Time Series Analysis and Prediction of COVID-19 Pandemic Using Dynamic Harmonic Regression Models

Rapidly spreading COVID-19 virus and its variants, especially in metropolitan areas around the world, became a major health public concern. The tendency of COVID-19 pandemic and statistical modelling represents an urgent challenge in the United States for which there are few solutions. In this paper, we demonstrate combining Fourier terms for capturing seasonality with ARIMA errors and other dynamics in the data. Therefore, we have analyzed 156 weeks COVID-19 dataset on national level using Dynamic Harmonic Regression model, including simulation analysis and accuracy improvement from 2020 to 2023. Most importantly, we provide new advanced pathways which may serve as targets for developing new solutions and approaches.

Time series modeling of animal bites

Objective:To explore the modeling of time series of animal bite occurrence in northwest Iran.Methods:In this study,we analyzed surveillance time series data for animal bite cases in the northwest Iran province of Iran from 2011 to 2017.We used decomposition methods to explore seasonality and long-term trends and applied the Autoregressive Integrated Moving Average(ARIMA)model to fit a univariate time series of animal bite incidence.The ARIMA modeling process involved selecting the time series,transforming the series,selecting the appropriate model,estimating parameters,and forecasting.Results:Our results using the Box Jenkins model showed a significant seasonal trend and an overall increase in animal bite incidents during the study period.The best-fitting model for the available data was a seasonal ARIMA model with drift in the form of ARIMA(2,0,0)(1,1,1).This model can be used to forecast the frequency of animal attacks in northwest Iran over the next two years,suggesting that the incidence of animal attacks in the region would continue to increase during this time frame(2018-2019).Conclusion:Our findings suggest that time series analysis is a useful method for investigating animal bite cases and predicting future occurrences.The existence of a seasonal trend in animal bites can also aid in planning healthcare services during different seasons of the year.Therefore,our study highlights the importance of implementing proactive measures to address the growing issue of animal bites in Iran.

Combined hybrid energy storage system and transmission grid model for peak shaving based on time series operation simulation

This study proposes a combined hybrid energy storage system(HESS) and transmission grid(TG) model, and a corresponding time series operation simulation(TSOS) model is established to relieve the peak-shaving pressure of power systems under the integration of renewable energy. First, a linear model for the optimal operation of the HESS is established, which considers the different power-efficiency characteristics of the pumped storage system, electrochemical storage system, and a new type of liquid compressed air energy storage. Second, a TSOS simulation model for peak shaving is built to maximize the power entering the grid from the wind farms and HESS. Based on the proposed model, this study considers the transmission capacity of a TG. By adding the power-flow constraints of the TG, a TSOS-based HESS and TG combination model for peak shaving is established. Finally, the improved IEEE-39 and IEEE-118 bus systems were considered as examples to verify the effectiveness and feasibility of the proposed model.

Dynamic Ensemble Multivariate Time Series Forecasting Model for PM2.5

In forecasting real time environmental factors,large data is needed to analyse the pattern behind the data values.Air pollution is a major threat towards developing countries and it is proliferating every year.Many methods in time ser-ies prediction and deep learning models to estimate the severity of air pollution.Each independent variable contributing towards pollution is necessary to analyse the trend behind the air pollution in that particular locality.This approach selects multivariate time series and coalesce a real time updatable autoregressive model to forecast Particulate matter(PM)PM2.5.To perform experimental analysis the data from the Central Pollution Control Board(CPCB)is used.Prediction is car-ried out for Chennai with seven locations and estimated PM’s using the weighted ensemble method.Proposed method for air pollution prediction unveiled effective and moored performance in long term prediction.Dynamic budge with high weighted k-models are used simultaneously and devising an ensemble helps to achieve stable forecasting.Computational time of ensemble decreases with paral-lel processing in each sub model.Weighted ensemble model shows high perfor-mance in long term prediction when compared to the traditional time series models like Vector Auto-Regression(VAR),Autoregressive Integrated with Mov-ing Average(ARIMA),Autoregressive Moving Average with Extended terms(ARMEX).Evaluation metrics like Root Mean Square Error(RMSE),Mean Absolute Error(MAE)and the time to achieve the time series are compared.

