Automated Machine Learning Algorithm Using Recurrent Neural Network to Perform Long-Term Time Series Forecasting

Long-term time series forecasting stands as a crucial research domain within the realm of automated machine learning(AutoML).At present,forecasting,whether rooted in machine learning or statistical learning,typically relies on expert input and necessitates substantial manual involvement.This manual effort spans model development,feature engineering,hyper-parameter tuning,and the intricate construction of time series models.The complexity of these tasks renders complete automation unfeasible,as they inherently demand human intervention at multiple junctures.To surmount these challenges,this article proposes leveraging Long Short-Term Memory,which is the variant of Recurrent Neural Networks,harnessing memory cells and gating mechanisms to facilitate long-term time series prediction.However,forecasting accuracy by particular neural network and traditional models can degrade significantly,when addressing long-term time-series tasks.Therefore,our research demonstrates that this innovative approach outperforms the traditional Autoregressive Integrated Moving Average(ARIMA)method in forecasting long-term univariate time series.ARIMA is a high-quality and competitive model in time series prediction,and yet it requires significant preprocessing efforts.Using multiple accuracy metrics,we have evaluated both ARIMA and proposed method on the simulated time-series data and real data in both short and long term.Furthermore,our findings indicate its superiority over alternative network architectures,including Fully Connected Neural Networks,Convolutional Neural Networks,and Nonpooling Convolutional Neural Networks.Our AutoML approach enables non-professional to attain highly accurate and effective time series forecasting,and can be widely applied to various domains,particularly in business and finance.

Time series analysis-based seasonal autoregressive fractionally integrated moving average to estimate hepatitis B and C epidemics in China

BACKGROUND Hepatitis B(HB)and hepatitis C(HC)place the largest burden in China,and a goal of eliminating them as a major public health threat by 2030 has been set.Making more informed and accurate forecasts of their spread is essential for developing effective strategies,heightening the requirement for early warning to deal with such a major public health threat.AIM To monitor HB and HC epidemics by the design of a paradigmatic seasonal autoregressive fractionally integrated moving average(SARFIMA)for projections into 2030,and to compare the effectiveness with the seasonal autoregressive integrated moving average(SARIMA).METHODS Monthly HB and HC incidence cases in China were obtained from January 2004 to June 2023.Descriptive analysis and the Hodrick-Prescott method were employed to identify trends and seasonality.Two periods(from January 2004 to June 2022 and from January 2004 to December 2015,respectively)were used as the training sets to develop both models,while the remaining periods served as the test sets to evaluate the forecasting accuracy.RESULTS There were incidents of 23400874 HB cases and 3590867 HC cases from January 2004 to June 2023.Overall,HB remained steady[average annual percentage change(AAPC)=0.44,95%confidence interval(95%CI):-0.94-1.84]while HC was increasing(AAPC=8.91,95%CI:6.98-10.88),and both had a peak in March and a trough in February.In the 12-step-ahead HB forecast,the mean absolute deviation(15211.94),root mean square error(18762.94),mean absolute percentage error(0.17),mean error rate(0.15),and root mean square percentage error(0.25)under the best SARFIMA(3,0,0)(0,0.449,2)12 were smaller than those under the best SARIMA(3,0,0)(0,1,2)12(16867.71,20775.12,0.19,0.17,and 0.27,respectively).Similar results were also observed for the 90-step-ahead HB,12-step-ahead HC,and 90-step-ahead HC forecasts.The predicted HB incidents totaled 9865400(95%CI:7508093-12222709)cases and HC totaled 1659485(95%CI:856681-2462290)cases during 2023-2030.CONCLUSION Under current interventions,China faces enormous challenges to eliminate HB and HC epidemics by 2030,and effective strategies must be reinforced.The integration of SARFIMA into public health for the management of HB and HC epidemics can potentially result in more informed and efficient interventions,surpassing the capabilities of SARIMA.

