Traditional Autoregressive Integrated Moving Average Research Articles

An Accurate Model for Covid-19 Positive Cases in India by using Traditional ARIMA and Artificial Neural Networks (LSTM and Bi-LSTM)

Objective: This study focuses on evaluating the accuracy of models that can be identified by taking the data of COVID-19-positive cases in India. Methods: To build the models by using the procedures, Artificial Neural Networks (ANN) and Auto Regressive Integrated Moving Average (ARIMA). The data has been taken for various time periods of (Covid-19 positive cases) from March 2022 to July 2023; March 2022 to Nov. 2022 and from Nov. 2022 to July 2023. The data was collected from the official website of the World Health Organization (WHO). The traditional ARIMA and Long Short-Term Memory (LSTM) deep learning methods were applied to build models for various time periods. Findings: Model performance is being measured with the error parameter (Root Mean Square Error) RMSE (215.74, 100.36 and 127.81) respectively for all the time periods. LSTM is performing better than the ARIMA with a minimum value of RMSE. Novelty: The study has been done for the time periods of Covid-19 positive cases with the help of LSTM, Bi-LSTM and ARIMA methods. The outcome of these methods gave; LSTM is the accurate and best performance model. Keywords: ARIMA, Neural Networks, LSTM, RMSE

Enhancing drought prediction precision with EEMD-ARIMA modeling based on standardized precipitation index.

This study introduces ensemble empirical mode decomposition (EEMD) coupled with the autoregressive integrated moving average (ARIMA) model for drought prediction. In the realm of drought forecasting, we assess the EEMD-ARIMA model against the traditional ARIMA approach, using monthly precipitation data from January 1970 to December 2019 in Herat province, Afghanistan. Our evaluation spans various timescales of standardized precipitation index (SPI) 3, SPI 6, SPI 9, and SPI 12. Statistical indicators like root-mean-square error, mean absolute error (MAE), mean absolute percentage error (MAPE), and R2 are employed. To comprehend data features thoroughly, each SPI series initially computed from the original monthly precipitation time series. Subsequently, each SPI undergoes decomposition using EEMD, resulting in intrinsic mode functions (IMFs) and one residual series. The next step involves forecasting each IMF component and residual using the corresponding ARIMA model. To create an ensemble forecast for the initial SPI series, the predicted outcomes of the modeled IMFs and residual series are finally added. Results indicate that EEMD-ARIMA significantly enhances drought forecasting accuracy compared to conventional ARIMA model.

Novel grey wolf optimizer based parameters selection for GARCH and ARIMA models for stock price prediction.

Stock price data often exhibit nonlinear patterns and dynamics in nature. The parameter selection in generalized autoregressive conditional heteroskedasticity (GARCH) and autoregressive integrated moving average (ARIMA) models is challenging due to stock price volatility. Most studies examined the manual method for parameter selection in GARCH and ARIMA models. These procedures are time-consuming and based on trial and error. To overcome this, we considered a GWO method for finding the optimal parameters in GARCH and ARIMA models. The motivation behind considering the grey wolf optimizer (GWO) is one of the popular methods for parameter optimization. The novel GWO-based parameters selection approach for GARCH and ARIMA models aims to improve stock price prediction accuracy by optimizing the parameters of ARIMA and GARCH models. The hierarchical structure of GWO comprises four distinct categories: alpha (α), beta (β), delta (δ) and omega (ω). The predatory conduct of wolves primarily encompasses the act of pursuing and closing in on the prey, tracing the movements of the prey, and ultimately launching an attack on the prey. In the proposed context, attacking prey is a selection of the best parameters for GARCH and ARIMA models. The GWO algorithm iteratively updates the positions of wolves to provide potential solutions in the search space in GARCH and ARIMA models. The proposed model is evaluated using root mean squared error (RMSE), mean squared error (MSE), and mean absolute error (MAE). The GWO-based parameter selection for GARCH and ARIMA improves the performance of the model by 5% to 8% compared to existing traditional GARCH and ARIMA models.

