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The Coronavirus (COVID-19) is one of the major pandemic diseases caused by a newly discovered virus that has been directly affecting the human respiratory system. Because of the gradually increasing magnitude of the COVID-19 pandemic across the world, it has been sparking emergencies and critical issues in the healthcare systems around the world. However, predicting the exact amount of daily reported new COVID cases is the most serious issue faced by governments around the world today. So, the purpose of this current study is to propose a novel hybrid grey exponential smoothing model (HGESM) to predicting transmission dynamics of the COVID-19 outbreak properly.

As a result of the complications relates to the traditional time series approaches, the proposed HGESM model is well defined to handle exponential data patterns in multidisciplinary systems. The proposed methodology consists of two parts as double exponential smoothing and grey exponential smoothing modeling approach respectively. The empirical analysis of this study was carried out on the basis of the 3rd outbreak of Covid-19 cases in Sri Lanka, from 1st March 2021 to 15th June 2021. Out of the total 90 daily observations, the first 85% of daily confirmed cases were used during the training, and the remaining 15% of the sample.

The new proposed HGESM is highly accurate (less than 10%) with the lowest root mean square error values in one head forecasting. Moreover, mean absolute deviation accuracy testing results confirmed that the new proposed model has given more significant results than other time-series predictions with the limited samples.

The findings suggested that the new proposed HGESM is more suitable and effective for forecasting time series with the exponential trend in a short-term manner.

The time series analysis is an essential methodology which comprises the tools for analyzing the time series data to identify the meaningful characteristics for making future ad-judgments. The purpose of this paper is to propose a Taylor series approximation and unbiased GM(1,1) based new hybrid statistical approach (HTS_UGM(1,1)) for forecasting time series data under the poor, incomplete and uncertain information systems in a short period of time manner.

The gray forecasting is a dynamical methodology which can be classified into different categories based on their respective functions. The new proposed methodology is made up of three different methodologies including the first-order unbiased GM(1,1), Markov chain and Taylor approximation. In addition to that, two different traditional gray operational mechanisms include GM(1,1) and unbiased GM(1,1) used as the comparisons. The main objective of this study is to forecast gold price demands in a short-term manner based on the data which were taken from the Central Bank of Sri Lanka from October 2017 to December 2017.

The error analysis results suggested that the new proposed HTS_UGM(1,1) is highly accurate (less than 10 percent) with lowest RMSE error values in a one head as well as weakly forecasting’s than separate gray forecasting methodologies.

The findings suggested that the new proposed hybrid approach is more suitable and effective way for forecasting time series indices than separate time series forecasting methodologies in a short-term manner.

China's population aging is gradually deepening and needs to be actively addressed. The purpose of this paper is to construct a novel model for analyzing the population aging.

To analyze the aging status of a region, this study has considered three major indicators: total population, aged population and the proportion of the aged population. Additionally, the authors have developed a novel grey population prediction model that incorporates the fractional-order accumulation operator and Gompertz model (GM). By combining these techniques, the authors' model provides a comprehensive and accurate prediction of population aging trends in Jiangsu Province. This research methodology has the potential to contribute to the development of effective policy solutions to address the challenges posed by the population aging.

The fractional-order discrete grey GM is suitable for predicting the aging population and has good performance. The population aging of Jiangsu Province will continue to deepen in the next few years.

The proposed model can be used to predict and analyze aging differences in Jiangsu Province. Based on the prediction and analysis results, identified some corresponding countermeasures are suggested to address the challenges of Jiangsu's future aging problem.

The fractional-order discrete grey GM is firstly proposed in this paper and this model is a novel grey population prediction model with good performance.

The time series forecasting is an essential methodology which can be used for analysing time series data in order to extract meaningful statistics based on the information obtained from past and present. These modelling approaches are particularly complicated when the available resources are limited as well as anomalous. The purpose of this paper is to propose a new hybrid forecasting approach based on unbiased GM(1,1) and artificial neural network (UBGM_BPNN) to forecast time series patterns to predict future behaviours. The empirical investigation was conducted by using daily share prices in Colombo Stock Exchange, Sri Lanka.

