【作者】 胡俊航；

【导师】 童恒庆；

【作者基本信息】 武汉理工大学 ， 应用数学， 2006， 硕士

【摘要】 多方程时间序列分析是时间序列分析的重要组成部分，它在宏观经济研究领域有着广泛的应用，越来越受到世界各国的关注。对于现实生活中与多方程时间序列有关的具体问题，不同的模型可能得到不同的拟合和预测效果，需要采用不同的建模方法和参数估计方法。一个理想的模型既要简单又要有比较好的拟合和预测效果，模型参数的估计具有优良的统计性质。本文基于上述观点对多方程时间序列进行了一些探索和研究，使其在理论研究上向前推进了一步，在实际应用中取得了较好的结果。 本文主要作了以下几方面的工作： 1．对VAR模型、交互影响的多元回归与多元时序混合模型、时间序列联立方程模型进行了改进，提出一个新模型。改进后的模型不但考虑到某个因变量与其它因变量当前值的关系，而且考虑到它与所有因变量滞后值的关系，还考虑到它与一些外生变量当前值与滞后值的关系，使模型更加合理。 2．对模型滞后阶数的确定、各个方程解释变量的选择方法进行了研究。滞后阶数采用AIC或者BIC定阶法。滞后变量确定后，用逐步回归的方法来选择方程的解释变量，这使模型既精简又实用。 3．着重对模型参数的估计方法作了详细探讨和研究。除传统方法外，本文又提出了三种新方法。(1)结构方程系数矩阵线性约束下的完全信息极大似然估计法。在一定条件下，该方法给出了模型参数估计的计算公式；(2)参数的修正间接广义岭估计法。本文不仅推导出了参数的修正间接广义岭估计计算公式，而且证明了用该方法估计出的参数统计性质优良，最后还给出了岭参数的选择方法；(3)复共线回归模型的病态分离算法。文中详细叙述了其方法步骤，并证明了该算法估计出的参数具有良好的渐近统计性质。 4．选择我国部分宏观经济变量来验证新模型的合理性。通过对模型的拟合和预测结果进行对比分析，得出模型的拟合和预测结果精确、有效，模型实用性很强。更多还原

【Abstract】 The time series analysis with multiple equations is an important part of time series analysis, which is widely applied in the field of macro-economics and draws more and more attention in the world. In practice, we may get different fitting and predicting results for different model and adopt different modeling approach and parameter estimation. A perfect model is not only simple but also has preferable fitted and predicted results. Meanwhile, the parameters estimated have excellent statistic properties. This paper does some researches on the time series analysis of multiple equations to get better results in theory and practical application.Firstly, we improve interactional multivariate regression and multivariate time series model, the VAR model and the time series simultaneous system model to present a new model. The improved model considers not only the relation between certain dependent variables and present value of other ones but also the relation between it and lagged value of all dependent variables. The new model still considers that between present value and lagged value of some external variables, which is more reasonable.Secondly, the methods of selecting lagged rank of model and interpretive variables of each equation are investigated. We adopt AIC or BIC to obtain the lagged rank and step-wise regression to choose the interpretive variables of equations, which makes new model simple and useful.Thirdly, the methods of estimating parameters of model are researched in detail. This paper proposes three new methods. The first is the full information maximum likelihood method with linear constraint of coefficient matrixes in structure equation. Under certain condition the calculation formula of parameters estimation is obtained. The second is the amendatory indirect generalized ridge estimates of the parameters. This paper not only educes its calculation expression but also proves that statistic properties of parameters estimated are excellent. Meanwhile, the method of selecting ridge parameters is given. The third is the ill-condition separation algorithm in multicollinear regression model. This paper gives the process in detail and proves that the asymptotic statistic properties of parameters estimated are excellent.Finally, this paper takes some macroeconomic variables for example to validate the rationality of new model and draws a conclusion that the fitted and predicted results of model are exact and efficient.更多还原