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The purpose of this paper is to apply GM (1, 1) and TFGM (1, 1) models on the healthcare sector, which is a new area, and to show TFGM (1, 1) forecasting accuracy on this sector.

GM (1, 1) and TFGM (1, 1) models are presented. A hospital’s nine months (monthly) demand data is used for forecasting. Models are applied to the data, and the results are evaluated with MAPE, MSE and MAD metrics. The results for GM (1, 1) and TFGM (1, 1) are compared to show the accuracy of forecasting models. The grey models are also compared with Holt–Winters method, which is a traditional forecasting approach and performs well.

The results of this study indicate that TFGM (1, 1) has better forecasting performance than GM (1, 1) and Holt–Winters. GM (1, 1) has 8.01 per cent and TFGM (1, 1) 7.64 per cent MAPE, which means excellent forecasting power. So, TFGM (1, 1) is also an applicable forecasting method for the healthcare sector.

Future studies may focus on developed grey models for health sector demand. To perform better results, parameter optimisation may be integrated to GM (1, 1) and TFGM (1, 1). The demand may be predicted not only for the total demand on hospital, but also for the demand of hospital departments.

This study contributes to relevant literature by proposing fuzzy grey forecasting, which is used to predict the health demand. Therefore, the new application area as the health sector is handled with the grey model.

Aiming to address the forecasting dilemma of seasonal air quality, the authors design the novel self-adaptive seasonal adjustment factor to extract the seasonal fluctuation information about the air quality index. Based on the novel self-adaptive seasonal adjustment factor, the novel seasonal grey forecasting models are established to predict the air quality in China.

This paper constructs a novel self-adaptive seasonal adjustment factor for quantifying the seasonal difference information of air quality. The novel self-adaptive seasonal adjustment factor reflects the periodic fluctuations of air quality. Therefore, it is employed to optimize the data generation of three conventional grey models, consisting of the GM(1,1) model, the discrete grey model and the fractional-order grey model. Then three novel self-adaptive seasonal grey forecasting models, including the self-adaptive seasonal GM(1,1) model (SAGM(1,1)), the self-adaptive seasonal discrete grey model (SADGM(1,1)) and the self-adaptive seasonal fractional-order grey model (SAFGM(1,1)), are put forward for prognosticating the air quality of all provinces in China .

The experiment results confirm that the novel self-adaptive seasonal adjustment factors promote the precision of the conventional grey models remarkably. Simultaneously, compared with three non-seasonal grey forecasting models and the SARIMA model, the performance of self-adaptive seasonal grey forecasting models is outstanding, which indicates that they capture the seasonal changes of air quality more efficiently.

Since air quality is affected by various factors, subsequent research may consider including meteorological conditions, pollutant emissions and other factors to perfect the self-adaptive seasonal grey models.

Given the problematic air pollution situation in China, timely and accurate air quality forecasting technology is exceptionally crucial for mitigating their adverse effects on the environment and human health. The paper proposes three self-adaptive seasonal grey forecasting models to forecast the air quality index of all provinces in China, which improves the adaptability of conventional grey models and provides more efficient prediction tools for air quality.

The self-adaptive seasonal adjustment factors are constructed to characterize the seasonal fluctuations of air quality index. Three novel self-adaptive seasonal grey forecasting models are established for prognosticating the air quality of all provinces in China. The robustness of the proposed grey models is reinforced by integrating the seasonal irregularity. The proposed methods acquire better forecasting precisions compared with the non-seasonal grey models and the SARIMA model.

The purpose of this paper is to summarize progress of grey forecasting modelling, explain mechanism of grey forecasting modelling and classify exist grey forecasting models.

General modelling process and mechanism of grey forecasting modelling is summarized and classification of grey forecasting models is done according to their differential equation structure. Grey forecasting models with linear structure are divided into continuous single variable grey forecasting models, discrete single variable grey forecasting models, continuous multiple variable grey forecasting models and discrete multiple variable grey forecasting models. The mechanism and traceability of these models are discussed. In addition, grey forecasting models with nonlinear structure, grey forecasting models with grey number sequences and grey forecasting models with multi-input and multi-output variables are further discussed.

It is clearly to explain differences between grey forecasting models with other forecasting models. Accumulation generation operation is the main difference between grey forecasting models and other models, and it is helpful to mining system developing law with limited data. A great majority of grey forecasting models are linear structure while grey forecasting models with nonlinear structure should be further studied.

