Study on unbiased interval grey number prediction model with new information priority

2019 ◽  
Vol 10 (1) ◽  
pp. 1-11 ◽  
Author(s):  
Ye Li ◽  
Juan Li
Keyword(s):  
Differential Equation ◽  
Difference Equation ◽  
Prediction Model ◽  
Response Function ◽  
Iteration Method ◽  
Time Response ◽  
Initial Value ◽  
Content Type ◽  
New Information ◽  
Grey Number

Purpose The purpose of this paper is to construct an unbiased interval grey number prediction model with new information priority for dealing with the jumping errors from difference equation to the differential equation in the prediction model of interval grey number. Design/methodology/approach First, this study obtains a set of linear equations about the model parameters by taking the minimum error sum of squares between the accumulative sequence and its simulation values as criterion, and solves them on the basis of the Crammer rule. Then, according to the new information priority principle, it selects the last number of the accumulated generation sequence as the initial value and gives the expression of the time response function by the recursive iteration method to establish the interval grey number prediction model. Findings This paper provides an unbiased interval grey number prediction model with new information priority, and the example analysis shows that the method proposed in this paper has higher prediction precision and practicality. Research limitations/implications If there is a better method to whiten the interval grey number, so as to fully tap the grey information contained in it, the accuracy of the model will be higher. Practical implications The model proposed in this paper can avoid the error caused by jumping from difference equation to differential equation and make full use of new information. It can be better used in a problem where new information has a great influence on prediction results. Originality/value This paper selects the last number of the accumulated generation sequence as the initial value and gives the expression of the time response function by the recursive iteration method. Then, it constructs an unbiased interval grey number prediction model with new information priority.

Development of a direct NGM(1,1) prediction model based on interval grey numbers

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Ye Li ◽  
Yuanping Ding ◽  
Yaqian Jing ◽  
Sandang Guo
Keyword(s):  
Genetic Algorithm ◽  
Markov Model ◽  
Prediction Model ◽  
Real Number ◽  
Content Type ◽  
Optimal Weight ◽  
Practical Applications ◽  
Number Sequences ◽  
Integral Development ◽  
Grey Number

PurposeThe purpose of this paper is to construct an interval grey number NGM(1,1) direct prediction model (abbreviated as IGNGM(1,1)), which need not transform interval grey numbers sequences into real number sequences, and the Markov model is used to optimize residual sequences of IGNGM(1,1) model.Design/methodology/approachA definition equation of IGNGM(1,1) model is proposed in this paper, and its time response function is solved by recursive iteration method. Next, the optimal weight of development coefficients of two boundaries is obtained by genetic algorithm, which is designed by minimizing the average relative error based on time weighted. In addition to that, the Markov model is used to modify residual sequences.FindingsThe interval grey numbers’ sequences can be predicted directly by IGNGM(1,1) model and its residual sequences can be amended by Markov model. A case study shows that the proposed model has higher accuracy in prediction.Practical implicationsUncertainty and volatility information is widespread in practical applications, and the information can be characterized by interval grey numbers. In this paper, an interval grey numbers direct prediction model is proposed, which provides a method for predicting the uncertainty information in the real world.Originality/valueThe main contribution of this paper is to propose an IGNGM(1,1) model which can realize interval grey numbers prediction without transforming them into real number and solve the optimal weight of integral development coefficient by genetic algorithm so as to avoid the distortion of prediction results. Moreover, the Markov model is used to modify residual sequences to further improve the modeling accuracy.

A Numerical Algorithm to Initial Value Problem of Caputo Fractional-Order Differential Equation

2015 ◽  
Author(s):  
Lu Bai ◽  
Dingyü Xue
Keyword(s):  
Differential Equation ◽  
Difference Equation ◽  
Error Analysis ◽  
Numerical Solution ◽  
Fractional Order ◽  
Numerical Algorithm ◽  
Initial Value Problem ◽  
Order Differential Equation ◽  
Fractional Order Differential Equation ◽  
Initial Value

A numerical algorithm is presented to solve the initial value problem of linear and nonlinear Caputo fractional-order differential equations. Firstly, nonzero initial value problem should be transformed into zero initial value problem. Error analysis has been done to polynomial algorithm, the reason has been found why the calculation error of the algorithm is large. A new algorithm called exponential function algorithm is proposed based on the analysis. The obtained fractional-order differential equation is transformed into difference equation. If the differential equation is linear, the obtained difference equation is explicit, the numerical solution can be solved directly; otherwise, the obtained difference equation is implicit, the predictor of the numerical solution can be obtained with extrapolation algorithm, substitute the predictor into the equation, the corrector can be solved. Error analysis has been done to the new algorithm, the algorithm is of first order.

