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Seasonal fluctuation interference often affects the relational analysis of economic time series. The main purpose of this paper is to propose a new grey relational model for relational analysis of seasonal time series and apply it to identify and eliminate the influence of seasonal fluctuation of retail sales of consumer goods in China.

First, the whole quarterly time series is divided into four groups by data grouping method. Each group only contains the time series data in the same quarter. Then, the new series of four-quarters are used to establish the grey correlation model and calculate its correlation coefficient. Finally, the correlation degree of factors in each group of data was calculated and sorted to determine its importance.

The data grouping method can effectively reflect the correlation between time series in different quarters and eliminate the influence of seasonal fluctuation.

In this paper, the main factors influencing the quarterly fluctuations of retail sales of consumer goods in China are explored by using the grouped grey correlation model. The results show that the main factors are different from quarter to quarter: in the first quarter, the main factors are money supply, tax and per capita disposable income of rural residents. In the second quarter are money supply, fiscal expenditure and tax. In the third quarter are money supply, fiscal expenditure and per capita disposable income of rural residents. In the fourth quarter are money supply, fiscal expenditure and tax.

This paper successfully realizes the application of grey relational model in quarterly time series and extends the applicable scope of grey relational model.

Since the issuance in 2009, the digital currency has enjoyed an increasing popularity and has become one of the most important options for global investors. The purpose of this paper is to propose a hybrid model ( KDJ–Markov chain) which integrates the advantages of the stochastic index (KDJ) and grey Markov chain methods and provide a useful decision support tool for investors participating in the digital currency market.

Taking Litecoin's closing price prediction as an example, the closing prices from May 2 to June 20, 2017, are used as the training set, while those from June 21 to August 9, 2017, are used as the test set. In addition, an adaptive KDJ–Markov chain is proposed to enhance the adaptability for dynamic transaction information. And the paper verifies the effectiveness of the KDJ–Markov chain method and adaptive KDJ–Markov chain method.

The results show that the proposed methods can provide a reliable foundation for market analysis and investment decisions. Under the circumstances the accuracy of the training set and the accuracy of the test set are 76% and 78%, respectively.

This study not only solves the problems that KDJ method cannot accurately predict the next day's state and the grey Markov chain method cannot divide the states very well, but it also provides two useful decision support tools for investors to make more scientific and reasonable decisions for digital currency where there are no existing methods to analyze the fluctuation.

A new approach to analyze the fluctuation of digital currency, in which there are no existing methods, is proposed based on the stochastic index (KDJ) and grey Markov chain methods. And both of these two models have high accuracy.

This research aims to establish an index system and a grey comprehensive evaluation model for analyzing the sustainability of urban tourism.

The sustainability evaluation of urban tourism is regarded as a multi-level and multi-index evaluation problem in this study. The evaluation index system of urban tourism sustainable development is constructed based on the ideas of holism and systems thinking. Then based on grey system correlation analysis theory, a new evaluation model is proposed to effectively solve the complex and uncertain problems in the sustainability evaluation system of urban tourism. An actual example of the five cities (Nanjing, Zhenjiang, Changzhou, Wuxi and Suzhou) in Southern Jiangsu Province of China is adopted to demonstrate the feasibility and practicability of the proposed model.

The grey comprehensive evaluation model can effectively convert the complex indices into comprehensive optimal membership degrees which are easy to be understood. The empirical study on the urban tourism sustainable development of South of Jiangsu found that: Suzhou, Nanjing and Wuxi were in the basic stage of sustainable development; Changzhou and Zhenjiang were in the preliminary stage of sustainable development. The social responsibility fulfillment of urban tourism in five cities fails to reach a satisfactory level, especially Zhenjiang and Changzhou remain in a low level in fulfillment of social responsibility.

Due to the difficulty of data collection, the authors can only use the data on 2010 to do a static evaluation in this study. If the authors can have more data on different years, it is feasible to develop a dynamic evaluation model to analyze the evolution law of the sustainability of urban tourism.

