﻿ 基于灰色预测及改进模型的留学人员预测 Forecast of Overseas Students Based on Grey Prediction and Improvement Model

Statistics and Application
Vol. 08  No. 04 ( 2019 ), Article ID: 31882 , 8 pages
10.12677/SA.2019.84079

Forecast of Overseas Students Based on Grey Prediction and Improvement Model

Tianhao Jin, Shaoling Ding

College of Science, Guilin University of Technology, Guilin Guangxi

Received: Aug. 6th, 2019; accepted: Aug. 16th, 2019; published: Aug. 26th, 2019

ABSTRACT

By comparing and analyzing the grey forecasting model with the improved grey forecasting model based on moving average, this paper establishes a fitting and forecasting model for the number of overseas students and returnees in China. The results show that the grey prediction model smoothed by moving average method is better than the grey prediction method alone in this empirical analysis. The new method improves the fitting accuracy, facilitates relevant state institutions to obtain the trend of studying abroad and the number of returnees, and gives priority to formulating relevant policies.

Keywords:Grey Prediction, Moving Average Method, The Number of Students Studying Abroad, The Number of Returned Students Studying Abroad

1. 引言

2. 方法介绍

2.1. 灰色预测及GM (1, 1)模型基本概念与具体方法

${X}^{\left(0\right)}=\left\{{X}^{\left(0\right)}\left(1\right),{X}^{\left(0\right)}\left(2\right),{X}^{\left(0\right)}\left(3\right),{X}^{\left(0\right)}\left(4\right),\cdots ,{X}^{\left(0\right)}\left(n\right)\right\}$ (1)

${X}^{\left(1\right)}=\left\{{X}^{\left(1\right)}\left(1\right),{X}^{\left(1\right)}\left(2\right),{X}^{\left(1\right)}\left(3\right),{X}^{\left(1\right)}\left(4\right),\cdots ,{X}^{\left(1\right)}\left(n\right)\right\}$ (2)

$\eta \left(k\right)=\frac{\mathrm{min}\mathrm{min}|{\stackrel{^}{X}}^{\left(0\right)}\left(k\right)-{X}^{\left(0\right)}\left(k\right)|+\rho \mathrm{max}\mathrm{max}|{\stackrel{^}{X}}^{\left(0\right)}\left(k\right)-{X}^{\left(0\right)}\left(k\right)|}{|{\stackrel{^}{X}}^{\left(0\right)}\left(k\right)-{X}^{\left(0\right)}\left(k\right)|+\rho \mathrm{max}\mathrm{max}|{\stackrel{^}{X}}^{\left(0\right)}\left(k\right)-{X}^{\left(0\right)}\left(k\right)|}$ (3)

$r=\frac{1}{n}{\sum }_{k=1}^{n}\eta \left(k\right)$ (4)

$\frac{\text{d}{X}^{\left(1\right)}}{\text{d}t}+a{X}^{\left(1\right)}=\mu$ (5)

$\stackrel{^}{a}={\left({B}^{\text{T}}B\right)}^{-1}{B}^{\text{T}}{Y}_{n}$ (6)

${\stackrel{^}{X}}^{\left(1\right)}\left(k+1\right)=\left[{\stackrel{^}{X}}^{\left(0\right)}\left(1\right)-\frac{\mu }{a}\right]{\text{e}}^{-ak}+\frac{\mu }{a}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\left(k=0,1,2,\cdots ,n\right)$ (7)

2.2. 移动平均模型

${F}_{t+1}={\stackrel{¯}{Y}}_{t}=\frac{{Y}_{t-k+1}+{Y}_{t-k+2}+\cdots +{Y}_{t-1}+{Y}_{t}}{k}$ (8)

2.3. 组合模型的构建

$\begin{array}{c}{F}_{t+1}={\stackrel{¯}{Y}}_{t}=\frac{{Y}_{t-k+1}+{Y}_{t-k+2}+\cdots +{Y}_{t-1}+{Y}_{t}}{k}\\ =\frac{{\stackrel{^}{X}}^{\left(1\right)}\left(t-k+1\right)+{\stackrel{^}{X}}^{\left(1\right)}\left(t-k+2\right)+\cdots +{\stackrel{^}{X}}^{\left(1\right)}\left(t-1\right)+{\stackrel{^}{X}}^{\left(1\right)}\left(t\right)}{k}\end{array}$ (9)

$\begin{array}{c}{F}_{t+1}={\stackrel{¯}{Y}}_{t+1}=\frac{{Y}_{t-k+2}+{Y}_{t-k+3}+\cdots +{Y}_{t}+{Y}_{t+1}}{k}\\ =\frac{{\stackrel{^}{X}}^{\left(1\right)}\left(t-k+2\right)+{\stackrel{^}{X}}^{\left(1\right)}\left(t-k+3\right)+\cdots +{\stackrel{^}{X}}^{\left(1\right)}\left(t\right)+{\stackrel{^}{X}}^{\left(1\right)}\left(t+1\right)}{k}\end{array}$ (10)

3. 实证分析

3.1. 灰色预测模型及其问题

Table 1. The forecast table of the number of overseas students based on the grey prediction model GM (1, 1)

Table 2. The forecast table of the number of overseas students and returned students based on the grey prediction model GM (1, 1)

Figure 1. Gray prediction of the number of overseas students and returnees

3.2. 移动平均法与灰色预测组合方法

3.3. 预测结果

Table 3. Grey moving average method for fitting table of the number of overseas students and returnees

Table 4. Grey moving average method for forecasting the number of overseas students and returnees

Figure 2. Grey moving average method for forecasting the number of overseas students and returnees

4. 结论

Forecast of Overseas Students Based on Grey Prediction and Improvement Model[J]. 统计学与应用, 2019, 08(04): 696-703. https://doi.org/10.12677/SA.2019.84079

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