Discrete Grey Forecasting Model Research Articles

Grey forecast of electricity production from coal and renewable sources in the USA, Japan and China

PurposeElectricity 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.Design/methodology/approachTwo 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).FindingsCoal-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).Originality/valueThe study confirms the reliability and validity of grey forecasting models to predict electricity production in the MEs.

A novel structure adaptive fractional discrete grey forecasting model and its application in China’s crude oil production prediction

Crude oil resources are related to all aspects of people's life, and play a vital role in the development of the national economy. Using nonlinear discrete data to reasonably predict crude oil production can help the government adjust energy structure and formulate energy development strategy, which has great practical significance. In this paper, a novel r-order accumulation operation with a parameter is proposed, and a novel structure adaptive fractional discrete grey forecasting model is established. Several classical optimization algorithms are compared, and the Grey Wolf Optimizer (GWO) is selected to calculate the parameters. For testifying the effectiveness of the model, a prediction model is constructed based on the total crude oil production in Qinghai, Liaoning and Shaanxi provinces of China, and a performance comparison experiment is designed with the existing six grey models. In addition, Monte Carlo simulation and probability density analysis provide a new perspective to further illustrate the robustness and accuracy of the proposed model. The experimental results show that this model is superior to the other six models in terms of fitting accuracy, prediction accuracy and model stability.

An enhanced multivariable dynamic time-delay discrete grey forecasting model for predicting China's carbon emissions

The importance for the accurate forecast of carbon emissions affected by many factors is gradually emerging. Carbon emissions usually lag behind the related factors, which cannot be dynamically reflected in the existing grey forecasting models. Therefore, investigating the dynamic lag relationships remains the key challenge to carbon emissions forecast. For this purpose, an enhanced dynamic time-delay discrete grey forecasting model, denoted as DTDGM(1,N,τ), is proposed to predict the systems having dynamic time-lag effects. More specifically, a time-lag driving term consisting of both the interval and intensity of the time lags is developed to reflect the lag process of different factors to carbon emissions. The impulse response analysis of the vector autoregressive (VAR) model is carried out for determining the dynamic lags between carbon emissions and the related factors. In addition, a linear correction term is designed in the proposed model to extend the grey forecasting theory. Extensive experimental results about carbon emissions prediction from 1995 to 2017 show that the DTDGM(1,N,τ) model considering the delayed relationships can significantly improve the fitting and prediction performance of the model in comparison with the six benchmark models, including the three existing grey forecasting models, two machine learning models and one statistical prediction approach.

A novel grey forecasting of greenhouse gas emissions from four industries of China and India

The increased greenhouse gas concentration in the atmosphere causes climate change. China and India are among the most significant contributors to global greenhouse gas emissions. The current study forecasts the emissions from the countries' four sectors – Transportation, Building, Waste, and Manufacturing/Construction. By extending the classical discrete grey forecasting model DGM (1, 1), a new data-driven time-series forecasting technique, called DGM (1, 1, α), is proposed and applied to forecast the emissions in these sectors till 2028 with an accuracy of over 95%. The results show that the emissions are generally increasing. However, China continues to show a decline in the emissions from the manufacturing and construction industries. Also, the Posterior-Variance Test is introduced to test whether a given forecasting model is qualified or unqualified for a given problem. The comparative analyses with three forecasting models – DGM (1,1), Even GM (1,1), and Grey Verhulst models –revealed the proposed model's feasibility, flexibility, and accuracy. The study concludes with important recommendations for the policy-makers to develop better emission mitigation policies.

Forecasting carbon dioxide emissions in APEC member countries by a new cumulative grey model

The continuous increase of global carbon dioxide emissions has been the focus of human concern. Discrete Grey forecasting Model (DGM) is used to forecast the CO2 mission in Asia-pacific Economic Cooperation (APEC) member countries in 2020–2023 using data from 2014 to 2019 and the accuracy of the model was tested by the MAPE value. The results show that among the 17 predicted member states, carbon dioxide emissions show an upward trend in 13 countries, while only 4 countries show a downward trend. Faced with the current situation, all countries should pay more attention to the issue of carbon dioxide emissions and adjust their climate and energy policies.

Fractional-Order Accumulative Linear Time-Varying Parameters Discrete Grey Forecasting Model

Traditional discrete grey forecasting model can effectively predict the development trend of the stabilizing system. However, when the system has disturbance information, the prediction result will have larger error, and there will appear significant downward trend in the stability of the model. In the presence of disturbance information, this paper presents a fractional-order linear time-varying parameters discrete grey forecasting model to deal with the system that contains both linear trend and nonlinear trend. The modeling process of the model and calculation method are given. The perturbation bounds of the new model are analyzed by using the least-squares method of perturbation theory. And it is compared with that of the first-order linear time-varying parameters discrete grey forecasting model. Finally, two real cases are given to verify the effectiveness and practicality of the proposed method.

