[신간의 별자리x] 우리/미술, 그리고 ‘슬픔의 박물관’

A novel fractional time delayed grey model with Grey Wolf Optimizer and its applications in forecasting the natural gas and coal consumption in Chongqing China

Forecasting short-term renewable energy consumption of China using a novel fractional nonlinear grey Bernoulli model

The novel fractional discrete multivariate grey system model and its applications

As a kind of mathematical model, grey systems predi ct ion model has been widely applied to economy, management and engineering technol ogy. In 1982, Professor Deng Ju-long presented GM prediction model. Then some o ther scholars made improvements on GM model. Of course, much still should be don e to develop it. What the scholars have done is to take the first component of X (1) as the starting conditions of the grey differential model. It occ urs that the new information can not be used enough. This paper is addressed to choose the nth component of X (1) as the starting conditions to improv e the models. The main results of the paper is given in Theorem 2: The time response function of the grey differential equation x (0)(k)+az (1)(k)=b is given by x (1)(k)=x (1)(n)-ba e -a(k-n )+ba. and Theorem4: The time response of the grey Verhulst model is given by (1)(k) =ax (1)(n)bx (1)(n)+(a-bx (1)(n))ae a(k-n). As the new information is fully used, the accuracy of prediction is improved gre atly. Therefore, the new model with a certain theoretical and practical value.

The GM Models That x(n) Be Taken as Initial Value

Optimal solution for novel grey polynomial prediction model

Grey models have been reported to be promising for time series prediction with small samples, but the diversity kinds of model structures and modelling assumptions restrains their further applications and developments. In this paper, a novel grey prediction model, named discrete grey polynomial model, is proposed to unify a family of univariate discrete grey models. The proposed model has the capacity to represent most popular homogeneous and non-homogeneous discrete grey models and furthermore, it can induce some other novel models, thereby highlighting the relationship between the models and their structures and assumptions. Based on the proposed model, a data-based algorithm is put forward to select the model structure adaptively. It reduces the requirement for modeler’s knowledge from an expert system perspective. Two numerical experiments with large-scale simulations are conducted and the results show its effectiveness. In the end, two real case tests show that the proposed model benefits from its adaptive structure and produces reliable multi-step ahead predictions.

Data-based structure selection for unified discrete grey prediction model

Understanding cumulative sum operator in grey prediction model with integral matching

Grey theory-based time series models are widely used in various fields and disciplines. While most of the research is focused on the development and improvement of novel discrete-time models, very limited attention has been paid to the relationships among diverse models. The current paper proposes a methodological and practical framework to unify the single-variable, multi-variable, and multi-output discrete-time grey models, making it easier for practitioners to select an appropriate model for a given time-series forecasting problem. The recursive extrapolation strategy is present to generate multi-step ahead forecasts and four model families are deduced within the universal framework. Large-scale simulation studies are conducted to evaluate the finite-sample fitting and multi-step ahead forecasting performance. The proposed approach is illustrated using application examples from the indirect measurement of the tensile strength of materials.

On unified framework for discrete-time grey models: Extensions and applications.

Since most of the research about grey forecasting models is focused on developing novel models and improving accuracy, relatively limited attention has been paid to the modelling mechanism and relationships among diverse kinds of models. This paper aims to unify and reconstruct continuous-time grey models, highlighting the differences and similarities among different models. First, the unified form of grey models is proposed and simplified into a reduced-order ordinary differential equation. Then, the integral matching that consists of integral transformation and least squares, is proposed to estimate the structural parameter and initial value simultaneously. The cumulative sum operator, an essential element in grey modelling, proves to be the discrete approximation of the integral transformation formula. Next, grey models are reconstructed by the integral matching-based ordinary differential equations. Finally, the existing grey models are compared with the reconstructed models through extensive simulation studies, and a real-world example shows how to apply and further verify the reconstructed model.

Baolei Wei

Papers

Optimal solution for novel grey polynomial prediction model

Data-based structure selection for unified discrete grey prediction model

Understanding cumulative sum operator in grey prediction model with integral matching

On unified framework for discrete-time grey models: Extensions and applications.

On unified framework for continuous-time grey models: an integral matching perspective