| Postgraduate examination is short for National Unified Entrance Examination for Postgraduate Students,which refers to the general term of relevant examinations organized by educational authorities and admission institutions for the selection of postgraduate students.It is the admission examination for fresh undergraduate graduates and students with the same degree to study for postgraduate students in colleges,similar to the college entrance examination required for high school graduates to study in universities.On the one hand,the statistical prediction of the number of students taking the postgraduate entrance examination can reflect the situation of postgraduate enrollment education in a country or region and show the national education level and talent training.On the other hand,it can guide the policy formulation of relevant education departments and the enrollment plan of schools and also provide data support for students who are aiming at postgraduate entrance examination.In this paper,the number of students taking the postgraduate entrance examination from 1994 to 2023 is selected as the observation set.The relevant training set and test set are selected according to the characteristics of different prediction models and the number of students taking the postgraduate entrance examination in the short term is predicted.Firstly,the GM(1,1)model,the optimized GM(1,1)model and the ARIMA model are established for the prediction of individual models.According to the prediction results and correlation test,the characteristics,advantages and disadvantages of each individual prediction model are given.The combined prediction model is established and the prediction and test are made on this basis.Finally,the advantages and disadvantages of the combined prediction model and each individual prediction model are analyzed comprehensively and the prediction of the number of students taking the postgraduate entrance examination in 2024-2025 is given.In this paper,the GM(1,1)model and the GM(1,1)model optimized with initial and background values are established respectively for prediction.Firstly,the sample data are preprocessed and the parameters of the whitening differential equation in the model are obtained by using matlab to fill the data through smoothness and quasi-exponential law test.Thus,the time response function of the whitening differential equation is obtained and the predicted value of the number of postgraduate entrance examinations in each year can be obtained by substituting the corresponding year parameters.By conducting correlation tests such as residual error,correlation test and posterior difference test,the prediction effect of the traditional GM(1,1)model is good,especially the prediction accuracy of the first two periods is higher and the optimized model can also improve the prediction accuracy of the model to a certain extent.This paper uses EViews statistical software and ARIMA model to fit the number of students taking the postgraduate entrance examination.The selected test set of the number of students taking the entrance examination is preliminarily judged to be a nonstationary sequence and the trend and seasonality contained in the original data are reduced by differential processing to transform it into a stationary data column.In order to reduce the subjectivity in the judgment process,unit root test and white noise test are carried out on the preliminary stable data and a set of stable non-white noise sequence is obtained.Then,according to the fitting nature and judgment criteria of ARIMA model,the optimal fitting model of the number of postgraduate entrance examination is ARIMA(0,1,3)model.Due to the relatively stable characteristics of ARIMA model and the impact of COVID-19 in the past three years,the predicted value of ARIMA model is small and the prediction accuracy is not as good as that of GM(1,1)model,but the overall prediction accuracy is also in an acceptable range.Combined with the advantages and disadvantages of GM(1,1)model and ARIMA model,a combination prediction model is established to learn from each other and fully extract all the information in postgraduate entrance examination data to improve the accuracy of prediction.The combined prediction model can better combine the exponential growth characteristic of GM(1,1)model with the relatively stable characteristic of ARIMA model and the prediction accuracy is higher than that of each single prediction model.In particular,the combined prediction model can make up for the defects of the increased prediction error of GM(1,1)model after the third stage and the insensitivity of ARIMA model to recent data.To sun up,we established the GM(1,1)model,ARIMA model and combined prediction model,among which the GM(1,1)model can better predict the number of postgraduate entrance exams in the first two periods and the combined prediction model improves the prediction accuracy after the third period,so that we can accurately make short-term prediction. |