Price Prediction of Seasonal Items Using Time Series Analysis

The price prediction task is a well-studied problem due to its impact on the business domain.There are several research studies that have been conducted to predict the future price of items by capturing the patterns of price change,but there is very limited work to study the price prediction of seasonal goods(e.g.,Christmas gifts).Seasonal items’prices have different patterns than normal items;this can be linked to the offers and discounted prices of seasonal items.This lack of research studies motivates the current work to investigate the problem of seasonal items’prices as a time series task.We proposed utilizing two different approaches to address this problem,namely,1)machine learning(ML)-based models and 2)deep learning(DL)-based models.Thus,this research tuned a set of well-known predictive models on a real-life dataset.Those models are ensemble learning-based models,random forest,Ridge,Lasso,and Linear regression.Moreover,two new DL architectures based on gated recurrent unit(GRU)and long short-term memory(LSTM)models are proposed.Then,the performance of the utilized ensemble learning and classic ML models are compared against the proposed two DL architectures on different accuracy metrics,where the evaluation includes both numerical and visual comparisons of the examined models.The obtained results show that the ensemble learning models outperformed the classic machine learning-based models(e.g.,linear regression and random forest)and the DL-based models.

Applications of time series analysis in epidemiology: Literature review and our experience during COVID-19 pandemic

Time series analysis is a valuable tool in epidemiology that complements the classical epidemiological models in two different ways:Prediction and forecast.Prediction is related to explaining past and current data based on various internal and external influences that may or may not have a causative role.Forecasting is an exploration of the possible future values based on the predictive ability of the model and hypothesized future values of the external and/or internal influences.The time series analysis approach has the advantage of being easier to use(in the cases of more straightforward and linear models such as Auto-Regressive Integrated Moving Average).Still,it is limited in forecasting time,unlike the classical models such as Susceptible-Exposed-Infectious-Removed.Its applicability in forecasting comes from its better accuracy for short-term prediction.In its basic form,it does not assume much theoretical knowledge of the mechanisms of spreading and mutating pathogens or the reaction of people and regulatory structures(governments,companies,etc.).Instead,it estimates from the data directly.Its predictive ability allows testing hypotheses for different factors that positively or negatively contribute to the pandemic spread;be it school closures,emerging variants,etc.It can be used in mortality or hospital risk estimation from new cases,seroprevalence studies,assessing properties of emerging variants,and estimating excess mortality and its relationship with a pandemic.

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.

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.

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.

Hydrodynamic characteristics of a typical karst spring system based on time series analysis in northern China

In order to study the hydrodynamic characteristics of the karst aquifers in northern China,time series analyses(correlation and spectral analysis in addition with hydrograph recession analysis)are applied on Baotu Spring and Heihu Spring in Jinan karst spring system,a typical karst spring system in northern China.Results show that the auto-correlation coefficient of spring water level reaches the value of 0.2 after 123 days and 117 days for Baotu Spring and Heihu Spring,respectively.The regulation time obtained from the simple spectral density function in the same period is 187 days and 175 days for Baotu Spring and Heihu Spring.The auto-correlation coefficient of spring water level reaches the value of 0.2 in 34-82 days,and regulation time ranges among 40-59 days for every single hydrological year.The delay time between precipitation and spring water level obtained from cross correlation function is around 56 days for the period of 2012-2019,and varies among 30-79 days for every single hydrological year.In addition,the spectral bands in cross amplitude functions and gain functions are small with 0.02,and the values in the coherence functions are small.All these behaviors illustrate that Jinan karst spring system has a strong memory effect,large storage capacity,noticeable regulation effect,and time series analysis is a useful tool for studying the hydrodynamic characteristics of karst spring system in northern China.

Time Series and Spatial Epidemiological Analysis of the Prevalence of Iodine Deficiency Disorders in China

Objective To recognize the spatial and temporal characteristics of iodine deficiency disorders(IDD),China national IDD surveillance data for the years of 1995–2018 were analyzed.Methods Time series analysis was used to describe and predict the IDD related indicators,and spatial analysis was used to analyze the spatial distribution of salt iodine levels.Results In China,the median urinary iodine concentration increased in 1995–1997,then decreased to adequate levels,and are expected to remain appropriate in 2019–2022.The goiter rate continually decreased and is expected to be maintained at a low level.Since 2002,the coverage rates of iodized salt and the consumption rates of qualified iodized salt(the percentage of qualified iodized salt in all tested salt) increased and began to decline in 2012;they are expected to continue to decrease.Spatial epidemiological analysis indicated a positive spatial correlation in 2016–2018 and revealed feature regarding the spatial distribution of salt related indicators in coastal areas and areas near iodine-excess areas.Conclusions Iodine nutrition in China showed gradual improvements.However,a recent decline has been observed in some areas following changes in the iodized salt supply in China.In the future,more regulations regarding salt management should be issued to strengthen IDD control and prevention measures,and avoid the recurrence of IDD.