On improved fitting using a new probability distribution and artificial neural network: Application

Statistical modeling and forecasting are crucial to understanding the depth of information in data from all sources. For precision purposes, researchers are always in search of ways to improve the quality of modeling and forecasting, whatever the complexity of the situation. To this end, new (probability) distributions and suitable forecasting methods are demanded. The first part of this paper contributes to this direction. Indeed, we introduce a modified version of the flexible Weibull distribution, called the modified flexible Weibull distribution. It is constructed by mixing the flexible Weibull distribution with the exponential T-X scheme. This strategy is winning; the new distribution has a larger panel of functionalities in comparison to those of the classical Weibull distribution, among other things. To check the quality of the fitting of the modified flexible Weibull distribution, two different datasets are analyzed. After analyzing these datasets, it is observed that the modified flexible Weibull distribution has improved fitting power compared to other similar distributions. Apart from this, the conventional time series model, namely, the autoregressive integrated moving average (ARIMA) model, and the modern artificial neural network (ANN) model are considered for forecasting results. Utilizing the two datasets discussed earlier, it was discovered that the ANN model is more effective than the traditional ARIMA model.

Price prediction of the Borsa Istanbul banks index with traditional methods and artificial neural networks

In terms of asset size, the banking system constitutes 83% of the financial markets in Turkiye. Given the importance of the banking system in the Turkish capital market, this study offers a price forecasting analysis of the Borsa Istanbul Banks Index, which represents the domestic banking system, between December 27, 1996, to August 31, 2023, using the traditional Autoregressive Integrated Moving Average (ARIMA) Model and two artificial intelligence-based deep learning models, namely, the Facebook Prophet Model (FPM) and Convolutional Neural Networks Model (CNNM). The findings indicate that the CNNM perform better than the other models. The results are useful for researchers working with time series data at the stage of method selection and investment firms and managers that are forecasting future stock price movements. Policy implications of the findings are discussed.

Hybrid Statistical and Machine Learning Methods for Daily Evapotranspiration Modeling

Machine learning (ML) models, including artificial neural networks (ANN), generalized neural regression networks (GRNN), and adaptive neuro-fuzzy interface systems (ANFIS), have received considerable attention for their ability to provide accurate predictions in various problem domains. However, these models may produce inconsistent results when solving linear problems. To overcome this limitation, this paper proposes hybridizations of ML and autoregressive integrated moving average (ARIMA) models to provide a more accurate and general forecasting model for evapotranspiration (ET0). The proposed models are developed and tested using daily ET0 data collected over 11 years (2010–2020) in the Samsun province of Türkiye. The results show that the ARIMA–GRNN model reduces the root mean square error by 48.38%, the ARIMA–ANFIS model by 8.56%, and the ARIMA–ANN model by 6.74% compared to the traditional ARIMA model. Consequently, the integration of ML with ARIMA models can offer more accurate and dependable prediction of daily ET0, which can be beneficial for many branches such as agriculture and water management that require dependable ET0 estimations.

Forecasting of Beijing PM2.5 with a hybrid ARIMA model based on integrated AIC and improved GS fixed-order methods and seasonal decomposition

Accurate particulate matter 2.5 (PM2.5) prediction plays a crucial role in the accurate management of air pollution and prevention of respiratory diseases. However, PM2.5, as a nonlinear time series with great volatility, is difficult to achieve accurate prediction. In this paper, a hybrid autoregressive integrated moving average (ARIMA) model is proposed based on the Augmented Dickey-Fuller test (ADF root test) of annual PM2.5 data, thus demonstrating the necessity of first-order difference. The new method of using integrated akaike information criterion (AIC) and improved grid search (GS) methods is proposed to avoid the bias caused by using AIC alone to determine the order because the data are not exactly normally distributed. The comprehensive evaluation coefficient (CEC) is used to select the optimal parameter structure of the prediction model by considering multiple evaluation perspectives. The entropy value of the decomposed series is obtained by using range entropy A (RangeEn_A), and the series is reconstructed according to the entropy value, and finally the reconstructed series is predicted. We used Beijing PM2.5 data for validation and the results showed that the new hybrid ARIMA model improved values of RMSE 99.23%, MAE 99.20%, R2 118.61%, TIC 99.28%, NMAE 98.71%, NMSE 99.97%, OPC 43.13%, MOPC 98.43% and CEC 99.25% compared with the traditional ARIMA model. The results show that the method does greatly improve the prediction performance and provides a convincing tool for policy formulation and governance.

