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The purpose of this paper is to present the terms of sequence operators and grey data mining.

The definitions of basic terms about sequence operators and grey data mining are presented one by one.

The reader could know the basic explanation about the important terms about sequence operators and grey data mining from this paper.

Many of the colleagues thought that unified definitions of key terms would be beneficial for both the readers and the authors.

It is a fundamental work to standardize all the definitions of terms for a new discipline. It is also propitious to spread the universal principles of grey system theory.

This paper aims to analyze general development trend of China’s population and to forecast China’s total population under the change of China’s family planning policy so as to measure shock disturbance effects on China’s population development.

China has been the most populous country for hundreds of years. And this state will be sustained in the forthcoming decade. Obviously, China is confronted with greater pressure on controlling total scale of population than any other country. Meanwhile, controlling population will be beneficial for not only China but also the whole world. This paper first analyzes general development trend of China’s population total amount, sex ratio and aging ratio. The mechanism for measurement of the impact effect of a policy shock disturbance is proposed. Linear regression model, exponential curve model and grey Verhulst model are adopted to test accuracy of simulation of China’s total population. Then considering the policy shock disturbance on population, discrete grey model, DGM (1, 1), and grey Verhulst model were adopted to measure how China’s one-child policy affected its total population between 1978 and 2015. And similarly, the grey Verhulst model and scenario analysis of economic developing level were further used to forecast the effect of adjustment from China’s one-child policy to two-child policy.

Results show that China has made an outstanding contribution toward controlling population; it was estimated that China prevented nearly 470 million births since the late 1970s to 2015. However, according to the forecast, with the adjustment of the one-child policy, the birth rate will be a little higher, China’s total population was estimated to reach 1,485.59 million in 2025. Although the scale of population will keep increasing, but it is tolerable for China and sex ratio and trend of aging will be relieved obviously.

The approach constructed in the paper can be used to measure the effect of population change under the policy shock disturbance. It can be used for other policy effect measurement problems under shock events’ disturbance.

The paper succeeded in studying the mechanism for the measurement of the post-impact effect of a policy and the effect of changes in China’s population following the revision of the one-child policy. The mechanism is useful for solving system forecasting problems and can contribute toward improving the grey decision-making models.

The purpose of this paper is to analyze the spectral characteristics of moving average operator and to propose a novel time-frequency hybrid sequence operator.

Firstly, the complex data is converted into frequency domain data by Fourier transform. An appropriate frequency domain operator is constructed to eliminate the impact of disturbance. Then, the inverse Fourier transform transforms the frequency domain data in which the disturbance is removed, into time domain data. Finally, an appropriate moving average operator of N items is selected based on spectral characteristics to eliminate the influence of periodic factors and noise.

Through the spectrum analysis of the real-time data sensed and recorded by microwave sensors, the spectral characteristics and the ranges of information, noise and shock disturbance factors in the data can be clarified.

The real-time data analysis results for a drug component monitoring show that the hybrid sequence operator has a good effect on suppressing disturbances, periodic factors and noise implied in the data.

Firstly, the spectral analysis of moving average operator and the novel time-frequency hybrid sequence operator were presented in this paper. For complex data, the ideal effect is difficult to achieve by applying the frequency domain operator or time domain operator alone. The more satisfactory results can be obtained by time-frequency hybrid sequence operator.

The mobile communication industry in China is vulnerable to competition, industry regulation, macroeconomy and so on, which leads to service income's volatility and non-stationarity. Traditional income prediction models fail to take account of these factors, thus resulting in a low precision. The purpose of this paper is to to set up a new mobile communication service income prediction model based on grey system theory to overcome the inconformity between traditional models and qualitative analysis.

At first, mobile telecommunication service income is divided into number of users (NU) and average revenue per user (ARPU) prediction, respectively. Then, grey buffer operators are introduced to preprocess the time series according to their features and tendencies to eliminate the effect of shock disturbance. As a result, two grey models based on GM(1, 1) are constructed to forecast NU and ARPU, and thus the service income is obtained. At last, a case on Zhujiang mobile communication company is studied. The result proves that the proposed method is not only more accurate, but also could discover the turning point of income.

The results are convincing: it is more effective and accurate to employ grey buffer operator theory to predict the mobile communication service income compared with other methods. Besides, this method is applicable to cases with less data samples and faster development.

It's common to come across a system with less data and poor information. At this case, the grey prediction method exposed in the paper can be used to forecast the future trend which will give the predictors advice to achieve fine outcomes. Buffer operators can reduce the effect of shock disturbance and the GM(1, 1) model has the advantages of exploiting information using only a couple of data.

Considering the fast development of China's mobile communication in recent years, only limited data can be acquired to predict the future, which will definitely reduce the prediction precision using traditional models. The paper succeeds in introducing GM(1, 1) model based on grey buffer operators into the income prediction and the outcome proves that it has higher prediction precision and extensive application.

The purpose of this paper is to predict the main economic indices of online shopping in China.

A fractional order weakening buffer operator (WBO) for the GM(1,1) model is put forward in order to solve the problem of limited nonlinear data. The order number of WBO can adjust in line with the scenario.

The experimental results indicate that the proposed method can consider the scenario and obtain more accurate forecasting results.

This study found that the slowdown of growth trend after the previous high speed expansion period will continue, and the online shopping sellers should make more efforts to develop potential consumers to increase its turnover.

According to the basic principle of grey system and third axiom buffer operator, aiming at the problem of disturbance, some new weakening buffer operators are established by analytical skills in the process of prediction. The problem of some contradictions between quantitative analysis and qualitative analysis existing in pretreatment for vibration data sequences is resolved effectively. An example shows that the kind of new weakening buffer operators increase the forecast precision of data forecast model remarkably. The aim of this paper is to attempt to resolve the problem of some contradictions between quantitative analysis and qualitative analysis existing in pretreatment for vibration data sequences.