Weapon equipment management cost prediction based on forgetting factor recursive GM (1,1) model

2019 ◽  
Vol 10 (1) ◽  
pp. 38-45
Author(s):  
Subing Liu ◽  
Yin Chunwu ◽  
Cao Dazhi
Keyword(s):  
Prediction Model ◽  
Recursive Estimation ◽  
Model Parameters ◽  
Grey Prediction ◽  
Forgetting Factor ◽  
Content Type ◽  
Grey Prediction Model ◽  
Model Based ◽  
New Information ◽  
Equipment System

Purpose The purpose of this paper is to provide a new recursive GM (1,1) model based on forgetting factor and apply it to the modern weapon and equipment system. Design/methodology/approach In order to distinguish the contribution of new and old data to the grey prediction model with new information, the authors add forgetting factor to the objective function. The purpose of the above is to realize the dynamic weighting of new and old modeling data, and to gradually forget the old information. Second, the recursive estimation algorithm of grey prediction model parameters is given, and the new information is added in real time to improve the prediction accuracy of the model. Findings It is shown that the recursive GM (1,1) model based on forgetting factor can achieve both high effectiveness and high efficiency. Originality/value The paper succeeds in proposing a recursive GM (1,1) model based on forgetting factor, which has high accuracy. The model is applied to the field of modern weapon and equipment system and the result the model is better than the GM(1,1) model. The experimental results show the effectiveness and the efficiency of the prosed method.

An iteration method for a nonlinear differential equation describing the convergence to equilibrium in a system of reacting polymers

1981 ◽  
Vol 375 (1763) ◽  
pp. 529-542
Keyword(s):  
Differential Equation ◽  
Initial Data ◽  
Global Solution ◽  
Nonlinear Differential Equation ◽  
Initial Value Problem ◽  
Iteration Method ◽  
Constructive Method ◽  
Convergence To Equilibrium ◽  
Initial Value

A constructive method is presented to give the global solution to a nonlinear initial value problem describing the convergence to equilibrium in a system of reacting polymers. The solution is proved to be unique and continuous with respect to small variations in the initial data.

Variational principle and its fractal approximate solution for fractal Lane-Emden equation

2020 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
KangLe Wang
Keyword(s):  
Differential Equation ◽  
Variational Principle ◽  
Iteration Method ◽  
Approximate Analytical Solution ◽  
Variational Iteration Method ◽  
Content Type ◽  
Emden Equation ◽  
Variational Iteration ◽  
Fractal Models ◽  
Fractal Differential Equation

Purpose The purpose of this paper is to describe the Lane–Emden equation by the fractal derivative and establish its variational principle by using the semi-inverse method. The variational principle is helpful to research the structure of the solution. The approximate analytical solution of the fractal Lane–Emden equation is obtained by the variational iteration method. The example illustrates that the suggested scheme is efficient and accurate for fractal models. Design/methodology/approach The author establishes the variational principle for fractal Lane–Emden equation, and its approximate analytical solution is obtained by the variational iteration method. Findings The variational iteration method is very fascinating in solving fractal differential equation. Originality/value The author first proposes the variational iteration method for solving fractal differential equation. The example shows the efficiency and accuracy of the proposed method. The variational iteration method is valid for other nonlinear fractal models as well.

Prediction model of three-parameter interval grey number based on kernel and double information domains

2020 ◽  
Vol 10 (4) ◽  
pp. 455-465
Author(s):  
Ye Li ◽  
Sandang Guo ◽  
Juan Li
Keyword(s):  
Prediction Model ◽  
Center Of Gravity ◽  
Grey Prediction ◽  
Content Type ◽  
Grey Prediction Model ◽  
Changing Trend ◽  
Parameter Interval ◽  
Grey Number ◽  
Definition Of ◽  
Information Domain

