# 限购政策与自贸区成立对海南省商品住宅价格影响分析Analysis of the Influence of the Purchase Restriction Policy and the Establishment of Free Trade Zone on the Price of Commodity Housing in Hainan Province

Abstract: We built a mathematical model based on the collected data on commercial housing in Hainan Province, and studied the price trend of Hainan commercial housing after the establishment of the purchase restriction policy and the Hainan Free Trade Zone (Hong Kong). For the first problem, this paper firstly analyzes the influencing factors of the commodity housing price in Hainan Province, and collects data such as the per capita GDP and the per capita disposable income of Hainan Province, and quantitatively analyzes the impact of various factors on the price of commercial housing. Using MATLAB and SPSS software to interpolate, fit and correlate various factors with house prices and various factors, the results obtained: the area of completion is negatively correlated with the price of commercial housing, R5 = −0.758. Other factors were positively correlated with house prices, R1 = 0.909, R2 = 0.938, R3 = 0.930, R4 = 0.971, R6 = 0.880. On the basis of the problem 1, the data is standardized by SPSS, and the factors are analyzed by principal component analysis. The relationship between the principal component and each factor is established by the score. Then the SPSS was used to analyze the relationship between the main component and the house price by linear regression. Finally, the model was tested by EXCEL randomly extracted data. For Question three, taking the price of commercial housing in Sanya as an example, first, the serial value label of the house price is used, and the processed data is fitted with SPSS to obtain the trend of the house price and the related data after fitting. By fitting the R square of the curve and the stationary R square value, it is known that after fitting the residual sequence is autocorrelation, and the R-square and the adjusted R-square corresponding to the overall fit map tend to be 1. The AMRIMA model in SPSS is used to predict the unsteady time series, and the trend chart of the house price in the coming year and the specific forecast value of the house price in the next year and the atmosphere of the predicted value are obtained.

1. 问题重述

1.1. 问题背景

1.2. 问题提出

1988年4月13日，海南建立海南经济特区，同年，海南省商品住宅价格平均为1350元每平方米，到了1993年短短五年期间便涨至7500元每平方米，之后几年商品住宅价格比较平稳略有小幅回落。2010年国家发改委批复了《海南国际旅游岛建设发展规划纲要》，海南省商品住宅价格再次迎来飙升期，由6000多元每平米，涨至1万多元每平米。其中，一些热门旅游城市例如海口由5000多元每平米涨至近9000元每平米，三亚由1万元每平米涨至近2万元每平米，飙升一倍。2018年4月13日，海南全岛建设自贸区(港)政策出台后，海口商品住宅价格每天涨幅达每平米500元到1000元，三亚商品住宅价格更是一夜之间每平米上涨3000元到8000元。

1) 请对海南省(主要考虑海口和三亚)商品住宅价格的影响因素进行定性和定量分析，并给出各因素之间的关系。

2) 请根据问题1的结果，建立相应的商品住宅价格的数学模型。

3) 若未出台2018年4月22日限购政策，请结合你们的数据和模型按月预测2018年6月~2019年5月海南省(主要考虑海口和三亚)商品住宅价格。

2. 问题分析

3. 模型的假设

4. 问题的求解及模型的建立

4.1. 问题一的求解

1) 供给与需求角度

a) 经济因素

Geoff Kenny (1999)分析了爱尔兰住宅市场的供求关系，结果表明：收入增加将会引起住宅需求量及房价的上涨。段家楠(2010)通过广东省1996~2009年的数据分析，证明人均储蓄对房价有显著影响。至此可知，居民收入以及人均储蓄都将影响房价。另外，由于房产具有投资属性，当居民购买能力提高将会导致房产需求增加，进而导致房价上涨。李春吉、孟晓宏(2005)在局部均衡模型的基础上对全国31省市1999~2003年的数据进行实证分析，分析表明：人均可支配收入以及对房产的投资额都是导致房价上涨的重要因素。

b) 人口因素

c) 金融环境

d) 心理因素

e) 租赁因素

f) 宏观调控

2) 其他角度

Figure 1. Gross per capita production (x) − average sales of commercial housing (y)

Figure 2. Year-end balance of urban and rural residents’ savings (x) − average sales of commercial housing (y)

Figure 3. Urban per capita disposable income (x) − average sales of commercial housing (y)

Figure 4. Developer's investment (x) − average sales of commercial housing (y)

Figure 5. Completion area (x) − average sales of commercial housing (y)

Figure 6. Sales area of residential commercial housing (x) − average sales of commercial housing (y)

Table 1. Correlation between per capita GDP and average sales of commercial housing

Table 2. Correlation between the per capita disposable income of residents and the average sales of commercial housing

Table 3. Correlation between sales area and average sales of commercial housing

Table 4. Correlation between the area of completion and the average sales of commercial housing

Table 5. Correlation between the year-end balance of urban and rural residents’ savings and the average sales of commercial housing

Table 6. Correlation between the investment amount of developers and the average sales of commercial housing

Table 7. Correlation coefficient matrix

4.2. 问题二的求解

4.2.1. 模型确定

4.2.2. 模型基本思想

1) 每个主成分为各原始因素的线性组合；

2) 主成分的数目大大少于原始因素的数目；

3) 主成分保留了原始因素绝大多数信息；

4) 各主成分之间互不相关；

4.2.3. 模型的求解

1) 主成分分析

Table 8. Explains the total variance

Table 9. Principal component coefficients

$Z1=0.231*X1+0.390*X2+0.352*X3-0.348*x4+0.397*X5+0.329*X6$

2) 建立回归模型

Table 10. Significance level

4.2.4. 结果分析

4.2.5. 模型检验

Table 11. Model test data

4.3. 问题三的求解

ARIMA模型。

4.3.1. 模型的确定

Figure 7. Trend of housing prices

Table 12. Model fitting results

Table 13. Model statistics

Figure 8. Trend of housing prices

4.3.2. 模型求解

Figure 9. Trend of housing prices

Table 14. Trends in house prices

Figure 10. Forecast of commodity housing prices in Haikou City

Table 15. Trends in house prices

5. 模型评价与推广

5.1. 模型的优点

1) 问题二用了主成分分析，提高了变量之间相关性的利用。

2) 问题二模型中数据标准化后，避免了单位带来的误差。

5.2. 模型的缺点

1) 在主成分分析时提取的主成分过于少，容易产生误差。

2) 问题三中的预测模型只选用了房价过于简单。

5.3. 模型的推广

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[2] 海南省统计局国家统计局海南调查总队. 海南统计年鉴[M]. 北京: 中国统计出版社, 2017.

[3] 中华人民共和国国家统计局. http://www.stats.gov.cn/, 2018-05-26.

[4] 海南省统计局. http://stats.hainan.gov.cn/, 2018-05-26.

[5] 张文彤. SPSS统计分析基础教程[M]. 第3版. 北京: 高等教育出版社, 2017.

[6] 安居客. 海口市2011-2018年月度商品住宅平均销售价格[EB/OL]. https://haikou.anjuke.com/, 2018-05-26.

[7] 安居客. 三亚市2011-2018年月度商品住宅平均销售价格[EB/OL]. https://sanya.anjuke.com/, 2018-05-26.

[8] 卓金武. MATLAB在数学建模中的应用[M]. 第2版. 北京: 北京航空航天出版社, 2014.

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