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英文文献：Maximum likelihood estimation of fractionally cointegrated systems-微协整系统的极大似然估计
英文文献作者：Katarzyna Lasak
英文文献摘要：
In this paper we consider a fractionally cointegrated error correction model and investigate asymptotic properties of the maximum likelihood (ML) estimators of the matrix of the cointegration relations, the degree of fractional cointegration, the matrix of the speed of adjustment to the equilibrium parameters and the variance-covariance matrix of the error term. We show that using ML principles to estimate jointly all parameters of the fractionally cointegrated system we obtain consistent estimates and provide their asymptotic distributions. The cointegration matrix is asymptotically mixed normal distributed, while the degree of fracional cointegration and the speed of adjustment to the equilibrium matrix have joint normal distribution, which proves the intuition that the memory of the cointegrating residuals affects the speed of convergence to the long-run equilibrium, but does not have any influence on the long-run relationship. The rate of convergence of the estimators of the long-run relationships depends on the cointegration degree but it is optimal for the strong cointegration case considered. We also prove that misspecification of the degree of fractional cointegation does not affect the consistency of the estimators of the cointegration relationships, although usual inference rules are not valid. We illustrate our results in finite samples by Monte Carlo analysis.
在本文中,我们考虑一个略微共合体误差修正模型和调查最大似然(ML)估计的渐近性质矩阵的协整关系,部分共整合的程度,矩阵的调整平衡的速度参数和误差项的variance-covariance矩阵。我们证明了利用ML原理联合估计微协整系统的所有参数，得到了一致的估计并给出了它们的渐近分布。协整矩阵混合正常渐近分布,而程度fracional协整和的速度调整平衡矩阵的联合正态分布,这证明了直觉,协整残差的记忆影响长期均衡收敛的速度,但对长期的关系没有任何影响。长期关系估计量的收敛速度取决于协整程度，但对于强协整的情况是最优的。我们还证明了分式协整程度的错误描述并不影响协整关系估计量的一致性，尽管通常的推理规则是无效的。我们用蒙特卡洛分析在有限样本中说明我们的结果。
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