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英文文献：An I(2) Cointegration Model with Piecewise Linear Trends: Likelihood Analysis and Application-分段线性趋势I(2)协整模型:似然分析与应用
英文文献作者：Takamitsu Kurita,Heino Bohn Nielsen,Anders Rahbek
英文文献摘要：
This paper presents likelihood analysis of the I(2) cointegrated vector autoregression with piecewise linear deterministic terms. Limiting behavior of the maximum likelihood estimators are derived, which is used to further derive the limiting distribution of the likelihood ratio statistic for the cointegration ranks, extending the result for I(2) models with a linear trend in Nielsen and Rahbek (2007) and for I(1) models with piecewise linear trends in Johansen, Mosconi, and Nielsen (2000). The provided asymptotic theory extends also the results in Johansen, Juselius, Frydman, and Goldberg (2009) where asymptotic inference is discussed in detail for one of the cointegration parameters. To illustrate, an empirical analysis of US consumption, income and wealth, 1965 - 2008, is performed, emphasizing the importance of a change in nominal price trends after 1980.
本文给出了具有分段线性确定性项的I(2)协整向量自回归的似然分析。限制行为的最大似然估计,用于进一步推导出似然比统计量的极限分布的协整,扩展我的结果(2)模型与线性趋势尼尔森和Rahbek(2007)和我(1)模型和分段线性趋势约翰森,Mosconi,尼尔森(2000)。所提供的渐近理论也扩展了Johansen, Juselius, Frydman，和Goldberg(2009)的结果，其中渐近推论详细讨论了一个协整参数。为了说明这一点，我们对1965 - 2008年美国的消费、收入和财富进行了实证分析，强调1980年后名义价格趋势变化的重要性。
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