Traffic flow prediction using bi-directional gated recurrent unit method

Traffic flow prediction plays an important role in intelligent transportation systems. To accurately capture the complex non-linear temporal characteristics of traffic flow, this paper adopts a Bi-directional Gated Recurrent Unit (Bi-GRU) model in traffic flow prediction. Compared to Gated Recurrent Unit (GRU), which can memorize information from the previous sequence, this model can memorize the traffic flow information in both previous and subsequent sequence. To demonstrate the model’s performance, a set of real case data at 1-hour intervals from 5 working days was used, wherein the dataset was separated into training and validation. To improve data quality, an augmented dickey-fuller unit root test and differential processing were performed before model training. Four benchmark models were used, including the Autoregressive Integrated Moving Average (ARIMA), Long Short-Term Memory (LSTM), Bidirectional Long Short-Term Memory (Bi-LSTM), and GRU. The prediction results show the superior performance of Bi-GRU. The Root Mean Square Error (RMSE), Mean Absolute Percentage Error (MAPE), and Mean Absolute Error (MAE) of the Bi-GRU model are 30.38, 9.88%, and 23.35, respectively. The prediction accuracy of LSTM, Bi-LSTM, GRU, and Bi-GRU, which belong to deep learning methods, is significantly higher than that of the traditional ARIMA model. The MAPE difference of Bi-GRU and GRU is 0.48% which is a small prediction error value. The results show that the prediction accuracy of the peak period is higher than that of the low peak. The Bi-GRU model has a certain lag on traffic flow prediction.

Comparison of ARIMA model, DNN model and LSTM model in predicting disease burden of occupational pneumoconiosis in Tianjin, China

BackgroundThis study aims to explore appropriate model for predicting the disease burden of pneumoconiosis in Tianjin by comparing the prediction effects of Autoregressive Integrated Moving Average (ARIMA) model, Deep Neural Networks (DNN) model and multivariate Long Short-Term Memory Neural Network (LSTM) models.MethodsDisability adjusted life year (DALY) was used to evaluate the disease burden of occupational pneumoconiosis. ARIMA model, DNN model and multivariate LSTM model were used to establish prediction model. Three performance evaluation metrics including Root Mean Squared Error (RMSE), Mean Absolute Error (MAE) and Mean Absolute Percentage Error (MAPE) were used to compare the prediction effects of the three models.ResultsFrom 1990 to 2021, there were 10,694 cases of pneumoconiosis patients in Tianjin, resulting in a total of 112,725.52 person-years of DALY. During this period, the annual DALY showed a fluctuating trend, but it had a strong correlation with the number of pneumoconiosis patients, the average age of onset, the average age of receiving dust and the gross industrial product, and had a significant nonlinear relationship with them. The comparison of prediction results showed that the performance of multivariate LSTM model and DNN model is much better than that of traditional ARIMA model. Compared with the DNN model, the multivariate LSTM model performed better in the training set, showing lower RMES (42.30 vs. 380.96), MAE (29.53 vs. 231.20) and MAPE (1.63% vs. 2.93%), but performed less stable than the DNN on the test set, showing slightly higher RMSE (1309.14 vs. 656.44), MAE (886.98 vs. 594.47) and MAPE (36.86% vs. 22.43%).ConclusionThe machine learning techniques of DNN and LSTM are an innovative method to accurately and efficiently predict the burden of pneumoconiosis with the simplest data. It has great application prospects in the monitoring and early warning system of occupational disease burden.

