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数据回归-空间自回归面板模型及在商品住宅价格依赖性中的应用研究.pdf
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数据回归-空间自回归面板模型及在商品住宅价格依赖性中的应用研究.pdf
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I
摘 要
城镇化进程的加快导致民众对住宅的刚需进一步扩大,一些城市的商品住
宅价格急剧飙升,日益凸显的“高房价”已然引发了全社会的密切关注。探讨
商品住宅价格的时空衍化规律,对了解商品住宅价格的走势有着重要意义。本
文考虑了所研究区域的经济变化特性,构建了一种融合了空间距离关系和经济
社会关系的动态变化空间权重矩阵。基于该矩阵以及扰动项的时间滞后效应建
立了含时间自回归误差项的空间自回归面板数据(Spatial Autoregressive Panel
Data, SAPD)模型,最后将建立的 SAPD 模型应用于上海市行政区商品住宅价格
的时空依赖性研究。主要研究内容如下:
首先,融合空间距离关系和经济社会关系,构建了动态变化空间权重矩阵。
对国内外各种经典的空间权重矩阵构造方法进行了比较分析,基于阈值距离权
重矩阵和灰色关联度分析,构建了一种融合空间距离关系和经济社会关系的动
态变化空间权重矩阵。
其次,采用动态变化空间权重矩阵,建立了扰动项具有时间自相关性的随
机效应
SAPD
模型。引入贝叶斯马尔可夫蒙特卡洛
(Markov Chain Monte Carlo,
MCMC)方法进行参数估计,系统地推导了模型中各参数的条件后验分布。给出
了 M-H(Metropolis-Hastings)算法和 Gibbs 抽样混合的抽样方法,对表征空间滞后
性和时间相关性的参数单独使用
M-H
方法进行抽样,并通过不同周期数的蒙特
卡洛实验得到了精度较高的估计结果,同时验证了 MCMC 估计方法用于该模型
的有效性。
最后,将建立的
SAPD
模型应用于上海市行政区商品住宅价格的时空依赖
性研究中。基于 Moran 指数分析了上海市各行政区商品住宅价格间的空间相关
性,用时滞灰关联分析计算了上海市行政区商品住宅价格各时期之间扰动项对
应的时滞值,建立了上海市行政区商品住宅价格
SAPD
模型。进行模型参数估
计及求解,结果表明:较空间权重矩阵固定不变的模型而言,空间权重矩阵动
态变化的 SAPD 模型具有更好的拟合精度;上海市相邻行政区之间的商品住宅
价格存在正向空间溢出效应;建立的商品住宅价格
SAPD
模型具备较好的应用
效果。
关键词:动态变化空间权重矩阵, 面板数据,空间自回归, 贝叶斯 MCMC 估计,
灰色关联分析
万方数据
II
Abstract
The acceleration of the urbanization process has led to further expansion of the
public housing demend. As a result, the commodity housing prices in some cities are
rising all the way. The increasingly prominent “high housing prices” has triggered a
close attention of the whole society. Discussing the temporal and spatial variation is
of great significance to understand the trend of commodity housing prices. In this
paper, we consider the change in economic in the time dimension and construct a
dynamic spatial weights matrix, which incoporates the economy-community relations
and the space-distance relations. Then, under the time varying spatial weights matrix,
we set up a random effects spatial autoregressive panel data (i.e. SAPD)model where
the disturbance has a time correlation. Finally, we use the established model to
explain the time-space dependence of Shanghai commodity housing prices. The main
contents are as follows:
First, the spatial weights matrix that incoporates the economy-community
relations and the space-distance relations is constructed. A variety of classic spatial
weights matrix construction methods are summarized. Moreover, the differences and
similarities of different spatial weights matrix are analyzed, and the advantages and
disadvantages are compared. Based on the existing threshold distance weights matrix,
the grey relational analysis is used to design an economy-community relations matrix
between spatial units. And then a time varying spatial weights matrix that
incorporates information from the economy-community relations matrix and the
space-distance relations matrix is developed.
