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The purpose of this paper is to simplify the computation of parameter estimation in the grey linear regression model and solve the problem that the development coefficient could not be computed in some sequence data, such as short‐term traffic flow.

Starting from the limitation that can be identified in the equation and analyzing the range using the method to estimate parameters, this paper researches the modelling mechanism and the other forms which are equivalent with the original form. At the same time, this paper gives an estimation method and gets the relationship in various forms and the relationship between the model and GM(1,1) model.

For the grey linear regression model, there exists a new method of parameter identification and three other forms as follows: the original form, the Whitenization equation and the connotation form.

The method of parameter identification exposed in the paper expanded the scope of the application of the grey linear regression model, and it can be used to model and forecast the urban road short‐time traffic flow.

This paper has solved some complicated problems such as the parameter estimation computation in the grey linear regression model. In addition, three kinds of representation forms of the model and its relationship between the model and GM(1,1) have also been presented. Finally, its application of the model in a short‐term traffic flow prediction has shown its superiority.

High-tech industries play an important role in promoting economic and social development. The purpose of this paper is to accurately predict and analyze the output value of high-tech products in Guangdong Province, China, by using a multivariable grey model.

Based on the principle of fractional order accumulation, this study proposes a multivariable grey prediction model. To further enhance the prediction ability and accuracy of the model, an optimized model is established by reconstructing the background value. The optimal parameters are solved by minimizing the average relative error of the system characteristic sequence with the constraint of parameter relationships.

The results from the study show that the two proposed models exhibit better simulation and prediction performance than the traditional models, while the optimized model can significantly improve the modelling precision. In addition, it is predicted that the output value of high-tech products is 12,269.443bn yuan in 2021, which will approximately double from 2016 to 2021.

The two proposed models can be used to forecast the trend of the system and are grown as an effective extension and supplement of the traditional multivariable grey forecasting models.

The forecast and analysis of the development prospects of high-tech industries would be useful for the government departments of Guangdong Province and professional forecasters to grasp the future of high-tech industries and formulate decision planning.

A new multivariable grey prediction model based on fractional order accumulation and its optimized model obtained by reconstructing the background value, which can improve the modelling accuracy of the traditional model, is proposed in this paper.

The purpose of this paper is to employ the Grey-Markov Chain Model for the scale prediction of cultivated land and took an empirical research with the case of Jiangsu province.

Along with China’s industrialization and urbanization accelerated, a large number of cultivated land converse into construction land. The change of utilization of cultivated land concerns national food security and sustainable development of economy and society. Due to the fact that the different investigation methods of arable land usually cause a uncertain. The Grey-Markov model combines the Grey GM(1,1) and Markov chain, with two advantages of dealing with poor information and long-term and volatile series. A numeric example of scale prediction of cultivated land in Jiangsu province is also computed in the third part of the paper.

The results show that the Grey-Markov Chain Model has a higher prediction accuracy compared with GM (1,1), which is a reliable guarantee for the change of cultivated land resources.

The forecast of cultivated land can provide useful information for the general land use planning.

The paper confirmed the feasibility of the Grey-Markov model in scale prediction of cultivated land.

This study aims to improve the accuracy of hyperspectral estimation of soil organic matter content.

Based on the uncertainty in spectral estimation, 76 soil samples collected in Zhangqiu District, Jinan City, Shandong Province, were studied in this paper. First, the spectral transformation of the spectral data after denoising was carried out by means of 11 transformation methods such as reciprocal and square, and the estimation factor was selected according to the principle of maximum correlation. Secondly, the grey weighted distance was used to calculate the grey relational degree between the samples to be estimated and the known patterns, and the local linear regression estimation model of soil organic matter content was established by using the pattern samples closest to the samples to be identified. Thirdly, the models were optimized by gradually increasing the number of modeling samples and adjusting the decision coefficient, and a comprehensive index was constructed to determine the optimal predicted value. Finally, the determination coefficient and average relative error are used to evaluate the validity of the model.

The results show that the maximum correlation coefficient of the seven estimated factors selected is 0.82; the estimation results of 14 test samples are of high accuracy, among which the determination coefficient R² = 0.924, and the average relative error is 6.608%.

Studies have shown that it is feasible and effective to estimate the content of soil organic matter by using grey correlation local linear regression model.

The paper succeeds in realizing both the soil organic matter hyperspectral grey relation estimating pattern based on the grey relational theory and the estimating pattern by using the local linear regression.

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.

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.

