Abstract
Accurate forecasting of the enrollment scale of higher education and education expenditure is the key to scientific decision-making in education. Nevertheless, education data sets are usually small and affected by uncertainties including economy, education system policies, and so on, which result in difficulty in modeling. To address the tissues, we presented a novel time-delayed grey model based on a fractional-order accumulation time term, abbreviated as FHTDGM. The hyperparameters of the model are optimized using the particle swarm optimization. The experiment’s results show that the FHTDGM model can fit and forecast enrollment scale and educational spending data with greater accuracy than a group of other grey models, and the forecast MAPEs are 2.396 and 1.244, respectively. The accurate prediction contributes to constructive suggestions for the decision-making of education.
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Data availability
The datasets used or analyzed during the current study are available from the corresponding author on reasonable request.
Notes
In this study, raw data were collected from the website of the China Statistics Bureau (http://www.stats.gov.cn/).
The raw data are collected from the official website of the China Statistics Bureau (http://www.stats.gov.cn/).
References
Al-Janabi S, Alkaim AF, Adel Z (2020) An innovative synthesis of deep learning techniques (dcapsnet & dcom) for generation electrical renewable energy from wind energy. Soft Comput 24:10943–10962. https://doi.org/10.1007/s00500-020-04905-9
Copas J (1993) A formula for the allocation of resources based on uncertain predictions of need. J R Stat Soc Ser A Stat Soc 156:107–113. https://doi.org/10.2307/2982863
Ding S, Li R (2021) Forecasting the sales and stock of electric vehicles using a novel self-adaptive optimized grey model. Eng Appl Artif Intell 100:104148. https://doi.org/10.1016/j.engappai.2020.104148
Du J, Liu S, Liu Y (2021) A novel grey multi-criteria three-way decisions model and its application. Comput Ind Eng 158:107405. https://doi.org/10.1016/j.cie.2021.107405
He J, Mao S, Kang Y (2023) Augmented fractional accumulation grey model and its application: class ratio and restore error perspectives. Math Comput Simul 209:220–247. https://doi.org/10.1016/j.matcom.2023.02.008
Heidari H, Zeng B (2023) An optimized grey transition Verhulst method. Eng Appl Artif Intell 120:105870. https://doi.org/10.1016/j.engappai.2023.105870
Kadhuim ZA, Al-Janabi S (2023) Intelligent deep analysis of dna sequences based on ffgm to enhancement the performance and reduce the computation. Egypt Inform J 24:173–190. https://doi.org/10.1016/j.eij.2023.02.004
LewisC D (1982) Industrial and business forecasting method. Butter-worth-Heinemann, London. https://doi.org/10.1002/for.3980020210
Liang Z (2010) A new method to predict enrollments based on fuzzy time series. Intell Control Autom. https://doi.org/10.1109/WCICA.2010.5553945
Liu S, Yang Y, Forrest J (2017) Grey data analysis, vol 10. Springer Singapore, Singapore, pp 978–981. https://doi.org/10.1007/978-981-10-1841-1
Liu L, Liu S, Fang Z, Jiang A, Shang G (2023) The recursive grey model and its application. Appl Math Model 119:447–464. https://doi.org/10.1016/j.apm.2023.02.033
Ma X, Liu Z (2017) Application of a novel time-delayed polynomial grey model to predict the natural gas consumption in china. J Comput Appl Math 324:17–24. https://doi.org/10.1016/j.cam.2017.04.020
Ma X, Xie M, Suykens JA (2021) A novel neural grey system model with Bayesian regularization and its applications. Neurocomputing 456:61–75. https://doi.org/10.1016/j.neucom.2021.05.048
Marini F, Walczak B (2015) Particle swarm optimization (PSO). A tutorial. Chemom Intell Lab Syst 149:153–165
Pattanayak RM, Behera HS, Panigrahi S (2023) A novel high order hesitant fuzzy time series forecasting by using mean aggregated membership value with support vector machine. Inf Sci 626:494–523. https://doi.org/10.1016/j.ins.2023.01.075