The methodology of this study is running under three main phases as follows. In the first phase, traditional grey operational mechanisms, namely, GM(1,1), unbiased GM(1,1) and nonlinear grey Bernoulli model, are used. In the second phase, the new proposed hybrid approach, namely, UBGM_BPNN was implemented successfully for forecasting short-term predictions under high volatility. In the last stage, to pick out the most suitable model for forecasting with a limited number of observations, three model-accuracy standards were employed. They are mean absolute deviation, mean absolute percentage error and root-mean-square error.

The empirical results disclosed that the UNBG_BPNN model gives the minimum error accuracies in both training and testing stages. Furthermore, results indicated that UNBG_BPNN affords the best simulation result than other selected models.

The authors strongly believe that this study will provide significant contributions to domestic and international policy makers as well as government to open up a new direction to develop investments in the future.

The new proposed UBGM_BPNN hybrid forecasting methodology is better to handle incomplete, noisy, and uncertain data in both model building and ex post testing stages.

The purpose of this paper is to explore a new approach to solve the problem of positive and negative offset in the calculation process of integral elements, then propose a series of new grey relational degree model for cross sequences.

The definitions of cross sequences and area elements have been proposed at first. Then the concept of difference degree between sequences has been put forward. Based on the definition of difference degree between sequences, various modified grey relational degree models for cross sequences have been proposed to solve the measurement problem of cross sequence correlation relationships.

(1) The new definition of cross sequences; (2) The area element; (3) Various modified grey relational degree models for cross sequences based on the definition of difference degree between sequences.

The grey relational analysis model of cross sequences is a difficult problem in grey relational analysis. The new model proposed in this article can effectively avoid the calculation deviation of grey relational analysis model for cross sequences, and reasonably measure the correlation between cross sequences. The new model was used to analyse the food consumer price index in Shaanxi Province, clarifying the relationship between different types of food consumer price indices, some interesting results that are not completely consistent with general economic theory were obtained.

The new definition of cross sequences, the area element and various modified grey relational degree models for cross sequences were proposed.

Because of the high volatility with unstable data patterns in the real world, the ability of forecasting price indices is notoriously embarrassing and represents a major challenge with traditional time series mechanisms; especially, most of the traditional approaches are weak to forecast future predictions in the high volatile and unbalanced frameworks under the global and local financial depressions. The purpose of this paper is to propose a new statistical approach for portfolio selection and stock market forecasting to assist investors as well as stock brokers to predict the future behaviors.

This study mainly takes an attempt to understand the trends, behavioral patterns and predict the future estimations under the new proposed frame for the Colombo Stock Exchange (CSE), Sri Lanka. The methodology of this study is carried out under the two main phases. In the first phase, constructed a new portfolio mechanism based on k-means clustering. In the second stage, proposed a nonlinear forecasting methodology based on grey mechanism for forecasting stock market indices under the high-volatile fluctuations. The autoregressive integrated moving average (ARIMA) predictions are used as comparison mode.

Initially, the k-mean clustering was applied to pick out the profitable sectors running under the CSE and results indicated that BFI is more significant than other 20 sectors. Second, the MAE, MAPE and MAD model comparison results clearly suggested that, the newly proposed nonlinear grey Bernoulli model (NGBM) is more appropriate than traditional ARIMA methods to forecast stock price indices under the non-stationary market conditions.

Because of the flexible nonlinear modeling capability, proposed novel concepts are more suitable for applying in various areas in the field of financial, economic, military, geological and agricultural systems for pattern recognition, classification, time series forecasting, etc.

For the large sample of data forecasting under the normality assumptions, the traditional time series methodologies are more suitable than grey methodologies. However, the NGBM is better both in model building and ex post testing stagers under the s-distributed data patterns with limited data forecastings.

Making decisions in finance have been regarded as one of the biggest challenges in the modern economy today; especially, analysing and forecasting unstable data patterns with limited sample observations under the numerous economic policies and reforms. The purpose of this paper is to propose suitable forecasting approach based on grey methods in short-term predictions.

