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The purpose of this paper is to establish a random simulation method to compare the forecasting performance between grey prediction models, and between grey model and other kinds of prediction models. Then, the different performance of three grey models and linear regression prediction model is studied, based on the proposed method.

A random simulation method was proposed to test the modelling accuracy of grey prediction model. This method was enlightened by Monte Carlo simulation method. It regarded a class of sequences as population, and selected a large sample from population though random sampling. Then, sample sequences were modeled by grey prediction model. Through modeling error calculation, the average error of grey model for the sample was obtained. Finally, the grey model accuracy for this kind of problem was acquired by statistical inference testing model. Through the statistical significant test method, the modeling accuracy of grey models for the same problem can be compared. Also, accuracy difference between grey prediction model and regression analysis, support vector machine, neural network, and other forecasting methods can be also compared.

Though random simulation experiments, the following conclusion was obtained. First, grey model can be applied to the long sequence whose growth rate was less than 20 per cent, and the short sequence whose growth rate was less than 50 per cent. Second, GM(1,1) cannot be applied to a long sequence with high growth. Third, growth rate was a more important factor than growth length on modeling accuracy of GM(1,1). Fourth, when the sequence length was short, accuracy of GM(1,1) model was higher than linear regression. While the length of the sequence was more than 15, and the growth rate in [0‐10 per cent], two kinds of modeling error was not significantly different.

The method proposed in the paper can be used to compare the performance of different prediction models, and to select appropriate model for a prediction problem.

The paper succeeded in establishing an accuracy test method for grey models and other prediction models. It will standardize the grey modelling and contribute to application of grey models.

Traditional multivariable grey prediction models define the background-value coefficients of the dependent and independent variables uniformly, ignoring the differences between their physical properties, which in turn affects the stability and reliability of the model performance.

A novel multivariable grey prediction model is constructed with different background-value coefficients of the dependent and independent variables, and a one-to-one correspondence between the variables and the background-value coefficients to improve the smoothing effect of the background-value coefficients on the sequences. Furthermore, the fractional order accumulating operator is introduced to the new model weaken the randomness of the raw sequence. The particle swarm optimization (PSO) algorithm is used to optimize the background-value coefficients and the order of the model to improve model performance.

The new model structure has good variability and compatibility, which can achieve compatibility with current mainstream grey prediction models. The performance of the new model is compared and analyzed with three typical cases, and the results show that the new model outperforms the other two similar grey prediction models.

This study has positive implications for enriching the method system of multivariable grey prediction model.

In order to more accurately predict the dynamics of the e-commerce market and increase the comprehensive value of the circular e-commerce industry, proposes to use Grey system theory to analyze the circular economy of the e-commerce market.

Construct a Grey system theory model, analyze the big data of e-commerce and circular economy of the e-commerce market and predict the development potential of China's e-commerce market.

The results show that the Grey system theory model can play an important role in the data analysis of circular economy of the e-commerce market.

Use Grey model to analyze e-commerce data, discover e-commerce market rules and problems and then optimize e-commerce market.

The purpose of this paper is to construct a prediction model of three-parameter interval grey number based on kernel and double information domains to expand the modeling object of grey prediction model from interval grey number to three-parameter interval grey number.

First, the study decomposes the grey valued interval into upper and lower cells with the “center of gravity” as the dividing point and defines the upper and lower information domains of the three-parameter interval grey number. Second, it calculates the kernel, the upper and lower information domains of the three-parameter interval grey number. Then, it constructs the prediction model for kernel sequence and upper and lower information domain sequences, respectively. By deducing the time response expressions of “center of gravity”, lower and upper limits of three-parameter interval grey number, a prediction model of three-parameter interval grey number based on kernel and double information domains is obtained.

This paper provides a prediction model of three-parameter interval grey number based on kernel and double information domains, and the example analysis shows that the method proposed in this paper has higher prediction accuracy and practicality.

In this paper, the modeling object of grey prediction model is extended to the three-parameter interval grey number, so it can be used for the prediction of uncertainty problems, such as stock changing trend, temperature and so on.

By decomposing the grey valued interval into upper and lower cells with the “center of gravity” as the dividing point, gives the definition of upper and lower information domains and then obtains a new method for whitening the three-parameter interval grey number.

The purpose of this study is to make a prediction of China's energy consumption structure from the perspective of compositional data and construct a novel grey model for forecasting compositional data.

Due to the existing grey prediction model based on compositional data cannot effectively excavate the evolution law of correlation dimension sequence of compositional data. Thus, the adaptive discrete grey prediction model with innovation term based on compositional data is proposed to forecast the integral structure of China's energy consumption. The prediction results from the new model are then compared with three existing approaches and the comparison results indicate that the proposed model generally outperforms existing methods. A further prediction of China's energy consumption structure is conducted into a future horizon from 2021 to 2035 by using the model.

China's energy structure will change significantly in the medium and long term and China's energy consumption structure can reach the long-term goal. Besides, the proposed model can better mine and predict the development trend of single time series after the transformation of compositional data.

The paper considers the dynamic change of grey action quantity, the characteristics of compositional data and the impact of new information about the system itself on the current system development trend and proposes a novel adaptive discrete grey prediction model with innovation term based on compositional data, which fills the gap in previous studies.

Prediction problems raised in uncertain environments require different solution approaches such as grey prediction models, which consider uncertainty in information and also enable the use of small data sets. The purpose of this paper is to investigate the comparative performances of grey prediction models (GM) and Markov chain integrated grey models in a demand prediction problem.

