Parameter estimation for grey system models: gradient matching versus integral matching

Abstract

PurposeThe cumulative sum (Cusum) operator, also referred to as accumulating generation operator, is the fundamental of grey system models and proves to be successful in various real-world applications. This paper aims to uncover the advantages of the Cusum operator from a parameter estimation perspective, i.e. comparing integral matching with classical gradient matching.Design/methodology/approachGrey system models are represented as a state space form to investigate the effect of measurement errors on estimation performance; subsequently, gradient matching and integral matching are respectively formulated to estimate parameters from noisy observations and, then, their quantitative relationships are established by using matrix computation tricks.FindingsExtensive simulations, which are conducted on both linear and non-linear models under different sample size and noise level combinations, show that integral matching is superior to gradient matching, and, also the former is less sensitive to measurement error.Originality/valueThis paper explains why the Cusum operator is widely utilized in grey system models, thereby further solidifying the mathematical fundamentals of grey system models.

Damping accumulated discrete MGM(1, m) power model and its application to forecasting agricultural output value share and employment share

“…It has been more than 40 years since grey system theory was first proposed by Professor Deng in 1982 (Deng, 1982), and it is now widely used in many fields such as agriculture, industry, water conservancy, economy and energy (Luo and Li, 2023;Tulkinov, 2023;Zhao et al, 2023;Hu, 2023). The Grey Forecasting Theory, as the core system of grey system theory, has achieved a series of important findings after years of research and development (Zhang et al, 2023;Sapnken, 2023;Li et al, 2023a;Wei et al, 2023). The economic and social system is inherently complex, comprising multiple factors and incomplete information, with various factors exerting mutual influences and constraints upon one another (Wang, 2017).…”

“…The Grey Forecasting Theory, as the core system of grey system theory, has achieved a series of important findings after years of research and development (Zhang et al ., 2023; Sapnken, 2023; Li et al. , 2023a; Wei et al ., 2023). The economic and social system is inherently complex, comprising multiple factors and incomplete information, with various factors exerting mutual influences and constraints upon one another (Wang, 2017).…”