High volatile fluctuations with instability patterns are the common phenomenon in the Colombo Stock Exchange (CSE), Sri Lanka. As a subset of the literature, very few studies have been focused to find the short-term forecastings in CSE. So, the current study mainly attempted to understand the trends and suitable forecasting model in order to predict the future behaviours in CSE during the period from October 2014 to March 2015. As a result of non-stationary behavioural patterns over the period of time, the grey operational models namely GM(1,1), GM(2,1), grey Verhulst and non-linear grey Bernoulli model were used as a comparison purpose.

The results disclosed that, grey prediction models generate smaller forecasting errors than traditional time series approach for limited data forecastings.

Finally, the authors strongly believed that, it could be better to use the improved grey hybrid methodology algorithms in real world model approaches.

However, for the large sample of data forecasting under the normality assumptions, the traditional time series methodologies are more suitable than grey methodologies; especially GM(1,1) give some dramatically unsuccessful results than auto regressive intergrated moving average in model pre-post stage.

In recent years, continuous expansion of the scale of the new energy export industry in China caused a boycott of American and European countries. Export injury early warning research is an urgent task to develop the new energy industry in China. The purpose of this paper is to build an indicator system of exports injury early warning of the new energy industry in China and corresponding quantitative early warning models.

In consideration of the actual condition of the new energy industry in China, this paper establishes an indicator system according to four aspects: export price, export quantity, impact on domestic industry and impact on macro economy. Based on the actual data of new energy industry and its five sub-industries (solar, wind, nuclear power, smart grid and biomass) in China from 2003 to 2013, GM (1,1) model is used to predict early warning index values for 2014-2018. Then, the principal component analysis (PCA) is used to obtain the comprehensive early warning index values for 2003-2018. The 3-sigma principle is used to divide the early warning intervals according to the comprehensive early warning index values for 2003-2018 and their standard deviation. Finally, this paper determines alarm degrees for 2003-2018.

Overall export condition of the new energy industry in China is a process from cold to normal in 2003-2013, and the forecast result shows that it will be normal from 2014 to 2018. The export condition of the solar energy industry experienced a warming process, tended to be normal, and the forecast result shows that it will also be normal in 2014-2018. The biomass and other new energy industries and nuclear power industry show a similar development process. Export condition of the wind energy industry is relatively unstable, and it will be partially hot in 2014-2018, according to the forecast result. As for the smart grid industry, the overall export condition of it is normal, but it is also unstable, in few years it will be partially hot or partially cold. The forecast result shows that in 2014-2018, it will maintain the normal state. In general, there is a rapid progress in the export competitiveness of the new energy industry in China in the recent decade.

Export injury early warning research of the new energy industry can help new energy companies to take appropriate measures to reduce trade losses in advance. It can also help the relevant government departments to adjust industrial policies and optimize the new energy industry structure.

This paper constructs an index system that can measure the alarm degrees of the new energy industry. By combining the GM (1,1) model and the PCA method, the problem of warning condition detection under small sample data sets is solved.

The purpose of this paper is to address and overcome the problem that a single prediction model cannot accurately fit a data sequence with large fluctuations.

Initially, the grey linear regression combination model was put forward. The Discrete Grey Model (DGM)(1,1) model and the multiple linear regression model were then combined using the entropy weight method. The grain yield from 2010 to 2015 was forecasted using DGM(1,1), a multiple linear regression model, the combined model and a GM(1,N) model. The predicted values were then compared against the actual values.

The results reveal that the combination model used in this paper offers greater simulation precision. The combination model can be applied to the series with fluctuations and the weights of influencing factors in the model can be objectively evaluated. The simulation accuracy of GM(1,N) model fluctuates greatly in this prediction.

The combined model adopted in this paper can be applied to grain forecasting to improve the accuracy of grain prediction. This is important as data on grain yield are typically characterised by large fluctuation and some information is often missed.

This paper puts the grey linear regression combination model which combines the DGM(1,1) model and the multiple linear regression model using the entropy weight method to determine the results weighting of the two models. It is intended that prediction accuracy can be improved through the combination of models used within this paper.