The purpose of this paper is to study a fractional grey model FAGM(1,1,tα) based on the GM(1,1,tα) model and the fractional accumulated generating operation, and then predict the national health expenditure, the government health expenditure and the out-of-pocket health expenditure of China.
The presented univariate grey model is systematically studied by using the grey modelling technique, the fractional accumulated generating operation and the trapezoid approximation formula of definite integral. The optimal system parameters r and α are evaluated by the particle swarm optimisation algorithm.
The expressions of the time response function and the restored values of this model are derived. The GM(1,1), NGM(1,1,k,c) and GM(1,1,tα) models are particular cases of the FAGM(1,1,tα) model with deterministic r and α. Compared with other forecasting models, the results of the FAGM(1,1,tα) model have higher precision.
The superiority of the new model has high potential to be used in the medicine and health fields and others. Results can provide a guideline for government decision making.
The univariate fractional grey model FAGM (1,1,tα) successfully studies the China’s health expenditure.
Erratum: It has come to the attention of the publisher that the article, Wenqing Wu, Xin Ma, Yuanyuan Zhang, Yong Wang and Xinxing Wu, “Analysis of novel FAGM(1,1,tα) model to forecast health expenditure of China” published in Grey Systems, Vol. 9 No. 2, incorrectly typed the author Wenqing Wu’s name as Wenging Wu. This error was introduced in the editorial process and has now been corrected in the online version. The publisher sincerely apologises for this error and for any inconvenience caused.
The research was supported by the National Natural Science Foundation of China (Nos 71771033, 71571157, 11601357), the Longshan Academic Talent Research supporting programme of SWUST (No. 17LZXY20), the Open Fund (PLN 201710) of State Key Laboratory of Oil and Gas Reservoir Geology and Exploitation (Southwest Petroleum University) and the Applied Basic Research Program of Science and Technology Commission Foundation of Sichuan Province (No. 2017JY0159) and the funding of V.C. & V.R. Key Lab of Sichuan Province (SCVCVR2018.08S, SCVCVR2018.10VS), and the Humanities and Social Science Project of Ministry of Education of China (No. 19YJCZH119).
Wu, W., Ma, X., Zhang, Y., Wang, Y. and Wu, X. (2019), "Analysis of novel FAGM(1,1,
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