A novel grey forecasting model and its optimization

Although the grey forecasting model has been successfully employed in many fields and demonstrated promising results, its prediction results may be inaccurate sometimes. For the purposes of enhancing the predictive performance of grey forecasting model and enlarging its suitable ranges, this paper puts forward a novel grey forecasting model termed NGM model and its optimized model, develops a calculative formula for solving the parameters of the novel NGM model through the least squares method, and obtains the time response sequence of NGM model by using differential equation as a procedure for reasoning. It performs a numerical demonstration on the prediction accuracy of NGM model and its optimized models. As shown in the results, the proposed model and it optimized model can enhance the prediction accuracy. Numerical results illustrate that the proposed NGM model and its optimized model are effective. They are suitable for predicting the data sequence with the characteristics of non-homogeneous exponential law. This work makes important contribution to the enrichment of grey prediction theory.     

A new multivariable grey prediction model with structure compatibility

A new multivariable grey prediction model was proposed by adding a dependent variable lag term, a linear correction term and a random disturbance term to the traditional GM(1,N) model. It was theoretically proved that the new model can be completely compatible with the mainstream single variable and multivariable grey prediction models by adjusting and changing the model's parameters. To test the performance of the new model, three case studies were performed. The simulation and prediction results of the new model were compared with those of other grey prediction models. Results showed that the new model had evidently superior performance to other grey models, which confirms that the structure design of the new model is more reasonable than those of the other existing grey prediction models.     

A mega-trend-diffusion grey forecasting model for short-term manufacturing demand

Accurate short-term demand forecasting is critical for developing effective production plans; however, a short forecasting period indicates that the product demands are unstable, rendering tracking of product development trends difficult. Determining the actual developing data patterns by using forecasting models generated using historical observations is difficult, and the forecasting performance of such models is unfavourable, whereas using the latest limited data for forecasting can improve management efficiency and maintain the competitive advantages of an enterprise. To solve forecasting problems related to a small data set, this study applied an adaptive grey model for forecasting short-term manufacturing demand. Experiments involving the monthly demand data for thin film transistor liquid crystal display panels and wafer-level chip-scale packaging process data showed that the proposed grey model produced favourable forecasting results, indicating its appropriateness as a short-term forecasting tool for small data sets.     

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.     

A new grey prediction model FGM(1, 1)

The effectiveness of the first entry of the original series by GM(1, 1) is researched in this paper. The results show that the modelling values and forecasts are independent of the first entry of the original series. The grey prediction model presented in this paper is called first-entry GM(1, 1), abbreviated as FGM(1, 1), which is based on the existing GM(1, 1) but modelled with data including the first-entry’s messages of the original series. A proof concerning this subject has been presented by other authors. However, the algorithm of their direct proof is too complicated. A more compact algorithm is presented in this paper to prove the first entry of the original series ineffective to the modelling values and forecasts by GM(1, 1). Then, an arbitrary number can be inserted in the front of the original series to extract the messages from its first entry. Only a few data (usually fewer than ten) are used for model building. This paper deals with the effectiveness of the first entry of the original series by GM(1, 1).     

A novel hybrid multivariate nonlinear grey model for forecasting the traffic-related emissions

In this paper, we proposed a novel forecasting method using grey system theory for the traffic-related emissions at a national level. In our tests, grey relational analysis was used to identify time lags between input and output variables. We introduced a multivariate nonlinear grey model based on the kernel method to improve the accuracy of traffic-related emissions prediction. By solving a convex optimization problem instead of using an ordinary least squares estimation, the proposed model overcame the limitations of the classic grey forecasting models. A model confidence set test on the realistic results of forecasting traffic-related emissions in European Union member countries showed that the proposed model demonstrated a marked superiority over robust linear regression and support vector regression. Based on the non-methane volatile organic compounds from road transport and the relevant factors of the emission from 2004 to 2016, a more stringent European Union emission reduction commitment to the road transport for each year from 2020 to 2029 was suggested. We also investigated the advantages of the proposed model via the analysis on convergence, robustness, and sensitivity.     