Examine the Reliability of Econometrics Software: An Empirical Comparison of Time Series Modelling

Researchers must understand that naively relying on the reliability of statistical software packages may result in suboptimal, biased, or erroneous results, which affects applied economic theory and the conclusions and policy recommendations drawn from it. To create confidence in a result, several software packages should be applied to the same estimation problem. This study examines the results of three software packages (EViews, R, and Stata) in the analysis of time-series econometric data. The time-series data analysis which presents the determinants of macroeconomic growth of Sri Lanka from 1978 to 2020 has been used. The study focuses on testing for stationarity, cointegration, and significant relationships among the variables. The Augmented Dickey-Fuller and Phillips Perron tests were employed in this study to test for stationarity, while the Johansen cointegration test was utilized to test for cointegration. The study employs the vector error correction model to assess the short-run and long-term dynamics of the variables in an attempt to determine the relationship between them. Finally, the Granger Causality test is employed in order to examine the linear causation between the concerned variables. The study revealed that the results produced by three software packages for the same dataset and the same lag order vary significantly. This implies that time series econometrics results are sensitive to the software that is used by the researchers while providing different policy implications even for the same dataset. The present study highlights the necessity of further analysis to investigate the impact of software packages in time series analysis of economic scenarios.

Time-Series Modeling and Prediction of Global Monthly Absolute Temperature for Environmental Decision Making

A generalized, structural, time series modeling framework was developed to analyze the monthly records of absolute surface temperature, one of the most important environmental parameters, using a deterministicstochastic combined （DSC） approach. Although the development of the framework was based on the characterization of the variation patterns of a global dataset, the methodology could be applied to any monthly absolute temperature record. Deterministic processes were used to characterize the variation patterns of the global trend and the cyclic oscillations of the temperature signal, involving polynomial functions and the Fourier method, respectively, while stochastic processes were employed to account for any remaining patterns in the temperature signal, involving seasonal autoregressive integrated moving average （SARIMA） models. A prediction of the monthly global surface temperature during the second decade of the 21st century using the DSC model shows that the global temperature will likely continue to rise at twice the average rate of the past 150 years. The evaluation of prediction accuracy shows that DSC models perform systematically well against selected models of other authors, suggesting that DSC models, when coupled with other ecoenvironmental models, can be used as a supplemental tool for short-term （10-year） environmental planning and decision making.

Multi-factor high-order intuitionistic fuzzy timeseries forecasting model

Fuzzy sets theory cannot describe the neutrality degreeof data, which has largely limited the objectivity of fuzzy time seriesin uncertain data forecasting. With this regard, a multi-factor highorderintuitionistic fuzzy time series forecasting model is built. Inthe new model, a fuzzy clustering algorithm is used to get unequalintervals, and a more objective technique for ascertaining membershipand non-membership functions of the intuitionistic fuzzy setis proposed. On these bases, forecast rules based on multidimensionalintuitionistic fuzzy modus ponens inference are established.Finally, contrast experiments on the daily mean temperature ofBeijing are carried out, which show that the novel model has aclear advantage of improving the forecast accuracy.

A Hybrid Neural Network and Box-Jenkins Models for Time Series Forecasting

Time series forecasting plays a significant role in numerous applications,including but not limited to,industrial planning,water consumption,medical domains,exchange rates and consumer price index.The main problem is insufficient forecasting accuracy.The present study proposes a hybrid forecastingmethods to address this need.The proposed method includes three models.The first model is based on the autoregressive integrated moving average(ARIMA)statistical model;the second model is a back propagation neural network(BPNN)with adaptive slope and momentum parameters;and the thirdmodel is a hybridization between ARIMA and BPNN(ARIMA/BPNN)and artificial neural networks and ARIMA(ARIMA/ANN)to gain the benefits of linear and nonlinearmodeling.The forecasting models proposed in this study are used to predict the indices of the consumer price index(CPI),and predict the expected number of cancer patients in the Ibb Province in Yemen.Statistical standard measures used to evaluate the proposed method include(i)mean square error,(ii)mean absolute error,(iii)root mean square error,and(iv)mean absolute percentage error.Based on the computational results,the improvement rate of forecasting the CPI dataset was 5%,71%,and 4%for ARIMA/BPNN model,ARIMA/ANN model,and BPNN model respectively;while the result for cancer patients’dataset was 7%,200%,and 19%for ARIMA/BPNNmodel,ARIMA/ANN model,and BPNNmodel respectively.Therefore,it is obvious that the proposed method reduced the randomness degree,and the alterations affected the time series with data non-linearity.The ARIMA/ANN model outperformed each of its components when it was applied separately in terms of increasing the accuracy of forecasting and decreasing the overall errors of forecasting.

Time Series Facebook Prophet Model and Python for COVID-19 Outbreak Prediction

COVID-19 comes from a large family of viruses identied in 1965;to date,seven groups have been recorded which have been found to affect humans.In the healthcare industry,there is much evidence that Al or machine learning algorithms can provide effective models that solve problems in order to predict conrmed cases,recovered cases,and deaths.Many researchers and scientists in the eld of machine learning are also involved in solving this dilemma,seeking to understand the patterns and characteristics of virus attacks,so scientists may make the right decisions and take specic actions.Furthermore,many models have been considered to predict the Coronavirus outbreak,such as the retro prediction model,pandemic Kaplan’s model,and the neural forecasting model.Other research has used the time series-dependent face book prophet model for COVID-19 prediction in India’s various countries.Thus,we proposed a prediction and analysis model to predict COVID-19 in Saudi Arabia.The time series dependent face book prophet model is used to t the data and provide future predictions.This study aimed to determine the pandemic prediction of COVID-19 in Saudi Arabia,using the Time Series Analysis to observe and predict the coronavirus pandemic’s spread daily or weekly.We found that the proposed model has a low ability to forecast the recovered cases of the COVID-19 dataset.In contrast,the proposed model of death cases has a high ability to forecast the COVID-19 dataset.Finally,obtaining more data could empower the model for further validation.