The evaluation results provide the necessary support to assist the tourism management departments of the five cities with their policy making.

This study not only supplements the evaluation modelling methods widely used in the area of tourism management, but also promotes the development of the grey systems theory itself.

The purpose of this paper is to provide a modeling approach using grey power model with first‐order one‐variable (abbreviated as GPM(1,1)) for forecasting small sample oscillating series.

An optimization method is used to determine the initial value in GPM(1,1) model, and furthermore, the power value in the model is optimized by utilizing a non‐linear programming model. An operations research software LINGO is employed to solve the non‐linear optimization model.

The results show that the optimized GPM(1,1) model can flexibly adjust the parameters to make the forecasting results more in line with the actual data; therefore, for a given small sample oscillating series, if an appropriate way to find the optimal parameters is taken, accurate predictions should be obtained.

The modeling approach proposed in the paper can be used to forecast new product sales, new industry development trend, equipment remaining life, disaster emergency material demand, etc.

The paper extends the application range of the grey model for forecasting small sample oscillating series by using grey power model GPM(1,1).

Urban water bodies play an important role in reducing summertime urban heat island (UHI) effects. Previous studies focused mainly on the impact of water bodies of large areas, and there is no analysis of the efficacy and scale effect of how small and medium-sized water bodies reduce the UHI effects. Hence, these studies could not provide theoretical support for the scientific planning and design of urban water bodies. This study aims to confirm, within different scale ranges, the efficacy of a water body in reducing the summertime UHI effects. We propose a scale sensitivity method to investigate the temporal and spatial relationship between urban water bodies and UHI. Based on the scale theory and geostatistical analysis method in landscape ecology, this study used the platforms of 3S, MATLAB, and SPSS to analyze the distance-decay law of water bodies in reducing summertime UHI effects, as well as the scale response at different water surface ratios. The results show that the influence of water surfaces on UHIs gradually decreases with increasing distance, and the temperature rises by 0.78 °C for every 100 m away from the water body. During daytime, there is a scaled sensitivity of how much water surfaces reduce the summertime UHI effects. The most sensitive radius from the water was found at the core water surface ratio of 200 m. A reduction of UHI intensity by 2.3 °C was observed for every 10% increase of the average core water surface ratio. This study provides a theoretical reference to the control of heat islands for the planning and design of urban water bodies.

Since the construction of China-ASEAN Free Trade Area (CAFTA) launched in 2002, the bilateral trade increased rapidly. The purpose of this paper is to test the competition and cooperation in trade relationships between China and the main trading partners (Singapore, Malaysia and Thailand (SMT)) from ASEAN in international trade under CAFTA.

Grey Lotka-Volterra competition models are established for testing the trade relationships between China and SMT, respectively, based on the data of import and export from 2003 to 2014. To improve modeling accuracy, the interpolated coefficients for dynamic background value are introduced into the grey Lotka-Volterra model. The optimal parameters are solved through minimizing the mean absolute percentage error and the constraint of parameter relationships. Besides, eigenvalues of the Jacobian matrix are adopted to carry out the stability of equilibrium points of the trade relationships.

As the beneficiary party, China has mutual benefit and win-win trade relationship with Singapore, while it has predator-prey trade relationships with Malaysia and Thailand. The future exports from SMT to China will stabilize at 462.31, 598.13 and 447.03 billion dollars, respectively. The future exports from China to SMT will stabilize at 637.16, 943.71 and 827.52 billion dollars, respectively.

This study can be regarded as an important reference for China and its trading partners from ASEAN. The modeling results can help the decision makers to formulate appropriate international trade strategies to gain and maintain competitive advantages.

A new approach to testing the trade relationships is proposed based on grey Lotka-Volterra competition model. The study also proposed a dynamic optimization method for the background value of grey Lotka-Volterra model.

The purpose of this paper is to propose a grey linear control system for regulating the price of China's real estate and provide the necessary support to assist the relevant management departments with their policy making.