灰色Verhulst模型的改进及其应用

针对灰色Verhulst模型的不足,讨论了灰色Verhulst模型的参数优化问题.首先,利用最小二乘原理给出了一种初值优化的改进模型.其次,在平均相对误差最小准则下,将Verhulst模型的参数优化转化为线性规划问题,然后利用粒子群优化算法估计Verhulst模型中的参数,得到另外一种改进模型.最后,给出了一个仿真实例,结果表明灰色Verhulst模型的改进方法是可行的和有效的,而且具有较高的拟合和预测精度.     

A research on the grey prediction model GM(1,n)

The grey theory can be applied in the research of prediction, decision-making and control, especially in prediction. The primary characteristic of a grey system is the incompleteness of information. A grey system could be whitened by way of inserting more messages in itself and its accuracy of prediction could be raised. The solution to the existing grey prediction model GM(1,n) is inaccurate and then its prediction accuracy cannot be expected. To solve the existing GM(1,n) by assuming step by step the first order accumulated generating operation data of the associated series to be constants is incorrect. The existing model GM(1,n) is seriously wrong even for a system having a nonnegative associated series with constant entries. There are currently only a few wrong papers based on the existing GM(1,n) model to be published. Almost all the improved prediction models based on the existing GM(1,n) model are correct. For example, the improved models are correct by convolution integral or fitting their forcing terms by several elementary functions. The algorithm of GMC(1,n) is applied to explain why the existing GM(1,n) model is incorrect in this article.     

A novel multivariate grey model for forecasting the sequence of ternary interval numbers

A novel multivariate grey model suitable for the sequence of ternary interval numbers is presented in the paper. New model takes into account the influencing factors on the system behavior characteristic. New parameter setting makes the model directly applicable to the sequence of ternary interval number without the need to convert the sequence into real sequence. A compensation coefficient taken as a ternary interval number is added to the model equation. The accumulation method based on the new information priority is proposed to estimate coefficients. A connotative prediction formula is derived to replace the white response equation of the classical multivariate grey model. The single variable grey model, which takes into account the development trend of system behavior itself, is combined with the novel multivariate grey model based on the degree of grey incidence. Interval forecasts for China's electricity generation and consumer price index show that the new model has good performance.     

Optimal solution for novel grey polynomial prediction model

The grey prediction model, as a time-series analysis tool, has been used in various fields only with partly known distribution information. The grey polynomial model is a novel method to solve the problem that the original sequence is in accord with a more general trend rather than the special homogeneous or non-homogeneous trend, but how to select the polynomial order still needs further study. In this paper the tuned background coefficient is introduced into the grey polynomial model and then the algorithmic framework for polynomial order selection, background coefficient search and parameter estimation is proposed. The quantitative relations between the affine transformation of accumulating sequence and the parameter estimates are deduced. The modeling performance proves to be independent of the affine transformation. The numerical example and application are carried out to assess the modeling efficiency in comparison with other conventional models.     

A comparison of the Lee-Carter model and AR-ARCH model for forecasting mortality rates

With the decline in the mortality level of populations, national social security systems and insurance companies of most developed countries are reconsidering their mortality tables taking into account the longevity risk. The Lee and Carter model is the first discrete-time stochastic model to consider the increased life expectancy trends in mortality rates and is still broadly used today. In this paper, we propose an alternative to the Lee-Carter model: an AR(1)-ARCH(1) model. More specifically, we compare the performance of these two models with respect to forecasting age-specific mortality in Italy. We fit the two models, with Gaussian and t-student innovations, for the matrix of Italian death rates from 1960 to 2003. We compare the forecast ability of the two approaches in out-of-sample analysis for the period 2004-2006 and find that the AR(1)-ARCH(1) model with t-student innovations provides the best fit among the models studied in this paper.     