Then, based on the dynamic spatial weights matrix, a random effects SAPD
model with a time autocorrelation in the disturbance is established. Simultaneously,
the Bayesian Markov Chain Monte Carlo estimation is introduced for parameter
estimation, which deduces the conditional posterior distribution systematically for
each parameter and gives the sampling method that mixes the M-H algorithm and
Gibbs sampling. The parameters to characterize the spatial lag and time correlation
are sampled by the M-H method. The Monte Carlo experiments with different cycles
are obtained with high accuracy and the validity of the MCMC estimation for the
万方数据
III
model is verified.
Finally, the established SAPD model is used to explain the time-space
dependence of Shanghai commodity housing prices. The spatial autocorrelation of the
commodity housing price across the Shanghai administrative regions is tested using
Moran'I index. Then, the SAPD model of commodity housing price is established.
The model parameter estimation and solution results are given, and the results show
that the estimation results of the dynamic spatial weights matrix are superior to the
estimation results of the fixed spatial weights matrix, there is a positive effect on the
commodity housing prices between neighboring administrative district in Shanghai,
and the SAPD model can better interpret the spatial effects of commodity housing
prices and has better applicability.
Key words: The dynamic spatial weights matrix, Panel data, Spatial autoregressive,
Bayesian MCMC estimations, Grey relational analysis
万方数据
IV
目 录
第 1 章 绪论.................................................................................................................1
1.1 研究背景及意义.............................................................................................1
1.2 国内外研究现状.............................................................................................3
1.2.1 空间自回归面板模型研究现状..........................................................3
1.2.2
空间权重矩阵研究现状
......................................................................5
1.2.3
商品住宅价格研究现状
......................................................................6
1.3 本文研究内容.................................................................................................8
1.3.1 研究思路..............................................................................................8
1.3.2 研究内容..............................................................................................8
1.4 本文章节安排.................................................................................................9
第
2
章 动态变化空间权重矩阵的构造
...................................................................10
2.1
经典空间权重矩阵生成方法
.......................................................................10
2.2 灰色关联度分析方法...................................................................................13
2.3 时滞灰关联分析...........................................................................................15
2.4 动态变化空间权重矩阵...............................................................................16
2.5 本章小结.......................................................................................................19
第
3
章 含时间自回归误差项的
SAPD
模型的建立
.............................................. 20
3.1
空间自回归面板模型
...................................................................................20
3.1.1 面板模型............................................................................................20
3.1.2 空间自回归模型................................................................................21
3.1.3 空间自回归面板模型........................................................................21
3.2 含时间自回归误差项的 SAPD 模型.......................................................... 22
3.3
建立模型的参数估计
...................................................................................23
3.3.1
模型的似然函数
................................................................................23
3.3.2 参数的条件后验分布........................................................................24
3.3.3 基于 Gibbs 结构的 Blocking 混合算法........................................... 28
3.3.4 蒙特卡罗结果....................................................................................30
3.4 本章小结.......................................................................................................35
第
4
章 上海市商品住宅价格的时空依赖性实证研究
...........................................36
4.1
数据来源
.......................................................................................................36
4.2 变量的选取与说明.......................................................................................38
4.3 空间相关性检验...........................................................................................39
4.4 上海市商品住宅价格的 SAPD 模型.......................................................... 40
4.5 结果分析.......................................................................................................43
4.6
本章小结
.......................................................................................................46
第
5
章 结论与展望
...................................................................................................47
万方数据
V
5.1
结论
...............................................................................................................47
5.2
本文主要创新点
...........................................................................................48
5.3 研究展望.......................................................................................................48
致 谢...........................................................................................................................49
参考文献.....................................................................................................................50
攻读硕士学位期间发表主要论文.............................................................................54
攻读硕士学位期间参加科研项目
.............................................................................55
附录
A.........................................................................................................................56
附录 B.........................................................................................................................57
万方数据
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