Mechanism and classification of grey forecasting models are very helpful to combine with suitable real applications.

The main contributions of this paper are to classify models according to models' structure are linear or nonlinear, to analyse relationships and differences of models in same class and to deconstruct mechanism of grey forecasting models.

Electricity plays an essential role in nations' economic development. However, coal and renewables currently play an important part in electricity production in major world economies. The current study aims to forecast the electricity production from coal and renewables in the USA, China and Japan.

Two intelligent grey forecasting models – optimized discrete grey forecasting model DGM (1,1,α), and optimized even grey forecasting model EGM (1,1,α,θ) – are used to forecast electricity production. Also, the accuracy of the forecasts is measured through the mean absolute percentage error (MAPE).

Coal-powered electricity production is decreasing, while renewable energy production is increasing in the major economies (MEs). China's coal-fired electricity production continues to grow. The forecasts generated by the two grey models are more accurate than that by the classical models EGM (1,1) and DGM (1,1) and the exponential triple smoothing (ETS).

The study confirms the reliability and validity of grey forecasting models to predict electricity production in the MEs.

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.

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.

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.

Tourism industry is a highly complex system surrounded by many uncertainties because of its innumerable connections with other supporting systems. Considering tourism, a grey system, the current study proposes optimistic–pessimistic method (OPM). This technique can aid in improving forecast accuracy of four tourism-related indicators, inbound tourism to China, outbound tourism from China, revenues collected through inbound tourism and expenses incurred on outbound tourism.

The study integrates OPM into EGM and then using the secondary data collected from the World Bank database, predicts the four tourism-related indicators. The mean absolute percentage error steered the performance of the models.

One of the main contributions of the study lies in its overall evaluation of one of the major travel and tourism countries of the world in light of four crucial indicators. The study highlights, four tourism-related indicators' recent information, contains more valuable information about the future.

OPM represents a novel application of concept of whitenization of interval grey number in grey forecasting theory.

In the daily energy dispatch process in a power system, accurate short-term electricity load forecasting is a very important tool used by spot market players. It is a critical requirement for optimal generator unit commitment, economic dispatch, system security and stability assessment, contingency and ancillary services management, reserve setting, demand side management, system maintenance and financial planning in power systems. The purpose of this study is to present an improved grey Verhulst electricity load forecasting model.

To test the effectiveness of the proposed model for short-term load forecast, studies made use of Kenya’s load demand data for the period from January 2014 to June 2019.

The convectional grey Verhulst forecasting model yielded a mean absolute percentage error of 7.82 per cent, whereas the improved model yielded much better results with an error of 2.96 per cent.

In the daily energy dispatch process in a power system, accurate short-term load forecasting is a very important tool used by spot market players. It is a critical ingredient for optimal generator unit commitment, economic dispatch, system security and stability assessment, contingency and ancillary services management, reserve setting, demand side management, system maintenance and financial planning in power systems. The fact that the model uses actual Kenya’s utility data confirms its usefulness in the practical world for both economic planning and policy matters.

In terms of generation and transmission investments, proper load forecasting will enable utilities to make economically viable decisions. It forms a critical cog of the strategic plans for power utilities and other market players to avoid a situation of heavy stranded investment that adversely impact the final electricity prices and the other extreme scenario of expensive power shortages.

This research combined the use of natural logarithm and the exponential weighted moving average to improve the forecast accuracy of the grey Verhulst forecasting model.

This paper applied grey wave forecasting in a decomposition–ensemble forecasting method for modelling the complex and non-linear features in time series data. This application aims to test the advantages of grey wave forecasting method in predicting time series with periodic fluctuations.

The decomposition–ensemble method combines empirical mode decomposition (EMD), component reconstruction technology and grey wave forecasting. More specifically, EMD is used to decompose time series data into different intrinsic mode function (IMF) components in the first step. Permutation entropy and the average of each IMF are checked for component reconstruction. Then the grey wave forecasting model or ARMA is used to predict each IMF according to the characters of each IMF.

In the empirical analysis, the China container freight index (CCFI) is applied in checking prediction performance. Using two different time periods, the results show that the proposed method performs better than random walk and ARMA in multi-step-ahead prediction.

The decomposition–ensemble method based on EMD and grey wave forecasting model expands the application area of the grey system theory and graphic forecasting method. Grey wave forecasting performs better for data set with periodic fluctuations. Forecasting CCFI assists practitioners in the shipping industry in decision-making.