Study of a discrete grey forecasting model based on the quality cost characteristic curve

PurposeThe purpose of this paper is to clarify several commonly used quality cost models based on Juran’s characteristic curve. Through mathematical deduction, the lowest point of quality cost and the lowest level of quality level (often depicted by qualification rate) can be obtained. This paper also aims to introduce a new prediction model, namely discrete grey model (DGM), to forecast the changing trend of quality cost.Design/methodology/approachThis paper comes to the conclusion by means of mathematical deduction. To make it more clear, the authors get the lowest quality level and the lowest quality cost by taking the derivative of the equation of quality cost and quality level. By introducing the weakening buffer operator, the authors can significantly improve the prediction accuracy of DGM.FindingsThis paper demonstrates that DGM can be used to forecast quality cost based on Juran’s cost characteristic curve, especially when the authors do not have much information or the sample capacity is rather small. When operated by practical weakening buffer operator, the randomness of time series can be obviously weakened and the prediction accuracy can be significantly improved.Practical implicationsThis paper uses a real case from a literature to verify the validity of discrete grey forecasting model, getting the conclusion that there is a certain degree of feasibility and rationality of DGM to forecast the variation tendency of quality cost.Originality/valueThis paper perfects the theory of quality cost based on Juran’s characteristic curve and expands the scope of application of grey system theory.

An improved seasonal rolling grey forecasting model using a cycle truncation accumulated generating operation for traffic flow

• A seasonal rolling grey forecasting model for urban traffic flow was proposed. • The new information priority of the proposed model was proved by rigorous matrix perturbation analysis. • The proposed model provides a new perspective on the seasonal and limited data characteristics of traffic flows. • Four time intervals of traffic forecasting show that the proposed model has good adaptability and stability. Accurate real-time prediction of urban traffic flows is one of the most important problems in traffic management and control optimization research. Short-term traffic flow has complex stochastic and nonlinear characteristics, and it shows a similar seasonality within intraday and weekly trends. Based on these properties, we propose an improved binding cycle truncation accumulated generating operation seasonal grey rolling forecasting model. In the new model, the traffic flow sequence of seasonal fluctuation is converted to a flat sequence using the cycle truncation accumulated generating operation. Then, grey modeling of the cycle truncation accumulated generating operation sequence weakens the stochastic disturbances and highlights the intrinsic grey exponential law after the sequence is accumulated. Finally, rolling forecasts of the limited data reflect the new information priority and timeliness of the grey prediction. Two numerical traffic flow examples from China and Canada, including four groups at different time intervals (1 h, 15 min, 10 min, and 5 min), are used to verify the performance of the new model under different traffic flow conditions. The prediction results show that the model has good adaptability and stability and can effectively predict the seasonal variations in traffic flow. In 15 or 10 min traffic flow forecasts, the proposed model shows better performance than the autoregressive moving average model, wavelet neural network model and seasonal discrete grey forecasting model.

Development of an optimization method for the GM(1,N) model

The multi-variable grey model represented by GM(1,N) is an important causal relationship forecasting model. However, since the structure of GM(1,N) is more complicated than that of the single-variable grey forecasting model GM(1,1), it is difficult to build a useful GM(1,N) model. The simulation and prediction errors of GM(1,N) models are usually greater than those of GM(1,1) models. The modeling process of the traditional GM(1,N) model is studied and three serious defects are observed in terms of “modeling mechanism”, “parameter estimation” and “model structure”, which are the major causes of low model precision. In this paper, a novel GM(1,N) model is proposed to improve the performance of the traditional GM(1,N) model by introducing a linear correction term and a grey action quantity term to the traditional GM(1,N) model. The new model has more reasonable modeling process and more stable structure, which solves the three defects of the traditional GM(1,N) model. In addition, the new model is entirely compatible with the single variable discrete grey forecasting model DGM(1,1)and the multi-variable grey forecasting model GM(0,N). To verify the effectiveness of the development, the new model is used to simulate the tensile strength of a material. The mean relative simulation and prediction percentage errors of the new model are 0.0707% and 5.7369%, in comparison with those of the traditional precision GM(1,N) model and the classical GM(1,1) model, which are 6.0011%, 18.4280% and 1.1020%, 12.5190% respectively. The findings show that the new model has the best performance, which on one hand testifies the correctness of the defect analysis, and on the other hand validates the effectiveness of the structure reform of the traditional GM(1,N) model.

Interval grey number sequence prediction by using non-homogenous exponential discrete grey forecasting model

This paper aims to study a new grey prediction approach and its solution for forecasting the main system variable whose accurate value could not be collected while the potential value set could be defined. Based on the traditional non-homogenous discrete grey forecasting model (NDGM), the interval grey number and its algebra operations are redefined and combined with the NDGM model to construct a new interval grey number sequence prediction approach. The solving principle of the model is analyzed, the new accuracy evaluation indices, i.e. mean absolute percentage error of mean value sequence (MAPEM) and mean percent of interval sequence simulating value set covered (MPSVSC), are defined and, the procedure of the interval grey number sequence based the NDGM (IG-NDGM) is given out. Finally, a numerical case is used to test the modelling accuracy of the proposed model. Results show that the proposed approach could solve the interval grey number sequence prediction problem and it is much better than the traditional DGM(1,1) model and GM(1,1) model.

