Generalized discrete GM (1,1) model

Tianxiang Yao (College of Economics and Management, Nanjing University of Information Science and Technology, Nanjing, China)
Jeffery Forrest (Department of Mathematics, Slippery Rock University, Slippery Rock, Pennsylvania, USA)
Zaiwu Gong (College of Economics and Management, Nanjing University of Information Science and Technology, Nanjing, China)

Grey Systems: Theory and Application

ISSN: 2043-9377

Publication date: 27 January 2012

Abstract

Purpose

The purpose of this paper is to expand discrete GM (1,1) model and solve the problem of non‐equidistance grey prediction problem with integral interval or digital interval.

Design/methodology/approach

Discrete GM (1,1) model can be utilized to simulate exponential sequence without errors, but it can't be utilized to simulate non‐equidistance data sequence. This paper applied optimization theories to establish generalized discrete GM (1,1) model. First, this paper established the time response of simulation sequence directly. Second, this paper established the steps of non‐equidistance data sequence. Finally, this paper utilized examples to test the method put forward.

Findings

The results indicate the generalized discrete GM (1,1) (GDGM) model can perfectly simulate non‐equidistance exponential series. Discrete GM (1,1) model is only the special form of GDGM model.

Practical implications

Though grey forecasting models are widely used, most of the forecasting models are based on the equal distance sequence. Due to many reasons, the raw data available usually is incomplete. There are mainly four reasons which caused non‐equidistance sequence. So generalized discrete GM (1,1) model can be utilized to simulate non‐equidistance sequence and has great application values.

Originality/value

The paper succeeds in establishing a generalized discrete GM (1,1) model which can be utilized to solve non‐equidistance data sequence forecasting. The GDGM model can be solved by MATLAB or other corresponding software.

Keywords

Citation

Yao, T., Forrest, J. and Gong, Z. (2012), "Generalized discrete GM (1,1) model", Grey Systems: Theory and Application, Vol. 2 No. 1, pp. 4-12. https://doi.org/10.1108/20439371211197622

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Publisher

:

Emerald Group Publishing Limited

Copyright © 2012, Emerald Group Publishing Limited

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