Https://www.ijmtst.com/vol8issue09.html

Many applications in intelligent transportation systems are demanding an accurate web application-based location prediction. In this study, we satisfy this demand by designing an automated mobile user location prediction system based on the well-known traditional Auto-Regressive Integrated Moving Average (ARIMA). To increase the proposed model accuracy, make it dynamic, and reduce its execution time, the traditional ARIMA model has been modified extensively by using different combinations of design options of the model. To perform user location prediction, the proposed model depends the previous recorded user locations to predict the user future locations. To make the proposed model dynamic, it is designed to regenerate all its parameters periodically. To deal with such dynamic environment, only a specified window of the historical data is used. To reduce the regeneration of the model execution time, the model selection process is enhanced and several model selection approaches are proposed. The proposed model and the different design options are evaluated using a realistic user location dataset trace that are recorded using a WIFI embedded, as well as, using traces from a previous study called the Kaggle Dataset. To deal with any imperfection in the data used in generating the model in this study. The results show that the proposed framework can generate ARIMA models that can predict the future user locations of a user accurately and with a reasonable execution time. The results also show that the proposed model can predict the user’s location for several future steps with an acceptable accuracy.

​​ARIMA-Genetic Algorithm Approach for Forecasting Milk Production in India

Background: Dairying in India has witnessed a radical transformation from a largely unorganised activity into a thriving organised industry. However, there are only a limited number of earlier attempts that specifically evaluated the milk production pattern of India. Moreover, most of these earlier studies are quite dated and have employed autoregressive integrated moving average (ARIMA) models, which suffer from the problem of local optima. To overcome this lacuna, we have utilised a genetic algorithm (GA) in the ARIMA framework. Its suitability to forecast the annual milk production in India has also been assessed comparatively with respect to the traditional ARIMA methodology. Methods: For the current study, data on annual milk production (in million tonnes) in India for the period from 1980 to 2019 have been utilised. For both the approaches under investigation, the whole data series is first divided into two sets, namely the training set and the testing set. The production data of 1980-2016 have been utilised for the model building purpose while retaining the last 3 years’ data for the post-sample evaluation. Result: Outcomes emanated from the post-sample assessment clearly suggest that the ARIMA-GA approach has outperformed the traditional ARIMA methodology in terms of root mean square error (RMSE) and mean absolute percentage error (MAPE) values. It is also evident that GA has substantially minimised the error related to the parameter estimation.

A novel hybrid model of ARIMA‐MCC and CKDE‐GARCH for urban short‐term traffic flow prediction

The linearity and heteroscedasticity are the important characteristics of short-term traffic flow data. Generally, the autoregressive integrated moving average (ARIMA) model and the generalized autoregressive conditional heteroscedasticity (GARCH) model are respectively used to explain these characteristics. However, the prerequisite for the use of ARIMA is that the training residuals should follow the standard Gaussian distribution, which is hard to be satisfied in practice. Meanwhile, the variance in the GARCH model usually neglects the time-varying characteristic. To address these problems, this paper proposes an innovative method based on the combination of ARIMA, maximum correntropy criterion (MCC), conditional kernel density estimation (CKDE), and GARCH. Specifically, the MCC method is first employed to estimate the coefficients of the ARIMA model (i.e. ARIMA-MCC), by which the linear prediction is conducted. Then, the CKDE model is established to describe the training residuals obtained by ARIMA-MCC and estimate the time-varying variance in the GARCH model (i.e. GARCH-CKDE). Case studies based on four groups of data measured in the urban road are used to evaluate the performance of the proposed method. Compared with the traditional ARIMA model, the improvement by the proposed method reaches 14.45% in terms of the evaluation criterion of mean absolute percentage error.

Forecasting COVID-19 Hospital Census: A Multivariate Time-Series Model Based on Local Infection Incidence.