A grey state equation of the real estate market price that can reflect both the market supply‐demand price mechanism and the production price mechanism is proposed based on the economic cybernetics. Also, the grey control linear theory is used to demonstrate the disequilibrium fluctuation control system for the China's real estate market with uncertain parameters.

The price disequilibrium fluctuation control system for China's real estate market has been in a critical state. The system would reach a balanced state in 2013, if the real estate price in 2010 and 2011 firstly decreased 244.41 yuan/m2 and 62.33 yuan/m2, respectively, and then increased 60.88 yuan/m2 in 2012. The disequilibrium state will continue for years before it reaches a balanced state.

Due to the complexity of operation of grey numbers, the present technique still cannot analyze the properties of the grey control system exactly and further research is needed.

The modelled results can help the relevant management departments steady China's real estate market by price regulation.

A new approach to study the price regulation system of a real estate market is proposed based on grey linear control theory.

The purpose of this paper is to propose an economic cybernetics model based on the grey differential equation GM(1,N) for China's high-tech industries and provide the necessary support to assist high-tech industries management departments with their policy making.

Based on the principle of grey differential equation GM(1,N), the grey differential equations of five high-tech industries in China are established using the net fixed assets, labor quantity and patent application quantity as cybernetics variables. After the discretization and first-order subtraction reduction to the simultaneous equation of the five grey models, a linear cybernetics model is resulted in. The structure parameters in the cybernetics system show explicit economic significance and can be identified through least square principle. At last, the actual data in 2004-2010 are introduced to empirically analyze the high-tech industrial system in China.

The cybernetics system for China's high-tech industries are stable, observable, and controllable. On the whole, China's high-tech industries show higher output coefficients of the patent application quantity than those of net fixed assets and labor quantity. This suggests that China's industry development mainly depends on technological innovation rather than capital or labor inputs. It is expected that the total output value of China's high-tech industries will grow at an average annual rate of 15 percent in 2011-2015, with contributions of pharmaceuticals, aircraft and spacecraft, electronic and telecommunication equipments, computers and office equipments, medical equipments and meters by 21, 16, 13, 10, and 28 percent, respectively. In addition, pharmaceuticals, as well as medical equipments and meters, present upward proportions in the gross of Chinese high-tech industries significantly. Electronic and telecommunication equipments, plus computers and office equipments exhibit an obvious decreasing proportion. The proportion of the output value of aircraft and spacecraft is basically stable.

Empirical analysis results are helpful for related management departments to formulate reasonable industrial policies to keep the sustained and stable development of the high-tech industries in China.

Based on the grey differential equation GM(1,N), this research puts forward an economic cybernetics model for the high-tech industries in China. This model is applicable to the economic system with small sample data set.

The purpose of this paper is to propose an extending correlation analysis method to deal with the correlation analysis between the sequences with incomplete information.

Based on the axiomatic definition of a grey number and its greyness degree in grey system theory, the whitenization mean, whitenization difference, whitenization covariance of sequences with interval grey numbers and their greyness degrees are defined in turn. In addition, the whitenization correlation coefficient and its greyness degree of sequences with interval grey numbers are also defined. By using the relationship between the greyness degree and kernel for a grey number, the transformation formula from the whitenization value and greyness degree of correlation coefficient to form of interval grey numbers are put forward further.

The whitenization value of correlation coefficient efficient of two arbitrary sequences with interval grey numbers have symmetry, with same greyness degree but without normalization in the interval [−1, 1]; the mean, difference, covariance and correlation coefficient defined in statistics are all the special cases of those in sequences with interval grey numbers.

Due to the complexity of operation of grey numbers, the reliability of correlation coefficient of interval numbers sequence is difficult to be tested by constructing statistics at present. The further research is needed.

The correlation analysis method of interval grey numbers can contribute to the further researches on the incomplete information system in the real world.

On the basis of grey system theory, a correlation analysis method for analyzing information incomplete sequences is proposed.