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英文文献：Nonstationary cointegration in the fractionally cointegrated VAR model-VAR模型的非平稳协整
英文文献作者：S?ren Johansen,Morten ?rregaard Nielsen
英文文献摘要：
We consider the fractional cointegrated vector autoregressive (CVAR) model of Johansen and Nielsen (2012a) and make two distinct contributions. First, in their consistency proof, Johansen and Nielsen (2012a) imposed moment conditions on the errors that depend on the parameter space, such that when the parameter space is larger, stronger moment conditions are required. We show that these moment conditions can be relaxed, and for consistency we require just eight moments regardless of the parameter space. Second, Johansen and Nielsen (2012a) assumed that the cointegrating vectors are stationary, and we extend the analysis to include the possibility that the cointegrating vectors are nonstationary. Both contributions require new analysis and results for the asymptotic properties of the likelihood function of the fractional CVAR model, which we provide. Finally, our analysis follows recent research and applies a parameter space large enough that the usual (non-fractional) CVAR model constitutes an interior point and hence can be tested against the fractional model using a khi2-test.
我们考虑了Johansen和Nielsen (2012a)的分数协整向量自回归(CVAR)模型，并做出了两种不同的贡献。首先，Johansen和Nielsen (2012a)在一致性证明中，对依赖于参数空间的误差施加了矩条件，当参数空间较大时，需要更强的矩条件。我们证明这些力矩条件可以放宽，并且为了一致性，我们只需要八个力矩而不考虑参数空间。其次，Johansen和Nielsen (2012a)假设协积分向量是平稳的，我们将分析扩展到考虑了协积分向量是非平稳的可能性。这两个贡献需要新的分析和结果的似然函数的渐近性质的分数CVAR模型，我们提供。最后，我们的分析遵循最近的研究，并应用一个足够大的参数空间，通常的(非分数式)CVAR模型构成一个内点，因此可以通过khi2检验与分数式模型进行比较。
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