A novel multi-information fusion grey model and its application in wear trend prediction of wind turbines

The small and fluctuating samples of lubricating oil data render the wear trend prediction a challenging task in operation and maintenance management of wind turbine gearboxes. To deal with this problem, this paper puts forward a method to enhance the prediction accuracy and robustness of the grey prediction model by introducing multi-source information into traditional grey models. Multi-source information is applied by creating a mapping sequence according to the sequence to be predicted. The significance of the key parameters in the proposed model was investigated by numerical experiments. Based on the results from the numerical experiments, the effectiveness of the proposed method was demonstrated using lubricating oil data captured from industrial wind turbine gearboxes. A comparative analysis was also conducted with a number of selected other models to illustrate the superiority of the proposed model in dealing with small and fluctuating data. Prediction results show that the proposed model is able to relax the quasi-smooth requirement of data sequence and is much more robust in comparison to exponential regression, linear regression and non-equidistance GM(1,1) models.     

初值修正灰色Verhulst模型的参数估计

研究了初值修正项为αz(1)(1)(其中α为修正参数)的灰色Verhuslt模型的修正参数估计方法.针对相关文献中,修正参数α求解无现成公式情况,通过最小化原始序列的一次累加序列与模拟序列之差,建立并求解一个非约束优化模型,获得了初值修正参数α的一个简单有效的计算公式,完善了相关文献中建立的初值修正灰色Verhuslt模型.最后,通过计算实例验证了修正参数公式可以有效提高初值修正灰色Verhuslt模型的精度.     

The novel fractional discrete multivariate grey system model and its applications

Fractional order accumulation is a novel and popular tool which is efficient to improve accuracy of the grey models. However, most existing grey models with fractional order accumulation are all developed on the conventional methodology of grey models, which may be inaccurate in the applications. In this paper an existing fractional multivariate grey model with convolution integral is proved to be a biased model, and then a novel fractional discrete multivariate grey model based on discrete modelling technique is proposed, which is proved to be an unbiased model with mathematical analysis and stochastic testing. An algorithm based on the Grey Wolf Optimizer is introduced to optimize the fractional order of the proposed model. Four real world case studies with updated data sets are executed to assess the effectiveness of the proposed model in comparison with nine existing multivariate grey models. The results show that the Grey Wolf Optimizer-based algorithm is very efficient to optimize the fractional order of the proposed model, and the proposed model outperforms other nine models in the all the real world case studies.     

Prediction of index futures returns and the analysis of financial spillovers—A comparison between GARCH and the grey theorem

This paper adopts the GM(1, 1) model to predict the rates of return of nine major index futures in the American and Eurasian markets. In a further step, by means of local grey relational analysis and by employing the GM(1, N) model for the first time, the variation relatedness and the main influencing factor among the above mentioned targeted markets is determined. Then, a comparison between GARCH/TGARCH and the grey theory with regard to predictive power is conducted. The findings reveal that the GARCH/TGARCH model performs better than the GM(1, 1), including the optimal α method, in terms of forecasting capabilities. Meanwhile, it is also found that GARCH and spillover effects indeed exist. Moreover, GM(1, N) also reveals that the daily rate of return of the Dow Jones index futures has the most influence on the rates of return of the other index futures.     

The effect of sample size on the grey system model

Some forecasting models have been developed, each has its own application condition. The grey model is used for small sample forecasting, but until now there is no reasonable explanation for the reason why it is not used for large sample. Therefore, in this paper, matrix perturbation theory is employed to explain the reason. The results of practical numerical examples from previous works demonstrate that the small sample usually has more accuracy than the large sample when establishing grey model in theory. Furthermore, we used the grey model with small samples to analyse the trend of syphilis incidence in China.     

Combined stress and human performance: a weighted digraph model

Weighted directed graphs are described and offered as possible aids to the analysis of the interactive effects of multiple independent variables on human behavior. Examples in which weighted digraphs represent the interactions among multiple stressors and performance indices are presented, and pulse process analysis is used to derive empirical predictions from the models.