BackgroundCOVID-19 has been one of the most serious global health crises in world history. During the pandemic, health care systems require accurate forecasts for key resources to guide preparation for patient surges. Forecasting the COVID-19 hospital census is among the most important planning decisions to ensure adequate staffing, number of beds, intensive care units, and vital equipment.ObjectiveThe goal of this study was to explore the potential utility of local COVID-19 infection incidence data in developing a forecasting model for the COVID-19 hospital census.MethodsThe study data comprised aggregated daily COVID-19 hospital census data across 11 Atrium Health hospitals plus a virtual hospital in the greater Charlotte metropolitan area of North Carolina, as well as the total daily infection incidence across the same region during the May 15 to December 5, 2020, period. Cross-correlations between hospital census and local infection incidence lagging up to 21 days were computed. A multivariate time-series framework, called the vector error correction model (VECM), was used to simultaneously incorporate both time series and account for their possible long-run relationship. Hypothesis tests and model diagnostics were performed to test for the long-run relationship and examine model goodness of fit. The 7-days-ahead forecast performance was measured by mean absolute percentage error (MAPE), with time-series cross-validation. The forecast performance was also compared with an autoregressive integrated moving average (ARIMA) model in the same cross-validation time frame. Based on different scenarios of the pandemic, the fitted model was leveraged to produce 60-days-ahead forecasts.ResultsThe cross-correlations were uniformly high, falling between 0.7 and 0.8. There was sufficient evidence that the two time series have a stable long-run relationship at the .01 significance level. The model had very good fit to the data. The out-of-sample MAPE had a median of 5.9% and a 95th percentile of 13.4%. In comparison, the MAPE of the ARIMA had a median of 6.6% and a 95th percentile of 14.3%. Scenario-based 60-days-ahead forecasts exhibited concave trajectories with peaks lagging 2 to 3 weeks later than the peak infection incidence. In the worst-case scenario, the COVID-19 hospital census can reach a peak over 3 times greater than the peak observed during the second wave.ConclusionsWhen used in the VECM framework, the local COVID-19 infection incidence can be an effective leading indicator to predict the COVID-19 hospital census. The VECM model had a very good 7-days-ahead forecast performance and outperformed the traditional ARIMA model. Leveraging the relationship between the two time series, the model can produce realistic 60-days-ahead scenario-based projections, which can inform health care systems about the peak timing and volume of the hospital census for long-term planning purposes.

Using a data driven neural network approach to forecast building occupant complaints

Occupant complaints are a reflection of poor building performance and an unsatisfactory indoor environment. One way to mitigate these complaints and to ensure occupants' satisfaction with building performance is through a well-performing facility management that is capable of planning for and addressing the maintenance services. This research work proposes a machine learning-based multistep generic framework to analyze building occupant complaints and to forecast the number of thermal complaints, in particular, as part of the facility management's predictive maintenance strategy. The developed forecasting model is benchmarked against a traditional statistical model to ensure a satisfactory performance. The proposed methodology was tested for a period of three years on a highly unstructured and unsolicited occupant-complaint data recorded by facility management operators in a residential complex composed of 16 buildings. Text mining results of more than 6,000 complaints showed that thermal complaints are among the most common ones thus require further attention of facility managers. The developed Multi-Layer Perceptron (MLP) models to forecast the number of thermal complaints for the upcoming week showed similar or better performance as compared to the traditional Autoregressive Integrated Moving Average (ARIMA) models with a higher ability to generalize to new data. For example, the cooling related complaints MLP model showed a RMSE of 0.878, which is 21% lower than the RMSE of the ARIMA model. It is also evident that the developed models could assist facility managers in planning for the staffing resources required to handle these complaints thus enhancing occupants' satisfaction and the building performance.

Determine neighboring region spatial effect on dengue cases using ensemble ARIMA models

The state of Selangor, in Malaysia consist of urban and peri-urban centres with good transportation system, and suitable temperature levels with high precipitations and humidity which make the state ideal for high number of dengue cases, annually. This study investigates if districts within the Selangor state do influence each other in determining pattern of dengue cases. Study compares two different models; the Autoregressive Integrated Moving Average (ARIMA) and Ensemble ARIMA models, using the Akaike Information Criterion (AIC) and Bayesian Information Criterion (BIC) measurement to gauge their performance tools. ARIMA model is developed using the epidemiological data of dengue cases, whereas ensemble ARIMA incorporates the neighbouring regions’ dengue models as the exogenous variable (X), into traditional ARIMA model. Ensemble ARIMA models have better model fit compared to the basic ARIMA models by incorporating neighbuoring effects of seven districts which made of state of Selangor. The AIC and BIC values of ensemble ARIMA models to be smaller compared to traditional ARIMA counterpart models. Thus, study concludes that pattern of dengue cases for a district is subject to spatial effects of its neighbouring districts and number of dengue cases in the surrounding areas.