PurposeThe purpose of this paper is to construct a prediction model of three-parameter interval grey number based on kernel and double information domains to expand the modeling object of grey prediction model from interval grey number to three-parameter interval grey number.Design/methodology/approachFirst, the study decomposes the grey valued interval into upper and lower cells with the “center of gravity” as the dividing point and defines the upper and lower information domains of the three-parameter interval grey number. Second, it calculates the kernel, the upper and lower information domains of the three-parameter interval grey number. Then, it constructs the prediction model for kernel sequence and upper and lower information domain sequences, respectively. By deducing the time response expressions of “center of gravity”, lower and upper limits of three-parameter interval grey number, a prediction model of three-parameter interval grey number based on kernel and double information domains is obtained.FindingsThis paper provides a prediction model of three-parameter interval grey number based on kernel and double information domains, and the example analysis shows that the method proposed in this paper has higher prediction accuracy and practicality.Practical implicationsIn this paper, the modeling object of grey prediction model is extended to the three-parameter interval grey number, so it can be used for the prediction of uncertainty problems, such as stock changing trend, temperature and so on.Originality/valueBy decomposing the grey valued interval into upper and lower cells with the “center of gravity” as the dividing point, gives the definition of upper and lower information domains and then obtains a new method for whitening the three-parameter interval grey number.

Investor protection and market reaction to unusual market activity replies

2020 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Chun-Teck Lye ◽  
Tuan-Hock Ng ◽  
Kwee-Pheng Lim ◽  
Chin-Yee Gan
Keyword(s):  
Market Reaction ◽  
Investor Protection ◽  
Abnormal Returns ◽  
Stock Exchanges ◽  
Uncertain Information ◽  
Information Uncertainty ◽  
Content Type ◽  
Market Activity ◽  
Information Hypothesis ◽  
New Information

PurposeThis study uses the unique setting of unusual market activity (UMA) replies to examine the market reaction and the effects of disclosure and investor protection amid information uncertainty.Design/methodology/approachA total of 1527 hand-collected UMA replies from the interlinked stock exchanges of Indonesia, Malaysia, Thailand and Singapore for the period of 2015–2017 were analysed using event study and Heckman two-step methods with market and matched control firm benchmarks.FindingsThe overall results support the uncertain information hypothesis. The UMA replies with new information were also found to reduce information uncertainty, but not information asymmetry, and they are complementary to investor protection in enhancing abnormal returns. The overall finding suggests that the UMA public query system can be an effective market intervention mechanism in improving information certainty and efficiency.Research limitations/implicationsThis study provides insight on the effects of news replies and investor protection on abnormal returns, and support for the uncertain information hypothesis. The finding is useful to policymakers and stock exchanges as they seek to understand how to alleviate investors' anxiety and to create an informationally efficient market. Nevertheless, this study is limited by the extensiveness of the hand-collected UMA replies and also the potential issue of simultaneity-induced endogeneity.Originality/valueThis study uses UMA replies and cross-country data taking into account the effects of market surroundings such as information uncertainty and the level of investor protection on market reaction.

scholarly journals p-adic confluence of q-difference equations

2008 ◽  
Vol 144 (4) ◽  
pp. 867-919 ◽  
Author(s):  
Andrea Pulita
Keyword(s):  
Differential Equation ◽  
Difference Equation ◽  
Differential Equations ◽  
Difference Equations ◽  
Root Of Unity

AbstractWe develop the theory of p-adic confluence of q-difference equations. The main result is the fact that, in the p-adic framework, a function is a (Taylor) solution of a differential equation if and only if it is a solution of a q-difference equation. This fact implies an equivalence, called confluence, between the category of differential equations and those of q-difference equations. We develop this theory by introducing a category of sheaves on the disk D−(1,1), for which the stalk at 1 is a differential equation, the stalk at q isa q-difference equation if q is not a root of unity, and the stalk at a root of unity ξ is a mixed object, formed by a differential equation and an action of σξ.

A GM(1,N)-based economic cybernetics model for the high-tech industries in China

Kybernetes ◽  
2014 ◽  
Vol 43 (5) ◽  
pp. 672-685 ◽  
Author(s):  
Zheng-Xin Wang
Keyword(s):  
Differential Equation ◽  
Patent Application ◽  
Small Sample ◽  
Total Output ◽  
High Tech ◽  
Data Set ◽  
Content Type ◽  
Fixed Assets ◽  
Grey Differential Equation ◽  
Medical Equipments

Purpose – 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. Design/methodology/approach – 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. Findings – 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. Practical implications – 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. Originality/value – 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.

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