Root--consistent estimation of weak fractional cointegration
Root--consistent estimation of weak fractional cointegration
复制标题
弱分数协整的根一致估计
DOI：
10.1016/j.jeconom.2006.07.004
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发表时间：
2007
影响因子：
6.3
通讯作者：
Hualde J
中科院分区：
文献类型：
--
作者：
Hualde J
经验证据表明，分数协整的可能性使得可观测时间序列的积分阶数δ和协整误差的积分阶数γ之间的差距β小于0.5。这包括观测量是平稳的或渐近平稳的，具有长记忆，因此δ<12，以及它们是非平稳的，因此δ <12。这种“弱协整”与传统的单位根观测量和短记忆协整误差（β=1）的计量经济学处方形成强烈对比。渐近推论理论也不同于这种情况和β>12类的其他成员，特别是当β<12时，协整向量ν的n-相容和渐近正态估计是可能的，正如我们在一个简单的二元模型中所探索的那样。估计值取决于γ和δ，或者更实际地说，取决于未知γ和δ的估计值。这些后一种估计需要是n-相容的，并且ν的估计的渐近分布对它们的精确形式敏感。我们提出了计算上相对方便的γ和δ的估计，仅依赖于单变量非线性优化。有限样本性能的方法进行检查通过Monte Carlo模拟，并包括几个应用程序的经验数据。
Empirical evidence has emerged of the possibility of fractional cointegration such that the gap, β, between the integration order δ of observable time series and the integration order γ of cointegrating errors is less than 0.5. This includes circumstances when observables are stationary or asymptotically stationary with long memory soδ<12 and when they are nonstationary soδ⩾12. This “weak cointegration” contrasts strongly with the traditional econometric prescription of unit-root observables and short memory cointegrating errors, where β=1. Asymptotic inferential theory also differs from this case and from other members of the class β>12, in particular n-consistent and asymptotically normal estimation of the cointegrating vector ν is possible when β<12, as we explore in a simple bivariate model. The estimate depends on γ and δ or, more realistically, on estimates of unknown γ and δ. These latter estimates need to be n-consistent, and the asymptotic distribution of the estimate of ν is sensitive to their precise form. We propose estimates of γ and δ that are computationally relatively convenient, relying on only univariate nonlinear optimization. Finite sample performance of the methods is examined by means of Monte Carlo simulations, and several applications to empirical data included.