A Kalman filter-based hybridization model of statistical and intelligent approaches for exchange rate forecasting

Purpose The purpose of this paper is to propose a comprehensive version of a hybrid autoregressive integrated moving average (ARIMA), and artificial neural networks (ANNs) in order to yield a more general and more accurate hybrid model for exchange rates forecasting. For this purpose, the Kalman filter technique is used in the proposed model to preprocess and detect the trend of raw data. It is basically done to reduce the existing noise in the underlying data and better modeling, respectively. Design/methodology/approach In this paper, ARIMA models are applied to construct a new hybrid model to overcome the above-mentioned limitations of ANNs and to yield a more general and more accurate model than traditional hybrid ARIMA and ANNs models. In our proposed model, a time series is considered as a function of a linear and nonlinear component, so, in the first phase, an ARIMA model is first used to identify and magnify the existing linear structures in data. In the second phase, a multilayer perceptron is used as a nonlinear neural network to model the preprocessed data, in which the existing linear structures are identified and magnified by ARIMA and to predict the future value of time series. Findings In this paper, a new Kalman filter based hybrid artificial neural network and ARIMA model are proposed as an alternate forecasting technique to the traditional hybrid ARIMA/ANNs models. In the proposed model, similar to the traditional hybrid ARIMA/ANNs models, the unique strengths of ARIMA and ANN in linear and nonlinear modeling are jointly used, aiming to capture different forms of relationship in the data; especially, in complex problems that have both linear and nonlinear correlation structures. However, there are no aforementioned assumptions in the modeling process of the proposed model. Therefore, in the proposed model, in contrast to the traditional hybrid ARIMA/ANNs, it can be generally guaranteed that the performance of the proposed model will not be worse than either of their components used separately. In addition, empirical results in both weekly and daily exchange rate forecasting indicate that the proposed model can be an effective way to improve forecasting accuracy achieved by traditional hybrid ARIMA/ANNs models. Originality/value In the proposed model, in contrast to the traditional hybrid ARIMA/ANNs, it can be guaranteed that the performance of the proposed model will not be worse than either of the components used separately. In addition, empirical results in exchange rate forecasting indicate that the proposed model can be an effective way to improve forecasting accuracy achieved by traditional hybrid ARIMA/ANNs models. Therefore, it can be used as an appropriate alternate model for forecasting in exchange ratemarkets, especially when higher forecasting accuracy is needed.

Performance of design options of automated ARIMA model construction for dynamic vehicle GPS location prediction

Many applications in intelligent transportation systems are demanding an accurate vehicle Global Position System (GPS) location prediction. In this study, we satisfy this demand by designing an automated GPS location prediction system based on the well known traditional Auto-Regressive Integrated Moving Average (ARIMA). To increase the proposed model accuracy, make it dynamic, and reduce its execution time, the traditional ARIMA model has been modified extensively by using different combinations of design options of the model. To perform GPS location prediction, the proposed model depends the previous recorded vehicle locations, speed, and bearing reading to predict the vehicle future locations. To make the proposed model dynamic, it is designed to regenerate all its parameters periodically. To deal with such dynamic environment, only a specified window of the historical data is used. To reduce the regeneration of the model execution time, the model selection process is enhanced and several model selection approaches are proposed. The proposed model and the different design options are evaluated using a realistic vehicle dataset traces that are recorded using a GPS receiver embedded in a smart phone, as well as, using traces from a previous study called the INFATI Dataset. To deal with any imperfection in the data used in generating the model in this study, we propose a novel anomaly detection and smoothing technique. The results show that the proposed framework can generate ARIMA models that can predict the future GPS locations of a vehicle accurately and with a reasonable execution time. The results also show that the proposed model can predict the vehicle’s location for several future steps with an acceptable accuracy.

