英文文献：Nonparametric Cointegration Analysis of Fractional Systems With Unknown Integration Orders-积分阶数未知分数系统的非参数协整分析
英文文献作者：Morten ?rregaard Nielsen
英文文献摘要：
In this paper a nonparametric variance ratio testing approach is proposed for determining the cointegration rank in fractionally integrated systems. The test statistic is easily calculated without prior knowledge of the integration order of the data, the strength of the cointegrating relations, or the cointegration vector(s). The latter property makes it easier to implement than regression-based approaches, especially when examining relationships between several variables with possibly multiple cointegrating vectors. Since the test is nonparametric, it does not require the specification of a particular model and is invariant to short-run dynamics. Nor does it require the choice of any smoothing parameters that change the test statistic without being reflected in the asymptotic distribution. Furthermore, a consistent estimator of the cointegration space can be obtained from the procedure. The asymptotic distribution theory for the proposed test is non-standard but easily tabulated or simulated. Monte Carlo simulations demonstrate excellent finite sample properties, even rivaling those of well-specified parametric tests. The proposed methodology is applied to the term structure of interest rates, where, contrary to both fractional and integer-based parametric approaches, evidence in favor of the expectations hypothesis is found using the nonparametric approach.

本文提出了一种确定微集成系统协整秩的非参数方差比检验方法。在不知道数据的积分顺序、协整关系的强度或协整向量的情况下，很容易计算出检验统计量。后一个特性使它比基于回归的方法更容易实现，特别是在检查几个变量之间的关系时，可能有多个协整向量。由于测试是非参数的，它不需要特定模型的说明，并且对短期动力学是不变的。它也不需要选择任何平滑参数，改变测试统计量，而不反映在渐近分布。此外，该过程还可以得到协整空间的一个一致估计。所提检验的渐近分布理论是非标准的，但易于表列或模拟。蒙特卡罗模拟证明了优良的有限样本性质，甚至比得上那些良好指定参数试验。该方法应用于利率期限结构，与基于分数和整数的参数方法相反，使用非参数方法发现了支持预期假设的证据。