Does Monetary Support Increase the Number of Scientific Papers？ An Interrupted Time Series Analysis

Purpose： One of the main indicators of scientific production is the number of papers published in scholarly journals. Turkey ranks 18th place in the world based on the number of scholarly publications. The objective of this paper is to find out if the monetary support program initiated in 1993 by the Turkish Scientific and Technological Research Council （TUBITAK） to incentivize researchers and increase the number, impact, and quality of international publications has been effective in doing so.Design/methodology/approach： We analyzed some 390,000 publications with Turkish affiliations listed in the Web of Science （WoS） database between 1976 and 2015 along with about 157,000 supported ones between 1997 and 2015. We used the interrupted time series （ITS） analysis technique （also known as ＂quasi-experimental time series analysis＂ or ＂intervention analysis＂） to test if TOBITAK＇s support program helped increase the number of publications. We defined ARIMA （1,1,0） model for ITS data and observed the impact of TOBiTAK＇s support program in 1994, 1997, and 2003 （after one, four and 10 years of its start, respectively）. The majority of publications （93%） were full papers （articles）, which were used as the experimental group while other types of contributions functioned as the control group. We also carried out a multiple regression analysis.Findings： TUBITAK＇s support program has had negligible effect on the increase of the number of papers with Turkish affiliations. Yet, the number of other types of contributions continued to increase even though they were not well supported, suggesting that TUBITAK＇s support program is probably not the main factor causing the increase in the number of papers with Turkish affiliations. Research limitations： Interrupted time series analysis shows if the ＂intervention＂ has had any significant effect on the dependent variable but it does not explain what caused the increase in the number of papers if it was not the intervention. Moreover, except the＂intervention＂, other ＂event（s）＂ that might affect the time series data （e.g., increase in the number of research personnel over the years） should not occur during the period of analysis, a prerequisite that is beyond the control of the researcher. Practical implications： TUBITAK＇s ＂cash-for-publication＂ program did not seem to have direct impact on the increase of the number of papers published by Turkish authors, suggesting that small amounts of payments are not much of an incentive for authors to publish more. It might perhaps be a better strategy to concentrate limited resources on a few high impact projects rather than to disperse them to thousands of authors as ＂micropayments.＂ Originality/value： Based on 25 years＇ worth of payments data, this is perhaps one of the first large-scale studies showing that ＂cash-for-publication＂ policies or ＂piece rates＂ paid to researchers tend to have little or no effect on the increase of researchers＇ productivity. The main finding of this paper has some implications for countries wherein publication subsidies are used as an incentive to increase the number and quality of papers published in international journals. They should be prepared to consider reviewing their existing support programs （based usually on bibliometric measures such as journal impact factors） and revising their reward policies.

STUDY OF MACHINING PROCESS MONITORING OF FMS BASED ON TIME SERIES ANALYSIS

FMS is a sort of highly automatic machining system, how to ensure partquality is master key to system highly active running. At first, series of machining dimension andprocess capability of flexible manufacturing system(FMS), is analyzed. Result of its, strongself-correlation of data series shows that time series analysis is applicable to data seriesanalyzed. Based on-line modeling and forecasting for data series, principle and method of feedbackcompensation control is proposed. On a foundation of the virtual instrument platform, Labview ofnational instrument (NI), FMS dimension and process capability monitoring system(monitoring system)is developed. In practice, it is proved that part quality and process capability of FMS are greatlyimproved.