A comparative study on the prediction of the BP artificial neural network model and the ARIMA model in the incidence of AIDS

BackgroundAs a kind of widely distributed disease in China, acquired immune deficiency syndrome (AIDS) has been quickly growing each year, become a serious problem and caused serious damage to the life and health of people and the social events of China and the world because of its high fatality rate. It has been much concerned by all aspects of society. Therefore, developing early warning technology and finding the trend of early development are of quite significance to prevent and control human immunodeficiency virus (HIV)/AIDS. This study aimed to explore a suitable model for the morbidity of AIDS in China and establish a professional and feasible disease prediction model for the prevention and control works of AIDS.MethodsAt present, the traditional linear model is still utilized by most scholars to predict the incidence of HIV/AIDS. In addition, some scholars may attempt to use the nonlinear prediction model. Both prediction models showed good fitting and prediction effects. In China, the incidence of AIDS presents linear and nonlinear characteristics. In this research, the nonlinear back propagation artificial neural network (BP-ANN) model and the typical auto-regressive integrated moving average (ARIMA) linear model were applied to predict the incidence of HIV/AIDS and compare their fitting effects.ResultsBoth models were capable of predicting the expected cases of AIDS. It was seen that ARIMA and BP-ANN models could be used to forecast the monthly incidence of HIV/AIDS, but the fitting and forecasting effects of the nonlinear BP neural network model were better than those of the traditional linear ARIMA model.ConclusionsIn summary, it was further concluded that the BP-ANN model was a suitable way to monitor and predict the change trend and morbidity of AIDS in China.

On the forecasting of high‐frequency financial time series based on ARIMA model improved by deep learning

AbstractThrough empirical research, it is found that the traditional autoregressive integrated moving average (ARIMA) model has a large deviation for the forecasting of high‐frequency financial time series. With the improvement in storage capacity and computing power of high‐frequency financial time series, this paper combines the traditional ARIMA model with the deep learning model to forecast high‐frequency financial time series. It not only preserves the theoretical basis of the traditional model and characterizes the linear relationship, but also can characterize the nonlinear relationship of the error term according to the deep learning model. The empirical study of Monte Carlo numerical simulation and CSI 300 index in China show that, compared with ARIMA, support vector machine (SVM), long short‐term memory (LSTM) and ARIMA‐SVM models, the improved ARIMA model based on LSTM not only improves the forecasting accuracy of the single ARIMA model in both fitting and forecasting, but also reduces the computational complexity of only a single deep learning model. The improved ARIMA model based on deep learning not only enriches the models for the forecasting of time series, but also provides effective tools for high‐frequency strategy design to reduce the investment risks of stock index.

Modeling carbon emission trajectory of China, US and India

Developing more effective carbon mitigation strategies requires accurate forecasting of carbon emissions. This is especially true for China, the United States and India, which produce over half of the world’s carbon emissions. China, the United States, and India represent three different types of carbon emissions data. The first data type is typical for China: rapid grows which is thereafter slowing down. The US carbon emissions data show volatile growth and decline. The third data type is common for India’s data: accelerated growth. To deal with the volatility of the data and to improve the forecasting accuracy, this paper combines Metabolic Nonlinear Grey Model (MNGM) with Autoregressive Integrated Moving Average (ARIMA) to develop the combined MNGM-ARIMA model, and MNGM with Back Propagation Neural Network (BPNN) to develop the new combined MNGM-BPNN model. In this way, ARIMA and BPNN could correct the modelling residual error of MNGM, to decrease the forecasting error. Through the quantitative data study of the countries in focus, we have made the following findings: First, the mean relative percent errors of the proposed MNGM-ARIMA and MNGM-BPNN models are 1.35% and 1.57%, which are lower than the traditional MNGM, ARIMA, and BPNN models. Besides, it is projected that during the period of 2019–2030, the US′ carbon emissions will keep a downward trend, while carbon emissions in China and India will continue to grow. Finally yet importantly, in the future periods of time, the carbon emissions growth rate in India will be faster than that for China. The above findings have led us to the following conclusions: (1) Error values of those two proposed approaches have proven that the strategy of correcting the forecasting error of the previous models with the latter models can effectively improve the forecasting accuracy. (2) The proposed two combined forecasting techniques have shown sound performance for the three types of data. It is reasonable to believe that new approaches will help to improve insight into better forecasting carbon emissions in other countries and regions of the world. (3) China and India will remain the major sources of global carbon emissions, and should therefore continue their efforts on carbon emission reduction.