Grey series time-delay predicting model in state estimation for power distribution networks

A new combined model is proposed to obtain predictive data value applied in state estimation for radial power distribution networks. The time delay part of the model is calculated by a recursive least squares algorithm of system identification, which can gradually forget past information. The grey series part of the model uses an equal dimension new information model (EDNIM) and it applies 3 points smoothing method to preprocess the original data and modify remnant difference by GM(1,1). Through the optimization of the coefficient of the model, we are able to minimize the error variance of predictive data. A case study shows that the proposed method achieved high calculation precision and speed and it can be used to obtain the predictive value in real time state estimation of power distribution networks.

Multimodality Prediction of Chaotic Time Series with Sparse Hard-Cut EM Learning of the Gaussian Process Mixture Model

The contribution of this work is twofold： （1） a multimodality prediction method of chaotic time series with the Gaussian process mixture （GPM） model is proposed, which employs a divide and conquer strategy. It automatically divides the chaotic time series into multiple modalities with different extrinsic patterns and intrinsic characteristics, and thus can more precisely fit the chaotic time series. （2） An effective sparse hard-cut expec- tation maximization （SHC-EM） learning algorithm for the GPM model is proposed to improve the prediction performance. SHO-EM replaces a large learning sample set with fewer pseudo inputs, accelerating model learning based on these pseudo inputs. Experiments on Lorenz and Chua time series demonstrate that the proposed method yields not only accurate multimodality prediction, but also the prediction confidence interval SHC-EM outperforms the traditional variational 1earning in terms of both prediction accuracy and speed. In addition, SHC-EM is more robust and insusceptible to noise than variational learning.

Genetic programming-based chaotic time series modeling

This paper proposes a Genetic Programming-Based Modeling (GPM) algorithm on chaotic time series. GP is used here to search for appropriate model structures in function space, and the Particle Swarm Optimization (PSO) algorithm is used for Nonlinear Parameter Estimation (NPE) of dynamic model structures. In addition, GPM integrates the results of Nonlinear Time Series Analysis (NTSA) to adjust the parameters and takes them as the criteria of established models. Experiments showed the effectiveness of such improvements on chaotic time series modeling.

Oil-Price Forecasting Based on Various Univariate Time-Series Models

Time-series-based forecasting is essential to determine how past events affect future events. This paper compares the performance accuracy of different time-series models for oil prices. Three types of univariate models are discussed: the exponential smoothing (ES), Holt-Winters (HW) and autoregressive intergrade moving average (ARIMA) models. To determine the best model, six different strategies were applied as selection criteria to quantify these models’ prediction accuracies. This comparison should help policy makers and industry marketing strategists select the best forecasting method in oil market. The three models were compared by applying them to the time series of regular oil prices for West Texas Intermediate (WTI) crude. The comparison indicated that the HW model performed better than the ES model for a prediction with a confidence interval of 95%. However, the ARIMA (2, 1, 2) model yielded the best results, leading us to conclude that this sophisticated and robust model outperformed other simple yet flexible models in oil market.

基于TimeSeries-Markov模型的煤矿瓦斯事故起数预测

本文以2001~2016年我国煤矿瓦斯事故起数为基础,利用时间序列预测模型及改进马尔科夫预测模型分别预测了2001~2010年、2001~2011年、…及2001~2015年中各年瓦斯事故起数,并计算了其相对误差。其中,TS分别计算的上述六组值的相对误差平均值在18.72%~23.4%之间,而TSM计算的对应值为5.79%~7.09%,且TSM的预测值的波动趋势更符合真实情况。将上述两种模型分别预测后计算的2011~2016各年瓦斯事故发生起数的相对误差进行线性拟合,发现TSM的预测精度更高。因此,用TSM预测煤矿瓦斯事故起数比用TS预测更可靠,这也间接反映了TSM比TS更多地考虑了因素的近期状况对预测值的影响。最后,用此法预测了2017~2020年我国煤矿瓦斯事故起数,其依次为6起、7起、6起及4起。

TIME SERIES NEURAL NETWORK MODEL FOR HYDROLOGIC FORECASTING

Time series analysis plays an important role in hydrologic forecasting,while the key to this analysis is to establish a proper model.This paper presents a time series neural network model with back propagation procedure for hydrologic forecasting.Free from the disadvantages of previous models,the model can be parallel to operate information flexibly and rapidly.It excels in the ability of nonlinear mapping and can learn and adjust by itself,which gives the model a possibility to describe the complex nonlinear hydrologic process.By using directly a training process based on a set of previous data, the model can forecast the time series of stream flow.Moreover,two practical examples were used to test the performance of the time series neural network model.Results confirm that the model is efficient and feasible.