Denoising Nonlinear Time Series Using Singular Spectrum Analysis and Fuzzy Entropy

We present a hybrid singular spectrum analysis （SSA） and fuzzy entropy method to filter noisy nonlinear time series. With this approach, SSA decomposes the noisy time series into its constituent components including both the deterministic behavior and noise, while fuzzy entropy automatically differentiates the optimal dominant components from the noise based on the complexity of each component. We demonstrate the effectiveness of the hybrid approach in reconstructing the Lorenz and Mackey--Class attractors, as well as improving the multi-step prediction quality of these two series in noisy environments.

Correlation between detrended fluctuation analysis and the Lempel-Ziv complexity in nonlinear time series analysis

We study the correlation between detrended fluctuation analysis（DFA） and the Lempel-Ziv complexity（LZC） in nonlinear time series analysis in this paper.Typical dynamic systems including a logistic map and a Duffing model are investigated.Moreover,the influence of Gaussian random noise on both the DFA and LZC are analyzed.The results show a high correlation between the DFA and LZC,which can quantify the non-stationarity and the nonlinearity of the time series,respectively.With the enhancement of the random component,the exponent α and the normalized complexity index C show increasing trends.In addition,C is found to be more sensitive to the fluctuation in the nonlinear time series than α.Finally,the correlation between the DFA and LZC is applied to the extraction of vibration signals for a reciprocating compressor gas valve,and an effective fault diagnosis result is obtained.

Research on Forecasting Water Requirement of Well Irrigation Rice by Time Series Analysis Method

The paper builds up the forecasting model of air temperature according to the data (1994～1998) of Fu Jin area.At the same time,the writer inquires into the relation of water requirement of well irrigation rice (ET) and average air temperature (T).Furthermore,the rice irrigation water requirement (ET) of Fu Jin area has been forecast in 1999.Thus,we can apply the model in irrigation management.

FAULT IDENTIFICATION IN HETEROGENEOUS NETWORKS USING TIME SERIES ANALYSIS

Fault management is crucial to pro vi de quality of service grantees for the future networks, and fault identification is an essential part of it. A novel fault identification algorithm is proposed in this paper, which focuses on the anomaly detection of network traffic. Since the fault identification has been achieved using statistical information in mana gement information base, the algorithm is compatible with the existing simple ne twork management protocol framework. The network traffic time series is verified to be non-stationary. By fitting the adaptive autoregressive model, the series is transformed into a multidimensional vector. The training samples and identif iers are acquired from the network simulation. A k-nearest neighbor classif ier identifies the system faults after being trained. The experiment results are consistent with the given fault scenarios, which prove the accuracy of the algo rithm. The identification errors are discussed to illustrate that the novel faul t identification algorithm is adaptive in the fault scenarios with network traff ic change.

Outlier Detection and Forecasting for Bridge Health Monitoring Based on Time Series Intervention Analysis

The method of time series analysis,applied by establishing appropriate mathematical models for bridge health monitoring data and making forecasts of structural future behavior,stands out as a novel and viable research direction for bridge state assessment.However,outliers inevitably exist in the monitoring data due to various interventions,which reduce the precision of model fitting and affect the forecasting results.Therefore,the identification of outliers is crucial for the accurate interpretation of the monitoring data.In this study,a time series model combined with outlier information for bridge health monitoring is established using intervention analysis theory,and the forecasting of the structural responses is carried out.There are three techniques that we focus on:(1)the modeling of seasonal autoregressive integrated moving average(SARIMA)model;(2)the methodology for outlier identification and amendment under the circumstances that the occurrence time and type of outliers are known and unknown;(3)forecasting of the model with outlier effects.The method was tested with a case study using monitoring data on a real bridge.The establishment of the original SARIMA model without considering outliers is first discussed,including the stationarity,order determination,parameter estimation and diagnostic checking of the model.Then the time-by-time iterative procedure for outlier detection,which is implemented by appropriate test statistics of the residuals,is performed.The SARIMA-outlier model is subsequently built.Finally,a comparative analysis of the forecasting performance between the original model and SARIMA-outlier model is carried out.The results demonstrate that proper time series models are effective in mining the characteristic law of bridge monitoring data.When the influence of outliers is taken into account,the fitted precision of the model is significantly improved and the accuracy and the reliability of the forecast are strengthened.

