马尔科夫链在江西省区域经济趋同中的应用

发布时间：2018-07-12 15:07

本文选题：马尔科夫链 + 区域经济趋同　；参考：《江西财经大学》2017年硕士论文

【摘要】：马尔科夫过程是随机过程理论中一个十分重要的分支,当马尔科夫过程的状态和时间均处于离散时,则将该马尔科夫过程称作马尔科夫链。马尔科夫链理论能够较好地应用于现实问题中,其中在医学、教育学、社会学以及经济学等学科领域中均有一定的研究成果。马尔科夫链之所以能够应用于如此多的领域,主要是不同领域的许多现象都满足马尔科夫性:系统在某一时刻所处的状态,可以决定系统在下一时刻所处的状态,而无需考虑该时刻以前系统所处的状态。江西省位于中国中部,在地理位置、矿质资源以及生态环境等方面都具有十分重要的战略地位。但是江西省的经济状况一直处于中部地区的较低阶段,其中各个地级市之间的经济水平也呈现出发展不平衡甚至两极分化的现象,因此,分析江西省各地级市之间的经济趋同现象,是研究江西省各地区经济协调发展的关键。以往的文献在研究经济趋同问题时的步骤通常是先建立空间马尔科夫链模型、设置空间滞后算子,从而构建空间权重矩阵,再得出滞后期的条件概率矩阵,最后分析该矩阵,得出相关结论。本文在此基础上,根据具体情况进行模型的改进和优化,首先将江西省各个地级市的人均GDP数据序列进行马尔科夫性检验,再依据有序聚类的思想,对分类方法进行相应的修正,之后建立空间权重矩阵时,改用邻边原则进行优化,并将矩阵标准化,最后得到优化后的滞后期条件概率矩阵。在对实际数据进行实证分析时,可以发现使用传统方法得到的矩阵主要表现出了经济发达地区的状态转移情况,而不能形象地描述出经济落后地区的状态转移情况。使用优化模型对数据作出分析后,得出的滞后期条件概率矩阵能够更好地反映出经济落后地区发生状态转移的趋势:当不发达地区附近存在发达地区时,转移到上一状态的概率将会增加;当欠发达地区附近存在发达地区时,其转移到下一状态的概率将会大幅增加。不同的地区受限于不同的外界因素影响,得到的结果也不尽相同,但是分析后的结果表现出了经济落后区域的经济发展趋势,为研究江西省各区市协调发展提供了理论基础。
[Abstract]:Markov process is a very important branch of stochastic process theory. When the state and time of Markov process are discrete, the Markov process is called Markov chain. Markov chain theory can be well applied to practical problems, among which there are some achievements in medicine, pedagogy, sociology and economics. The reason why Markov chains can be applied to so many fields is that many phenomena in different fields satisfy the Markov property: the state of the system at a certain moment can determine the state of the system at the next moment. Without considering the state of the system prior to that moment. Jiangxi Province is located in the central part of China and plays an important strategic role in geographical location, mineral resources and ecological environment. However, the economic situation of Jiangxi Province has always been in the lower stage of the central region, in which the economic level of various prefecture-level cities has also shown a phenomenon of uneven development and even polarization. Therefore, It is the key to study the coordinated development of regional economy in Jiangxi Province by analyzing the phenomenon of economic convergence among prefecture-level cities in Jiangxi Province. The steps of the previous literature in studying economic convergence are usually to establish the spatial Markov chain model and the spatial lag operator to construct the spatial weight matrix, and then to obtain the conditional probability matrix of the lag period, and finally to analyze the matrix. Draw relevant conclusions. On this basis, this paper improves and optimizes the model according to the specific situation. Firstly, the data series of per capita GDP of every prefecture-level city in Jiangxi Province are tested by Markov property test, and then according to the idea of orderly clustering. The classification method is modified accordingly, and when the spatial weight matrix is established, the adjacent edge principle is used to optimize the matrix, and the matrix is standardized. Finally, the lagged conditional probability matrix after optimization is obtained. In the empirical analysis of the actual data, it can be found that the matrix obtained by the traditional method mainly shows the state transfer situation in the economically developed areas, but cannot describe the state transfer situation in the economically backward areas. After using the optimization model to analyze the data, the lag conditional probability matrix can better reflect the trend of state transition in the economically backward areas: when there are developed areas near the undeveloped areas, The probability of transferring to the previous state will increase, and when there is a developed region near the less developed region, the probability of transferring to the next state will increase significantly. Different regions are limited by different external factors, and the results obtained are different, but the analysis results show the economic development trend of the backward regions, which provides a theoretical basis for the study of coordinated development of Jiangxi provinces and cities.
【学位授予单位】：江西财经大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：F127;O211.62

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