The modeling process of grey models is initially described, and then an integrated model called the Grey-Markov model is presented for the convenience of applications. The analyses are conducted on a monthly demand prediction problem to demonstrate the modeling accuracies of the GM (1,1), GM (2,1), GM (1,1)-Markov, and GM (2,1)-Markov models.

Numerical results reveal that the Grey-Markov model based on GM (2,1) achieves better prediction performance than the other models.

It is thought that the methodology and the findings of the study will be a significant reference for both academics and executives who struggle with similar demand prediction problems in their fields of interest.

The novelty of this study comes from the fact that the GM (2,1)-Markov model has been first used for demand prediction. Furthermore, the GM (2,1)-Markov model represents a relatively new approach, and this is the second paper that addresses the GM (2,1)-Markov model in any area.

Research on grey systems is becoming more sophisticated, and grey relational and prediction analyses are receiving close review worldwide. Particularly, the application of grey systems in marine economics is gaining importance. The purpose of this paper is to summarize and review literature on grey models, providing new directions in their application in the marine economy.

This paper organized seminal studies on grey systems published by Chinese core journal database – CNKI, Web of Science and Elsevier from 1982 to 2018. After searching the aforementioned database for the said duration, the authors used the CiteSpace visualization tools to analyze them.

The authors sorted the studies according to their countries/regions, institutions, keywords and categories using the CiteSpace tool; analyzed current research characteristics on grey models; and discussed their possible applications in marine businesses, economy, scientific research and education, marine environment and disasters. Finally, the authors pointed out the development trend of grey models.

Although researches are combining grey theory with fractals, neural networks, fuzzy theory and other methods, the applications, in terms of scope, have still not met the demand. With the increasingly in-depth research in marine economics and management, international marine economic research has entered a new period of development. Grey theory will certainly attract scholars’ attention, and its role in marine economy and management will gain considerable significance.

In recent years, domestic smog has become increasingly frequent and the adverse effects of smog have increasingly become the focus of public attention. It is a way to analyze such problems and provide solutions by mathematical methods.

This paper establishes a new gray model (GM) (1,N) prediction model based on the new kernel and degree of grayness sequences under the case that the interval gray number distribution information is known. First, the new kernel and degree of grayness sequences of the interval gray number sequence are calculated using the reconstruction definition of the kernel and degree of grayness. Then, the GM(1,N) model is formed based on the above new sequences to simulate and predict the kernel and degree of the grayness of the interval gray number sequence. Finally, the upper and lower bounds of the interval gray number are deduced based on the calculation formulas of the kernel and degree of grayness.

To verify further the practical significance of the model proposed in this paper, the authors apply the model to the simulation and prediction of smog. Compared with the traditional GM(1,N) model, the new GM(1,N) prediction model established in this paper has better prediction effect and accuracy.

This paper improves the traditional GM(1,N) prediction model and establishes a new GM(1,N) prediction model in the case of the known distribution information of the interval gray number of the smog pollutants concentrations data.

Many factors affect the emergence and development of crop diseases and insect pests. Traditional methods for investigating this subject are often difficult to employ and produce limited data with considerable uncertainty. The purpose of this paper is to predict the annual degree of cotton spider mite infestations by employing grey theory.

The authors established a GM(1,1) model to forecast mite infestation degree based on the analysis of historical data. To improve the prediction accuracy, the authors modified the grey model using Markov chain and BP neural network analyses. The prediction accuracy of the GM(1,1), Grey-Markov chain, and Grey-BP neural network models was 84.31, 94.76, and 96.84 per cent, respectively.

Compared with the single grey forecast model, both the Grey-Markov chain model and the Grey-BP neural network model had higher forecast accuracy, and the accuracy of the latter was highest. The improved grey model can be used to predict the degree of cotton spider mite infestations with high accuracy and overcomes the shortcomings of traditional forecasting methods.

The two new models were used to estimate mite infestation degree in 2015 and 2016. The Grey-Markov chain model yielded respective values of 1.27 and 1.15, whereas the Grey-BP neural network model yielded values 1.4 and 1.68; the actual values were 1.5 and 1.8.

The improved grey model can be used for medium- and long-term predictions of the occurrence of cotton spider mites and overcomes problems caused by data singularity and fluctuation. This research method can provide a reference for the prediction of similar diseases.

The purpose of this paper is to evaluate the forecasting performance of grey prediction models on educational attainment vis-à-vis that of exponential smoothing combined with multiple linear regression employed by the National Center for Education Statistics (NCES).

An out-of-sample forecasting experiment was carried out to compare the forecasting performances on educational attainments among GM(1,1), GM(1,1) rolling, FGM(1,1) derived from the grey system theory and exponential smoothing prediction combined with multivariate regression. The predictive power of each model was measured based on MAD, MAPE, RMSE and simple F-test of equal variance.

The forecasting efficiency evaluated by MAD, MAPE, RMSE and simple F-test of equal variance revealed that the GM(1,1) rolling model displays promise for use in forecasting educational attainment.

Since the possible inadequacy of MAD, MAPE, RMSE and F-type test of equal variance was documented in the literature, further large-scale forecasting comparison studies may be done to test the prediction powers of grey prediction and its competing out-of-sample forecasts by other alternative measures of accuracy.

The findings of this study would be useful for NCES and professional forecasters who are expected to provide government authorities and education policy makers with accurate information for planning future policy directions and optimizing decision-making.

As a continuing effort to evaluate the forecasting efficiency of grey prediction models, the present study provided accumulated evidence for the predictive power of grey prediction on short-term forecasts of educational statistics.