Sapnken FE, Ahmat KA, Boukar M, Nyobe SLB, Tamba JG (2023) Learning latent dynamics with a grey neural ode prediction model and its application. Grey Syst Theory Appl. https://doi.org/10.1108/GS-12-2022-0119
Wang Z, Li Q (2019) Modelling the nonlinear relationship between co2 emissions and economic growth using a PSO algorithm-based grey Verhulst model. J Clean Prod 207:214–224. https://doi.org/10.1016/j.jclepro.2018.10.010
Wang Y, Nie R, Ma X, Liu Z, Chi P, Wu W, Guo B, Yang X, Zhang L (2021) A novel Hausdorff fractional ngmc (p, n) grey prediction model with grey wolf optimizer and its applications in forecasting energy production and conversion of china. Appl Math Model 97:381–397. https://doi.org/10.1016/j.apm.2021.03.047
Wei B, Yang L, Xie N (2023) Nonlinear grey Bernoulli model with physics-preserving Cusum operator. Expert Syst Appl 229:120466. https://doi.org/10.1016/j.eswa.2023.120466
Xie W, Liu C, Wu W-Z (2020) The fractional non-equidistant grey opposite-direction model with time-varying characteristics. Soft Comput 24:6603–6612. https://doi.org/10.1007/s00500-020-04799-7
Xie W, Liu C, Wu W-Z, Li W, Liu C (2020) Continuous grey model with conformable fractional derivative. Chaos, Solitons Fractals 139:110285. https://doi.org/10.1016/j.chaos.2020.110285
Xie W, Liu C, Wu W-Z (2023) A novel fractional grey system model with non-singular exponential kernel for forecasting enrollments. Expert Syst Appl 219:119652. https://doi.org/10.1016/j.eswa.2023.119652
Xie W, Wu W-Z, Xu Z, Liu C, Zhao K (2023) The fractional neural grey system model and its application. Appl Math Model 121:43–58. https://doi.org/10.1016/j.apm.2023.04.028
Xie X, Liu X, Blanco C (2023) Evaluating and forecasting the niche fitness of regional innovation ecosystems: a comparative evaluation of different optimized grey models. Technol Forecast Soc Change 191:122473. https://doi.org/10.1016/j.techfore.2023.122473
Yan S, Su Q, Gong Z, Zeng X, Herrera-Viedma E (2023) Online public opinion prediction based on rolling fractional grey model with new information priority. Inf Fusion 91:277–298. https://doi.org/10.1016/j.inffus.2022.10.012
Yang L, Feng L, Zhang L, Tian L (2021) Predicting freshmen enrollment based on machine learning. J Supercomput 77:11853–11865. https://doi.org/10.1007/s11227-021-03763-y
Zeng B, Zhou W, Zhou M (2021) Forecasting the concentration of sulfur dioxide in Beijing using a novel grey interval model with oscillation sequence. J Clean Prod 311:127500. https://doi.org/10.1016/j.jclepro.2021.127500
Zeng B, Li H, Mao C, Wu Y (2022) Modeling, prediction and analysis of new energy vehicle sales in china using a variable-structure grey model. Expert Syst Appl 10:118879
Zhang X, Dang Y, Ding S, Wang J (2023) A novel discrete multivariable grey model with spatial proximity effects for economic output forecast. Appl Math Model 115:431–452
Zhang Y, Guo H, Sun M, Liu S, Forrest J (2023) A novel grey Lotka–Volterra model driven by the mechanism of competition and cooperation for energy consumption forecasting. Energy 264:126154. https://doi.org/10.1016/j.energy.2022.126154
Zhou W, Jiang R, Ding S, Cheng Y, Li Y, Tao H (2021) A novel grey prediction model for seasonal time series. Knowl-Based Syst 229:107363. https://doi.org/10.1016/j.knosys.2021.107363
Zhu H, Xiao X, Huang X, Rao C, Xiang X (2023) Time-lead nonlinear grey multivariable prediction model with applications. Appl Math Model. https://doi.org/10.1016/j.apm.2023.07.003
Funding
The work in this paper was supported by National Natural Science Foundation of China (Grant No. 62007028), and Doctoral Research Foundation of Jiangsu Normal University (Grant No. 21XSRX005).
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Xie, W., Liu, C. A novel fractional time-delayed grey model with discrete fractal derivative and its applications in predicting enrollments and educational expenditure. Soft Comput 27, 16523–16535 (2023). https://doi.org/10.1007/s00500-023-09158-w
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DOI: https://doi.org/10.1007/s00500-023-09158-w