摘要翻译：
本文提出并检验了美国实际人均GDP演变的双分量模型。国内生产总值增长率的第一个组成部分代表一种经济趋势，与实际人均国内生产总值本身的达到水平成反比，提名者随着时间的推移保持不变。第二个组成部分负责围绕经济趋势的波动，被定义为9岁儿童人数增长率的一半。在美国，人均实际GDP增长率和9岁儿童数量之间的非线性关系被检验为协整。为了线性化问题，用原始关系计算预测的人口时间序列。实测和预测的单岁人口时间序列均为1阶积分。恩格尔-格兰杰方法用于测量和预测时间序列的差值和残差或相应的线性回归。两个检验都表明存在协整关系。Johansen检验的结果是协整秩1。由于9岁儿童的实测数与预测数之间存在协整关系，因此采用VAR、VECM和线性回归来估计拟合优度和均方根误差RMSE。在VAR表示中得到了最大的R2=0.95和最优的RMSE。从经济学角度来看，协整检验表明，美国实际经济增长与经济趋势的偏离（由实际人均GDP的不变年增长率定义）是由9岁儿童数量的变化驱动的。
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英文标题：
《Modelling real GDP per capita in the USA: cointegration test》
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作者：
Ivan O. Kitov, Oleg I. Kitov, Svetlana A. Dolinskaya
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最新提交年份：
2008
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分类信息：

一级分类：Quantitative Finance        数量金融学
二级分类：General Finance        一般财务
分类描述：Development of general quantitative methodologies with applications in finance
通用定量方法的发展及其在金融中的应用
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一级分类：Physics        物理学
二级分类：Physics and Society        物理学与社会
分类描述：Structure, dynamics and collective behavior of societies and groups (human or otherwise). Quantitative analysis of social networks and other complex networks. Physics and engineering of infrastructure and systems of broad societal impact (e.g., energy grids, transportation networks).
社会和团体（人类或其他）的结构、动态和集体行为。社会网络和其他复杂网络的定量分析。具有广泛社会影响的基础设施和系统（如能源网、运输网络）的物理和工程。
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英文摘要：
  A two-component model for the evolution of real GDP per capita in the USA is presented and tested. The first component of the GDP growth rate represents an economic trend and is inversely proportional to the attained level of real GDP per capita itself, with the nominator being constant through time. The second component is responsible for fluctuations around the economic trend and is defined as a half of the growth rate of the number of 9-year-olds. This nonlinear relationship between the growth rate of real GDP per capita and the number of 9-year-olds in the USA is tested for cointegration. For linearization of the problem, a predicted population time series is calculated using the original relationship. Both single year of age population time series, the measured and predicted one, are shown to be integrated of order 1. The Engel-Granger approach is applied to the difference of the measured and predicted time series and to the residuals or corresponding linear regression. Both tests show the existence of a cointegrating relation. The Johansen test results in the cointegrating rank 1. Since a cointegrating relation between the measured and predicted number of 9-year-olds does exist, the VAR, VECM, and linear regression are used in estimation of the goodness of fit and root mean-square errors, RMSE. The highest R2=0.95 and the best RMSE is obtained in the VAR representation. Econometrically, the tests for cointegration show that the deviations of real economic growth in the USA from the economic trend, as defined by the constant annual increment of real per capita GDP, are driven by the change in the number of 9-year-olds.
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PDF链接：
https://arxiv.org/pdf/0811.0490