The purpose of this paper is to establish the grey relational estimating model of soil pH value based on hyper-spectral data.

As to the uncertainty of the factors affecting the soil pH value estimation based on hyper-spectral, the grey weighted relation estimation model was set up according to the grey system theory. Then the linear regression correction model is established according to the difference and grey relation degree information between the estimated samples and their corresponding pattern. At the same time, the model was applied to Hengshan county of Shanxi province.

The results are convincing: not only that the linear regression correction model of grey relation estimating pattern of soil pH value based on hyper-spectral data is valid, but also the model’s estimating accuracy is higher, which the corrected average relative error is 0.2578 per cent, and the decision coefficient R²=0.9876.

The method proposed in the paper can be used at soil pH value hyper-spectral inversion and even for other similar forecast problem.

The paper succeeds in realising both the soil pH value hyper-spectral grey relation estimating pattern based on the grey relational theory and the correction model of the estimating pattern by using the linear regression.

This study aims to use gray models to predict abnormal stock returns.

Data are collected from listed companies in the Tehran Stock Exchange during 2005-2015. The analyses portray three models, namely, the gray model, the nonlinear gray Bernoulli model and the Nash nonlinear gray Bernoulli model.

Results show that the Nash nonlinear gray Bernoulli model can predict abnormal stock returns that are defined by conditions other than gray models which predict increases, and then after checking regression models, the Bernoulli regression model is defined, which gives higher accuracy and fewer errors than the other two models.

The stock market is one of the most important markets, which is influenced by several factors. Thus, accurate and reliable techniques are necessary to help investors and consumers find detailed and exact ways to predict the stock market.

Weather forecasting is the trending topic around the world as it is the way to predict the threats posed by extreme rainfall conditions that lead to damage the human life and properties. These issues can be managed only when the occurrence of the worse weather is predicted in advance, and sufficient warnings can be executed in time. Thus, keeping in mind the importance of the rainfall prediction system, the purpose of this paper is to propose an effective rainfall prediction model using the nonlinear auto-regressive with external input (NARX) model.

The paper proposes a rainfall prediction model using the time-series prediction that is enabled using the NARX model. The time-series prediction ensures the effective prediction of the rainfall in a particular area or the locality based on the rainfall data in the previous term or month or year. The proposed NARX model serves as an adaptive prediction model, for which the rainfall data of the previous period is the input, and the optimal computation is based on the proposed algorithm. The adaptive prediction using the proposed algorithm is exhibited in the NARX, and the proposed algorithm is developed based on the Grey Wolf Optimization and the Levenberg–Marqueret (LM) algorithm. The proposed algorithm inherits the advantages of both the algorithms with better computational time and accuracy.

The analysis using two databases enables the better understanding of the proposed rainfall detection methods and proves the effectiveness of the proposed prediction method. The effectiveness of the proposed method is enhanced and the accuracy is found to be better compared with the other existing methods and the mean square error and percentage root mean square difference of the proposed method are found to be around 0.0093 and 0.207.

The rainfall prediction is enabled adaptively using the proposed Grey Wolf Levenberg–Marquardt (GWLM)-based NARX, wherein an algorithm, named GWLM, is proposed by the integration of Grey Wolf Optimizer and LM algorithm.

The widespread application of traditional grey model (GM) in different academic fields such as electrical engineering, education, mechanical engineering and agriculture provided the authors with an incentive to conduct the present empirical research in an accounting field, in particular, auditing practice. In this regard, the purpose of this paper is to employ the nonlinear type of the original GM to forecast the drastically changed data on audit reports, primarily due to the fact that the linear nature of GM is unable to forecast nonlinear data precisely. In essence, this paper adds value to the strand of audit report literature by examining the impact of different financial ratios on auditors’ opinion and then forecasting audit reports by employing GMs.

The grey forecasting model is known as a system containing uncertain information presented by grey numbers, equations and matrices. The grey forecasting model is employed by using a differential equation in an uncertain system with limited data set which is suitable for smoothing discrete data. In addition, the analyses are conducted by applying a sample of top 50 listed companies on the Tehran Stock Exchange during 2011-2016.

The findings suggest that audit reports are most influenced by the current ratio and conversely, least influenced by the ratio of working capital turnover. Moreover, the authors argue that the Nash nonlinear grey Bernoulli model is more precise than the nonlinear grey Bernoulli model and GM in forecasting audit reports.

The current study may give more strength to stakeholders in order to analyse and forecast audit report.