Using time series analysis to assess tidal effect on coastal groundwater level in Southern Laizhou Bay, China

Sea water intrusion is an environmental problem cause by the irrational exploitation of coastal groundwater resources and has attracted the attention of many coastal countries.In this study,we used time series monitoring data of groundwater levels and tidal waves to analyze the influence of tide flow on groundwater dynamics in the southern Laizhou Bay.The auto-correlation and cross-correlation coefficients between groundwater level and tidal wave level were calculated specifically to measure the boundary conditions along the coastline.In addition,spectrum analysis was employed to assess the periodicity and hysteresis of various tide and groundwater level fluctuations.The results of time series analysis show that groundwater level fluctuation is noticeably influenced by tides,but the influence is limited to a certain distance and cannot reach the saltwater-freshwater interface in the southern Laizhou Bay.There are three main periodic components of groundwater level in tidal effect range(i.e.23.804 h,12.500 h and 12.046 h),the pattern of which is the same as the tides.The affected groundwater level fluctuations lag behind the tides.The dynamic analysis of groundwater indicates that the coastal aquifer has a hydraulic connection with seawater but not in a direct way.Owing to the existence of the groundwater mound between the salty groundwater(brine)and fresh groundwater,the maximum influencing distance of the tide on the groundwater is 8.85 km.Considering that the fresh-saline groundwater interface is about 30 km away from the coastline,modern seawater has a limited contribution to sea-salt water intrusion in Laizhou Bay.The results of this study are expected to provide a reference for the study on sea water intrusion.

Using Interrupted Time Series Design to Analyze Changes in Hand, Foot, and Mouth Disease Incidence during the Declining Incidence Periods of 2008-2010 in China

Objective To identify patterns of hand, foot and mouth disease （HFMD） incidence in China during declining incidence periods of 2008, 2009, and 2010. Methods Reported HFMD cases over a period of 25 months were extracted from the National Disease Reporting System （NDRS） and analyzed. An interrupted time series （ITS） technique was used to detect changes in HFMD incidence rates in terms of level and slope between declining incidence periods of the three years. Results Over 3.58 million HFMD cases younger than 5 years were reported to the NDRS between May 1, 2008, and May 31, 2011. Males comprised 63.4% of the cases. ITS analyses demonstrated a significant increase in incidence rate level （P〈0.0001） when comparing the current period with the previous period. There were significant changes in declining slopes when comparing 2010 to 2009, and 2010 to 2008 （all P〈O.O05）, but not 2009 to 2008. Conclusion Incremental changes in incidence rate level during the declining incidence periods of 2009 and 2010 can potentially be attributed to a few factors. The more steeply declining slope in 2010 compared with previous years could be ascribed to the implementation of more effective interventions and preventive strategies in 2010. Further investigation is required to examine this possibility.

Forecasting the number of zoonotic cutaneous leishmaniasis cases in south of Fars province, Iran using seasonal ARIMA time series method

Objective: To predict the trend of cutaneous leishmaniasis and assess the relationship between the disease trend and weather variables in south of Fars province using Seasonal Autoregressive Integrated Moving Average(SARIMA) model,Methods: The trend of cutaneous leishmaniasis was predicted using Mini tab software and SARIMA model,Besides,information about the disease and weather conditions was collected monthly based on time series design during January 2010 to March 2016,Moreover,various SARIMA models were assessed and the best one was selected,Then,the model's fitness was evaluated based on normality of the residuals' distribution,correspondence between the fitted and real amounts,and calculation of Akaike Information Criteria(AIC) and Bayesian Information Criteria(BIC),Results: The study results indicated that SARIMA model(4,1,4)(0,1,0)(12) in general and SARIMA model(4,1,4)(0,1,1)(12) in below and above 15 years age groups could appropriately predict the disease trend in the study area,Moreover,temperature with a three-month delay(lag3) increased the disease trend,rainfall with a four-month delay(lag4) decreased the disease trend,and rainfall with a nine-month delay(lag9) increased the disease trend,Conclusions: Based on the results,leishmaniasis follows a descending trend in the study area in case drought condition continues,SARIMA models can suitably measure the disease trend,and the disease follows a seasonal trend.

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.