Forecasting China’s energy demand and self-sufficiency rate by grey forecasting model and Markov model

Abstract This paper applies novel models to forecast the developing trends of China’s energy production and consumption under the influence of China’s energy saving policy. An optimized single variable discrete grey forecasting model is adopted to forecast the total amount of energy production and consumption while a novel Markov approach based on quadratic programming model is proposed to forecast the trends of energy production and consumption structures. The proposed models are used to simulate China’s energy production and consumption during 2006–2011 and forecast its trends in 2015 and 2020. Results demonstrate that proposed models can effectively simulate and forecast the total amounts and structures of energy production and consumption. And by comparing with regression model, results show proposed model is a little better than regression in simulating and forecasting the case. Although the growth rate of energy consumption in China has decreased under the energy saving policy, total amount of energy consumption and the proportions of natural gas and other energies keep growing while the self-sufficiency rate of crude oil and natural gas continues to drop.

Expansion modelling of discrete grey model based on multi-factor information aggregation

This paper aims to study a novel expansion discrete grey forecasting model, which could aggregate input information more effectively. In general, existing multi-factor grey forecasting models, such as one order and h variables grey forecasting model (GM (1, h)), always aggregate the main system variable and independent variables in a linear form rather than a nonlinear form, while a nonlinear form could be used in more cases than the linear form. And the nonlinear form could aggregate collinear independent factors, which widely lie in many multi-factor forecasting problems. To overcome this problem, a new approach, named as the Solow residual method, is proposed to aggregate independent factors. And a new expansion model, feedback multi-factor discrete grey forecasting model based on the Solow residual method (abbreviated as FDGM (1, h)), is proposed accordingly. Then the feedback control equation and the parameters' solution of the FDGM (1, h) model are given. Finally, a real application is used to test the modelling accuracy of the FDGM (1, h) model. Results show that the FDGM (1, h) model is much better than the non-homogeneous discrete grey forecasting model (NDGM) and the GM (1, h) model.

Forecasting energy consumption in China following instigation of an energy-saving policy

China is in a key stage of industrialization and urbanization, which brings a high economic growth rate accompanied by high energy consumption. To alleviate the unsustainable demand for energy consumption, China’s government has instigated an energy-saving policy to decrease energy consumption per unit gross domestic product (GDP) so as to improve energy efficiency. Based on analysing historical trends of energy consumption and GDP, we have applied an optimized single-variable discrete grey forecasting model [OSDGM (1, 1)] to measure the instigation effects of the energy-saving policy and forecast whether the planned reduction rate of energy consumption per unit GDP in the implementation stage could be accomplished or not. The results illustrate that China’s government has made major progress on energy saving even though the task is tough in the long run. The forecasting results indicate that it is difficult to accomplish the planned reduction rate of energy consumption per unit GDP at both the national and provincial levels. According to the economic growth rate of 2011 and 2012, nearly half of the provinces could not reach their planned reduction rate objectives. These conclusions are very important for China’s government both in terms of policy monitoring and development.

A seasonal discrete grey forecasting model for fashion retailing

In the fashion retail industry, level of forecasting accuracy plays a crucial role in retailers’ profit. In order to avoid stock-out and maintain a high inventory fill rate, fashion retailers require specific and accurate sales forecasting systems. One of the key factors of an effective forecasting system is the availability of long and comprehensive historical data. However, in the fashion retail industry, the sales data stored in the point-of-sales (POS) systems are always not comprehensive and scattered due to various reasons. This paper presents a new seasonal discrete grey forecasting model based on cycle truncation accumulation with amendable items to improve sales forecasting accuracy. The proposed forecasting model is to overcome two important problems: seasonality and limited data. Although there are several works suitable with one of them, there is no previous research effort that overcome both problems in the context of grey models. The proposed algorithms are validated using real POS data of three fashion retailers selling high-ended, medium and basic fashion items. It was found that the proposed model is practical for fashion retail sales forecasting with short historical data and outperforms other state-of-art forecasting techniques.

Discrete grey forecasting model and its optimization

Although the grey forecasting model has been successfully adopted in various fields and demonstrated promising results, the literatures show its performance could be further improved. For this purpose, this paper proposes a novel discrete grey forecasting model termed DGM model and a series of optimized models of DGM. This paper modifies the algorithm of GM(1, 1) model to enhance the tendency catching ability. The relationship between the two models and the forecasting precision of DGM model based on the pure index sequence is discussed. And further studies on three basic forms and three optimized forms of DGM model are also discussed. As shown in the results, the proposed model and its optimized models can increase the prediction accuracy. When the system is stable approximately, DGM model and the optimized models can effectively predict the developing system. This work contributes significantly to improve grey forecasting theory and proposes more novel grey forecasting models.