价格系统的非线性动力学研究与随机梯度回归分析
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摘要
随着全球经济一体化进程的深入,影响经济运行的因素及这些因素之间的关系更为复杂,这一点在价格系统中表现尤为显著,传统经济学理论已无法全面描述,因此,非线性经济学逐渐成为当代经济研究的前沿领域。本文运用现代非线性动力学理论与随机非线性动力学理论,研究价格系统的运行规律,并对房地产价格系统进行了实证研究,主要完成了以下工作:
系统地分析研究了经济理论中多种价格模型:首先分析了典型的蛛网价格理论模型的缘起、应用条件与假设,离散情形的蛛网价格模型、连续情形的蛛网价格模型,并对蛛网理论的应用进行了评价;又研究了线性动态价格模型中的线性差分模型、有存货的线性物价模型以及线性微分方程物价模型;价格的非线性动态模型,并在此基础上,建立了考虑供需双方非线性因素的价格非线性动态模型,并给出了模型各参数的含义。
采用非线性动力学理论对建立的考虑供需双方非线性特性的价格模型进行分析,得出系统稳定性条件;采用MATLAB程序,对模型进行数值仿真,并得出各参数对系统稳定性的影响和不同参数对系统状态的影响。
基于随机非线性动力学理论,采用随机平均法、随机动力系统的稳定性分析与李亚普诺夫指数的计算方法、一维扩散过程的边界分析以及二维Markov随机过程的概率密度的计算方法,建立了随机价格非线性动态模型,并对其进行了局域稳定性与全局稳定性的分析,从而计算出该系统的稳定性条件;还研究了该系统的随机Hopf分岔行为,以及相应的实际经济意义和作用。
在受政策影响下的市场价格体系中,首先分析了影响房屋价格构成及其波动的主要因素,然后采用随机梯度回归法,分析了近十年来的天津市、石家庄市、南京市以及郑州市的商品房销售价格的实际数据,从而得到了影响城市商品房价格变化的主要因素对房地产价格的影响程度,并采用随机梯度回归等方法对房价进行了预测和验证。
With the global economy integration, the factors affecting the economy and the relations of the factors become more complex, which is most marked in the price system. As the traditional economic theory cannot describe them, nonlinear economics become the research focus and have made rapid progress. This dissertation studies the price operation phenomenon in the property prices system with the aid of modern nonlinear dynamics and stochastic dynamics theory. The main content is as follows:
Summarize several prices models systemically: summarize the origination, application condition, consumptions of cobweb price model, introduce the discrete case and continuous case of the model, evaluate the application of the cobweb theory, the linear difference model of dynamic linear price models, linear price model in stock, linear differential equation price model as well as nonlinear dynamic price model have been studied. On the basis of the above models, a nonlinear dynamic price model is set up considering the nonlinear factors between supply and demand. And the meanings of each parameters of the model have been explained.
Based on the nonlinear dynamic price model considering supplier and retailer, the system stable theory has been obtained from the analysis of the model using nonlinear dynamics; after numerical simulating of the model with MATLAB, present the influence of different parameters on the system stable has been obtained, in which the influence of the parameters on the system conditions has also been considered.
First introduce the basic theory of random dynamical system, stochastic averaging method, stochastic differential equation, the stability of random dynamical system, calculation of Lyapunov exponent, the boundary analysis of one-dimension diffuse and the probability density function calculation of two-dimension Markov stochastic process. Then present a nonlinear random price model: the stability condition of the model is figured out through stability analysis. The stochastic Hopf bifurcation behavior and the economic significance of the system have been studied.
Analyze the composition of property price and the main factors influencing the price fluctuation in the market price system which is influenced by the police, then analyze the actual datum of the property in Tianjin, Shijiazhuang, Nanjing and Zhengzhou by stochastic gradient regression method, present the influences of each main factors to the price change in Tianjin, Shijiazhuang, Nanjing and Zhengzhou, forecast the property price prospect in these cities by the method also.
系统地分析研究了经济理论中多种价格模型:首先分析了典型的蛛网价格理论模型的缘起、应用条件与假设,离散情形的蛛网价格模型、连续情形的蛛网价格模型,并对蛛网理论的应用进行了评价;又研究了线性动态价格模型中的线性差分模型、有存货的线性物价模型以及线性微分方程物价模型;价格的非线性动态模型,并在此基础上,建立了考虑供需双方非线性因素的价格非线性动态模型,并给出了模型各参数的含义。
采用非线性动力学理论对建立的考虑供需双方非线性特性的价格模型进行分析,得出系统稳定性条件;采用MATLAB程序,对模型进行数值仿真,并得出各参数对系统稳定性的影响和不同参数对系统状态的影响。
基于随机非线性动力学理论,采用随机平均法、随机动力系统的稳定性分析与李亚普诺夫指数的计算方法、一维扩散过程的边界分析以及二维Markov随机过程的概率密度的计算方法,建立了随机价格非线性动态模型,并对其进行了局域稳定性与全局稳定性的分析,从而计算出该系统的稳定性条件;还研究了该系统的随机Hopf分岔行为,以及相应的实际经济意义和作用。
在受政策影响下的市场价格体系中,首先分析了影响房屋价格构成及其波动的主要因素,然后采用随机梯度回归法,分析了近十年来的天津市、石家庄市、南京市以及郑州市的商品房销售价格的实际数据,从而得到了影响城市商品房价格变化的主要因素对房地产价格的影响程度,并采用随机梯度回归等方法对房价进行了预测和验证。
With the global economy integration, the factors affecting the economy and the relations of the factors become more complex, which is most marked in the price system. As the traditional economic theory cannot describe them, nonlinear economics become the research focus and have made rapid progress. This dissertation studies the price operation phenomenon in the property prices system with the aid of modern nonlinear dynamics and stochastic dynamics theory. The main content is as follows:
Summarize several prices models systemically: summarize the origination, application condition, consumptions of cobweb price model, introduce the discrete case and continuous case of the model, evaluate the application of the cobweb theory, the linear difference model of dynamic linear price models, linear price model in stock, linear differential equation price model as well as nonlinear dynamic price model have been studied. On the basis of the above models, a nonlinear dynamic price model is set up considering the nonlinear factors between supply and demand. And the meanings of each parameters of the model have been explained.
Based on the nonlinear dynamic price model considering supplier and retailer, the system stable theory has been obtained from the analysis of the model using nonlinear dynamics; after numerical simulating of the model with MATLAB, present the influence of different parameters on the system stable has been obtained, in which the influence of the parameters on the system conditions has also been considered.
First introduce the basic theory of random dynamical system, stochastic averaging method, stochastic differential equation, the stability of random dynamical system, calculation of Lyapunov exponent, the boundary analysis of one-dimension diffuse and the probability density function calculation of two-dimension Markov stochastic process. Then present a nonlinear random price model: the stability condition of the model is figured out through stability analysis. The stochastic Hopf bifurcation behavior and the economic significance of the system have been studied.
Analyze the composition of property price and the main factors influencing the price fluctuation in the market price system which is influenced by the police, then analyze the actual datum of the property in Tianjin, Shijiazhuang, Nanjing and Zhengzhou by stochastic gradient regression method, present the influences of each main factors to the price change in Tianjin, Shijiazhuang, Nanjing and Zhengzhou, forecast the property price prospect in these cities by the method also.
引文
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