction of future claim amounts based on past or present claims is a challenging task for insurance companies. According to research carried out by Michael Barth and David L. Eccles (2009); claim costs constitute large proportion of insurers expenses in evaluating the premium growth on the loss ratio of property causality insurers. Various statistical techniques have been employed to analyze claims data and assess its impact on productivity. Autoregressive (AR), Moving Average (MA), and Auto Regressive Moving Average (ARMA) processes are commonly used to model the temporal dependencies and trends in the data. These techniques enable insurance companies to understand the dynamics of claim incidence and their effects on productivity over time (Philip J, 2016). Advanced modeling techniques such as generalized additive models, negative binomial regression, and multinomial logit models have been used to evaluate claims processes, predict claim occurrence, and model claim severity (Renshaw A.E, 1994; Edward. W Frees et al., 2008; Daiane Aparecida Zanetti et al., 2006). These models consider various factors such as driver age, gender, vehicle type, and no claim discount to assess their impact on claim incidence and productivity. Previous studies have overlooked the comprehensive examination of the impact of insurance claims on productivity on insurance companies. Therefore, this research aims to address this gap by investigating the factors associated with insurance motor claims and their effects on the productivity of insurance companies by employing statistical techniques like appropriate probability distribution, incorporation of moving average technique, Autoregressive process and ARMA process, as identified by industry professionals and experts. The results obtained from the real-life data for distinctive 11 years indicated the potential strength of ARMA models to provide insurance company's claim amount prediction that could assist the companies to have better planning. The findings of this study, if adopted by various keynote players in the insurance and regulatory sectors, can be highly beneficial in formulating appropriate policies to enhance the management of motor insurance claims and improve the productivity of insurance companies.

News Popularity Prediction in West Sumatera Using Autoregressive Integrated Moving Average

The increasing public interest in reading online news is undoubtedly a challenge for news portals as online news providers. Therefore, this research was conducted to predict news popularity in West Sumatra through the FajarSumbar.com news portal using the Autoregressive Integrated Moving Average (ARIMA) model. This research aims to develop a forecasting model that can assist in estimating the popularity of each news category so that news portals can devise more effective content strategies. The data used in this study includes the number of monthly news impressions from March 2021 to June 2024, which are grouped into various categories such as Religion Culture, Industrial Economics, Criminal Law, etc. Using the ARIMA method, which can handle time series data and overcome data non-stationarity problems through differencing and the use of grid search in optimization to find the best parameters based on the lowest evaluation metric. The results show that the ARIMA model can provide reasonably accurate predictions, although the level of accuracy varies between categories. The Mean Absolute Percentage Error (MAPE) values obtained are as follows: Religion Culture 26%, Industrial Economy 29%, Criminal Law 29%, Health 40%, Sports 38%, Tourism Entertainment 26%, Education 27%, Government Politics 31%, Social Environment 27%, and Technology 51%. The Technology and Health news categories show higher error rates than others, while Religion Culture and Tourism Entertainment have better accuracy rates. Thus, the ARIMA model can be used to predict future trends in news popularity, helping editors plan content strategies that are more relevant and interesting to readers. However, improvements are needed for news categories that have high variability.