In view of the problem of some contradictions between quantitative analysis and qualitative analysis existing in pretreatment for vibration data sequences, according to the basic principle of grey system and third axiom buffer operator, some new weakening buffer operators are established by analytical skills. As an example, the kind of new weakening buffer operators can increase the forecast precision of data forecast model remarkably.

The results show that the new weakening buffer operators can increase the forecast precision of data forecast model remarkably.

The new weakening buffer operators exposed in the paper can be used to resolve the problem of some contradictions between quantitative analysis and qualitative analysis existing in pretreatment for vibration data sequences and increase the forecast precision of data forecast model remarkably.

The paper succeeds in increasing the forecast precision of data forecast model remarkably.

Accurate prediction of seasonal power consumption trends with impact disturbances provides a scientific basis for the flexible balance of the long timescale power system. Consequently, it fosters reasonable scheduling plans, ensuring the safety of the system and improving the economic dispatching efficiency of the power system.

First, a new seasonal grey buffer operator in the longitudinal and transverse dimensional perspectives is designed. Then, a new seasonal grey modeling approach that integrates the new operator, full real domain fractional order accumulation generation technique, grey prediction modeling tool and fruit fly optimization algorithm is proposed. Moreover, the rationality, scientificity and superiority of the new approach are verified by designing 24 seasonal electricity consumption forecasting approaches, incorporating case study and amalgamating qualitative and quantitative research.

Compared with other comparative models, the new approach has superior mean absolute percentage error and mean absolute error. Furthermore, the research results show that the new method provides a scientific and effective mathematical method for solving the seasonal trend power consumption forecasting modeling with impact disturbance.

Considering the development trend of longitudinal and transverse dimensions of seasonal data with impact disturbance and the differences in each stage, a new grey buffer operator is constructed, and a new seasonal grey modeling approach with multi-method fusion is proposed to solve the seasonal power consumption forecasting problem.

The highlights of the paper are as follows:

1. A new seasonal grey buffer operator is constructed.

2. The impact of shock perturbations on seasonal data trends is effectively mitigated.

3. A novel seasonal grey forecasting approach with multi-method fusion is proposed.

4. Seasonal electricity consumption is successfully predicted by the novel approach.

5. The way to adjust China's power system flexibility in the future is analyzed.

A new seasonal grey buffer operator is constructed.

The impact of shock perturbations on seasonal data trends is effectively mitigated.

A novel seasonal grey forecasting approach with multi-method fusion is proposed.

Seasonal electricity consumption is successfully predicted by the novel approach.

The way to adjust China's power system flexibility in the future is analyzed.

The purpose of this paper is to analyze the mechanism and filter efficacy of accumulation generation operator (AGO)/inverse accumulation generation operator (IAGO) in the frequency domain.

The AGO/IAGO in time domain will be transferred to the frequency domain by the Fourier transform. Based on the consistency of the mathematical expressions of the AGO/IAGO in the gray system and the digital filter in digital signal processing, the equivalent filter model of the AGO/IAGO is established. The unique methods in digital signal processing systems “spectrum analysis” of AGO/IAGO are carried out in the frequency domain.

Through the theoretical study and practical example, benefit of spectrum analysis is explained, and the mechanism and filter efficacy of AGO/IAGO are quantitatively analyzed. The study indicated that the AGO is particularly suitable to act on the system's behavior time series in which the long period parts is the main factor. The acted sequence has good effect of noise immunity.

The AGO/IAGO has a wonderful effect on the processing of some statistical data, e.g. most of the statistical data related to economic growth, crop production, climate and atmospheric changes are mainly affected by long period factors (i.e. low-frequency data), and most of the disturbances are short-period factors (high-frequency data). After processing by the 1-AGO, its high frequency content is suppressed, and its low frequency content is amplified. In terms of information theory, this two-way effect improves the signal-to-noise ratio greatly and reduces the proportion of noise/interference in the new sequence. Based on 1-AGO acting, the information mining and extrapolation prediction will have a good effect.

The authors find that 1-AGO has a wonderful effect on the processing of data sequence. When the 1-AGO acts on a data sequence X, its low-pass filtering effect will benefit the information fluctuations removing and high-frequency noise/interference reduction, so the data shows a clear exponential change trends. However, it is not suitable for excessive use because its equivalent filter has poles at the non-periodic content. But, because of pol effect at zero frequency, the 1-AGO will greatly amplify the low-frequency information parts and suppress the high-frequency parts in the information at the same time.

The intention of the empirics is to contribute to the general understanding of investor responses to market price shocks. The authors review assumptions about investor behavior in response to price shocks and investigate alternative rebalancing heuristics.

The authors use market data over 40 years to define market shocks. Portfolio rebalancing implements constrained Markowitz mean-variance (MV) heuristics.

Momentum rebalancing in portfolio management outperforms contrarian rebalancing in the study interval. Sensitivity analysis by decade, sector constraints and proportion of security holdings bought or sold continue to support momentum rebalancing.

The results are consistent with under-responding to price shocks at consensus levels in financial markets. The theoretical background provides a basis for experimental lab studies of shocks of different magnitudes under conditions in which participants have information on the levels of other participants and a condition in which they can only observe their previous estimates.

Managing portfolios in the face of price disturbances of different magnitudes is informed by empirical studies and their implications for investor behavior.

This is the first study the authors can locate that uses market data with alternative rebalancing heuristics to estimate price returns from the respective heuristics over a time interval of 40 years. The authors support the results with sensitivity estimates and consider implications for the underlying agent heuristics in light of background studies.