TIME SERIES AND GREY MODEL DIAGNOSIS METHOD USED TO CRACK PROBLEMS

In this paper,the vibration signals in the fatigue crack growth process in a chinese steel used in a mining machinery were analyzed by the frequency spectrum, the time series and grey system model,and the critical criterion for crack initiation was proposed.

Gross errors identification and correction of in-vehicle MEMS gyroscope based on time series analysis

This paper presents a novel approach to identify and correct the gross errors in the microelectromechanical system （MEMS） gyroscope used in ground vehicles by means of time series analysis. According to the characteristics of autocorrelation function （ACF） and partial autocorrelation function （PACF）, an autoregressive integrated moving average （ARIMA） model is roughly constructed. The rough model is optimized by combining with Akaike＇s information criterion （A/C）, and the parameters are estimated based on the least squares algorithm. After validation testing, the model is utilized to forecast the next output on the basis of the previous measurement. When the difference between the measurement and its prediction exceeds the defined threshold, the measurement is identified as a gross error and remedied by its prediction. A case study on the yaw rate is performed to illustrate the developed algorithm. Experimental results demonstrate that the proposed approach can effectively distinguish gross errors and make some reasonable remedies.

Fault Prediction Based on Dynamic Model and Grey Time Series Model in Chemical Processes

This paper combines grey model with time series model and then dynamic model for rapid and in-depth fault prediction in chemical processes. Two combination methods are proposed. In one method, historical data is introduced into the grey time series model to predict future trend of measurement values in chemical process. These predicted measurements are then used in the dynamic model to retrieve the change of fault parameters by model based diagnosis algorithm. In another method, historical data is introduced directly into the dynamic model to retrieve historical fault parameters by model based diagnosis algorithm. These parameters are then predicted by the grey time series model. The two methods are applied to a gravity tank example. The case study demonstrates that the first method is more accurate for fault prediction.

Application of uncertainty reasoning based on cloud model in time series prediction

Time series prediction has been successfully used in several application areas, such as meteoro-logical forecasting, market prediction, network traffic forecasting, etc. , and a number of techniques have been developed for modeling and predicting time series. In the traditional exponential smoothing method, a fixed weight is assigned to data history, and the trend changes of time series are ignored. In this paper, an uncertainty reasoning method, based on cloud model, is employed in time series prediction, which uses cloud logic controller to adjust the smoothing coefficient of the simple exponential smoothing method dynamically to fit the current trend of the time series. The validity of this solution was proved by experiments on various data sets.

Time Series Models for Short Term Prediction of the Incidence of Japanese Encephalitis in Xianyang City, P R China

Objective To construct a model of Seasonal Autoregressive Integrated Moving Average （SARIMA） for forecasting the epidemic of Japanese encephalitis （JE） in Xianyang, Shaanxi, China, and provide valuable reference information for JE control and prevention. Methods Theoretically epidemiologic study was employed in the research process. Monthly incidence data on JE for the period from Jan 2005 to Sep 2014 were obtained from a passive surveillance system at the Center for Diseases Prevention and Control in Xianyang, Shaanxi province. An optimal SARIMA model was developed for JE incidence from 2005 to 2013 with the Box and Jenkins approach. This SARIMA model could predict JE incidence for the year 2014 and 2015. Results SARIMA （1, 1, 1） （2, 1, 1）12 was considered to be the best model with the lowest Bayesian information criterion, Akaike information criterion, Mean Absolute Error values, the highest R2, and a lower Mean Absolute Percent Error. SARIMA （1, 1, 1） （2, 1, 1）12 was stationary and accurate for predicting JE incidence in Xianyang. The predicted incidence, around 0.3/100 000 from June to August in 2014 with low errors, was higher compared with the actual incidence. Therefore, SARIMA （1, 1, 1） （2, 1, 1）12 appeared to be reliable and accurate and could be applied to incidence prediction. Conclusions The proposed prediction model could provide clues to early identification of the JE incidence that is increased abnormally （≥0.4/100 000）. According to the predicted results in 2014, the JE incidence in Xianyang will decline slightly and reach its peak from June to August.The authors wish to thank the staff from the CDCs from 13 counties of Xianyang, Shaanxi province, China, for their contribution to Japanese encephalitis cases reporting.